[{"data":1,"prerenderedAt":38075},["ShallowReactive",2],{"post-\u002Fblog\u002F2026\u002F0005-yin-guo-jie-gou-mo-xing-jian-lun":3,"i-mingcute:time-line":38067,"i-boxicons:location":38071,"i-ci:tag":38073},{"post":4,"nextPost":37769,"prevPost":37778},{"id":5,"title":6,"body":7,"description":37763,"draft":37764,"enableComment":37765,"extension":37766,"image":4127,"important":37764,"location":37767,"meta":37768,"navigation":37765,"ogImage":37769,"path":37770,"seo":37771,"stem":37772,"summary":37773,"tags":37774,"time":37776,"__hash__":37777},"blog\u002Fblog\u002F2026\u002F0005-yin-guo-jie-gou-mo-xing-jian-lun.md","因果结构模型简论",{"type":8,"value":9,"toc":37733},"minimark",[10,499,506,1297,1304,1308,1313,2250,3157,3223,3744,3751,4189,4193,4324,4330,4409,4663,4843,4851,4861,4940,5152,5309,5387,5701,6246,6340,6344,6347,7000,7381,7876,7915,7919,7922,8215,8221,8284,8290,8761,8771,8774,9153,9160,9433,9436,9443,9447,11058,11563,11949,11953,12393,12952,13623,13630,13634,13689,15922,16074,16077,16125,16129,16594,17172,17176,18065,18458,18799,19544,21818,21997,22001,22514,23015,24242,25189,25344,25725,25731,25992,25995,25999,26075,26346,26352,26713,27797,27901,28078,28401,28407,28757,29292,29708,29712,29870,30292,31908,32177,32180,32639,32757,32768,33486,34508,34511,34547,34550,34553,34557,34564,35138,35273,35660,35961,36305,36309,36312,36390,36393,36479,36482,36486,36489,36789,36792,36850,36854,36857,36994,37001,37005,37008,37397,37403,37406,37409,37720,37723,37730],[11,12,13,14,83,84,149,150,219,220,303,304,308,309,365,366,431,432,498],"p",{},"为什么概率论不足以回答因果问题？设 ",[15,16,20,51],"span",{"className":17,"translate":19},[18],"katex","no",[15,21,24],{"className":22},[23],"katex-mathml",[25,26,28],"math",{"xmlns":27},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[29,30,31,46],"semantics",{},[32,33,34,38,43],"mrow",{},[35,36,37],"mi",{},"X",[39,40,42],"mo",{"separator":41},"true",",",[35,44,45],{},"Y",[47,48,50],"annotation",{"encoding":49},"application\u002Fx-tex","X, Y",[15,52,55],{"className":53,"ariaHidden":41},[54],"katex-html",[15,56,59,64,70,74,79],{"className":57},[58],"base",[15,60],{"className":61,"style":63},[62],"strut","height:0.8778em;vertical-align:-0.1944em;",[15,65,37],{"className":66,"style":69},[67,68],"mord","mathnormal","margin-right:0.0785em;",[15,71,42],{"className":72},[73],"mpunct",[15,75],{"className":76,"style":78},[77],"mspace","margin-right:0.1667em;",[15,80,45],{"className":81,"style":82},[67,68],"margin-right:0.2222em;"," 为两个随机变量，概率论所能给出的全部工具是联合分布 ",[15,85,87,115],{"className":86,"translate":19},[18],[15,88,90],{"className":89},[23],[25,91,92],{"xmlns":27},[29,93,94,112],{},[32,95,96,99,103,105,107,109],{},[35,97,98],{},"P",[39,100,102],{"stretchy":101},"false","(",[35,104,37],{},[39,106,42],{"separator":41},[35,108,45],{},[39,110,111],{"stretchy":101},")",[47,113,114],{"encoding":49},"P(X,Y)",[15,116,118],{"className":117,"ariaHidden":41},[54],[15,119,121,125,129,133,136,139,142,145],{"className":120},[58],[15,122],{"className":123,"style":124},[62],"height:1em;vertical-align:-0.25em;",[15,126,98],{"className":127,"style":128},[67,68],"margin-right:0.1389em;",[15,130,102],{"className":131},[132],"mopen",[15,134,37],{"className":135,"style":69},[67,68],[15,137,42],{"className":138},[73],[15,140],{"className":141,"style":78},[77],[15,143,45],{"className":144,"style":82},[67,68],[15,146,111],{"className":147},[148],"mclose","、条件分布 ",[15,151,153,178],{"className":152,"translate":19},[18],[15,154,156],{"className":155},[23],[25,157,158],{"xmlns":27},[29,159,160,175],{},[32,161,162,164,166,168,171,173],{},[35,163,98],{},[39,165,102],{"stretchy":101},[35,167,45],{},[39,169,170],{},"∣",[35,172,37],{},[39,174,111],{"stretchy":101},[47,176,177],{"encoding":49},"P(Y\\mid X)",[15,179,181,207],{"className":180,"ariaHidden":41},[54],[15,182,184,187,190,193,196,200,204],{"className":183},[58],[15,185],{"className":186,"style":124},[62],[15,188,98],{"className":189,"style":128},[67,68],[15,191,102],{"className":192},[132],[15,194,45],{"className":195,"style":82},[67,68],[15,197],{"className":198,"style":199},[77],"margin-right:0.2778em;",[15,201,170],{"className":202},[203],"mrel",[15,205],{"className":206,"style":199},[77],[15,208,210,213,216],{"className":209},[58],[15,211],{"className":212,"style":124},[62],[15,214,37],{"className":215,"style":69},[67,68],[15,217,111],{"className":218},[148],"，以及由此导出的独立性关系 ",[15,221,223,252],{"className":222,"translate":19},[18],[15,224,226],{"className":225},[23],[25,227,228],{"xmlns":27},[29,229,230,249],{},[32,231,232,234,237,241,243,245,247],{},[35,233,37],{},[39,235,236],{},"⊥",[238,239,240],"mtext",{}," ⁣",[238,242,240],{},[238,244,240],{},[39,246,236],{},[35,248,45],{},[47,250,251],{"encoding":49},"X \\perp\\!\\!\\!\\perp Y",[15,253,255,281,293],{"className":254,"ariaHidden":41},[54],[15,256,258,262,265,268,271,275,278],{"className":257},[58],[15,259],{"className":260,"style":261},[62],"height:0.6944em;",[15,263,37],{"className":264,"style":69},[67,68],[15,266],{"className":267,"style":199},[77],[15,269,236],{"className":270},[203],[15,272],{"className":273,"style":274},[77],"margin-right:-0.1667em;",[15,276],{"className":277,"style":274},[77],[15,279],{"className":280,"style":274},[77],[15,282,284,287,290],{"className":283},[58],[15,285],{"className":286,"style":261},[62],[15,288,236],{"className":289},[203],[15,291],{"className":292,"style":199},[77],[15,294,296,300],{"className":295},[58],[15,297],{"className":298,"style":299},[62],"height:0.6833em;",[15,301,45],{"className":302,"style":82},[67,68],"。这套语言在数学上是自洽的，但存在一个根本性的表达力缺陷：",[305,306,307],"strong",{},"概率分布对「对称性」是不敏感的","。若已知 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",[15,367,369,392],{"className":368,"translate":19},[18],[15,370,372],{"className":371},[23],[25,373,374],{"xmlns":27},[29,375,376,390],{},[32,377,378,380,382,384,386,388],{},[35,379,98],{},[39,381,102],{"stretchy":101},[35,383,45],{},[39,385,170],{},[35,387,37],{},[39,389,111],{"stretchy":101},[47,391,177],{"encoding":49},[15,393,395,419],{"className":394,"ariaHidden":41},[54],[15,396,398,401,404,407,410,413,416],{"className":397},[58],[15,399],{"className":400,"style":124},[62],[15,402,98],{"className":403,"style":128},[67,68],[15,405,102],{"className":406},[132],[15,408,45],{"className":409,"style":82},[67,68],[15,411],{"className":412,"style":199},[77],[15,414,170],{"className":415},[203],[15,417],{"className":418,"style":199},[77],[15,420,422,425,428],{"className":421},[58],[15,423],{"className":424,"style":124},[62],[15,426,37],{"className":427,"style":69},[67,68],[15,429,111],{"className":430},[148]," 与 ",[15,433,435,459],{"className":434,"translate":19},[18],[15,436,438],{"className":437},[23],[25,439,440],{"xmlns":27},[29,441,442,456],{},[32,443,444,446,448,450,452,454],{},[35,445,98],{},[39,447,102],{"stretchy":101},[35,449,37],{},[39,451,170],{},[35,453,45],{},[39,455,111],{"stretchy":101},[47,457,458],{"encoding":49},"P(X\\mid Y)",[15,460,462,486],{"className":461,"ariaHidden":41},[54],[15,463,465,468,471,474,477,480,483],{"className":464},[58],[15,466],{"className":467,"style":124},[62],[15,469,98],{"className":470,"style":128},[67,68],[15,472,102],{"className":473},[132],[15,475,37],{"className":476,"style":69},[67,68],[15,478],{"className":479,"style":199},[77],[15,481,170],{"className":482},[203],[15,484],{"className":485,"style":199},[77],[15,487,489,492,495],{"className":488},[58],[15,490],{"className":491,"style":124},[62],[15,493,45],{"className":494,"style":82},[67,68],[15,496,111],{"className":497},[148]," 皆可通过贝叶斯定理相互推出，二者在信息量上完全等价，谁也不比谁更「根本」。然而在实际世界中，「气压下降导致下雨」与「下雨导致气压下降」显然不是对称的两种表述——只有前者是对的。这种方向性、非对称性的知识，是概率分布本身无法编码的，必须由额外的结构承载。",[11,500,501,502,505],{},"Judea Pearl 将因果知识的层级组织为三层，通常称为",[305,503,504],{},"因果推断阶梯（Ladder of Causation）","：",[507,508,509,669,841],"ul",{},[510,511,512,515,516,585,586,639,640,668],"li",{},[305,513,514],{},"第一层（关联，Association）","：回答形如 ",[15,517,519,545],{"className":518,"translate":19},[18],[15,520,522],{"className":521},[23],[25,523,524],{"xmlns":27},[29,525,526,542],{},[32,527,528,530,532,535,537,540],{},[35,529,98],{},[39,531,102],{"stretchy":101},[35,533,534],{},"y",[39,536,170],{},[35,538,539],{},"x",[39,541,111],{"stretchy":101},[47,543,544],{"encoding":49},"P(y\\mid x)",[15,546,548,573],{"className":547,"ariaHidden":41},[54],[15,549,551,554,557,560,564,567,570],{"className":550},[58],[15,552],{"className":553,"style":124},[62],[15,555,98],{"className":556,"style":128},[67,68],[15,558,102],{"className":559},[132],[15,561,534],{"className":562,"style":563},[67,68],"margin-right:0.0359em;",[15,565],{"className":566,"style":199},[77],[15,568,170],{"className":569},[203],[15,571],{"className":572,"style":199},[77],[15,574,576,579,582],{"className":575},[58],[15,577],{"className":578,"style":124},[62],[15,580,539],{"className":581},[67,68],[15,583,111],{"className":584},[148]," 的问题，即「观察到 ",[15,587,589,608],{"className":588,"translate":19},[18],[15,590,592],{"className":591},[23],[25,593,594],{"xmlns":27},[29,595,596,605],{},[32,597,598,600,603],{},[35,599,37],{},[39,601,602],{},"=",[35,604,539],{},[47,606,607],{"encoding":49},"X=x",[15,609,611,629],{"className":610,"ariaHidden":41},[54],[15,612,614,617,620,623,626],{"className":613},[58],[15,615],{"className":616,"style":299},[62],[15,618,37],{"className":619,"style":69},[67,68],[15,621],{"className":622,"style":199},[77],[15,624,602],{"className":625},[203],[15,627],{"className":628,"style":199},[77],[15,630,632,636],{"className":631},[58],[15,633],{"className":634,"style":635},[62],"height:0.4306em;",[15,637,539],{"className":638},[67,68]," 时，",[15,641,643,656],{"className":642,"translate":19},[18],[15,644,646],{"className":645},[23],[25,647,648],{"xmlns":27},[29,649,650,654],{},[32,651,652],{},[35,653,45],{},[47,655,45],{"encoding":49},[15,657,659],{"className":658,"ariaHidden":41},[54],[15,660,662,665],{"className":661},[58],[15,663],{"className":664,"style":299},[62],[15,666,45],{"className":667,"style":82},[67,68]," 的分布是什么」。这一层是纯统计学的领地。",[510,670,671,515,674,760,761,811,812,840],{},[305,672,673],{},"第二层（干预，Intervention）",[15,675,677,711],{"className":676,"translate":19},[18],[15,678,680],{"className":679},[23],[25,681,682],{"xmlns":27},[29,683,684,708],{},[32,685,686,688,690,692,694,697,700,702,704,706],{},[35,687,98],{},[39,689,102],{"stretchy":101},[35,691,534],{},[39,693,170],{},[35,695,696],{},"d",[35,698,699],{},"o",[39,701,102],{"stretchy":101},[35,703,539],{},[39,705,111],{"stretchy":101},[39,707,111],{"stretchy":101},[47,709,710],{"encoding":49},"P(y\\mid do(x))",[15,712,714,738],{"className":713,"ariaHidden":41},[54],[15,715,717,720,723,726,729,732,735],{"className":716},[58],[15,718],{"className":719,"style":124},[62],[15,721,98],{"className":722,"style":128},[67,68],[15,724,102],{"className":725},[132],[15,727,534],{"className":728,"style":563},[67,68],[15,730],{"className":731,"style":199},[77],[15,733,170],{"className":734},[203],[15,736],{"className":737,"style":199},[77],[15,739,741,744,747,750,753,756],{"className":740},[58],[15,742],{"className":743,"style":124},[62],[15,745,696],{"className":746},[67,68],[15,748,699],{"className":749},[67,68],[15,751,102],{"className":752},[132],[15,754,539],{"className":755},[67,68],[15,757,759],{"className":758},[148],"))"," 的问题，即「若外部强行使 ",[15,762,764,781],{"className":763,"translate":19},[18],[15,765,767],{"className":766},[23],[25,768,769],{"xmlns":27},[29,770,771,779],{},[32,772,773,775,777],{},[35,774,37],{},[39,776,602],{},[35,778,539],{},[47,780,607],{"encoding":49},[15,782,784,802],{"className":783,"ariaHidden":41},[54],[15,785,787,790,793,796,799],{"className":786},[58],[15,788],{"className":789,"style":299},[62],[15,791,37],{"className":792,"style":69},[67,68],[15,794],{"className":795,"style":199},[77],[15,797,602],{"className":798},[203],[15,800],{"className":801,"style":199},[77],[15,803,805,808],{"className":804},[58],[15,806],{"className":807,"style":635},[62],[15,809,539],{"className":810},[67,68],"，",[15,813,815,828],{"className":814,"translate":19},[18],[15,816,818],{"className":817},[23],[25,819,820],{"xmlns":27},[29,821,822,826],{},[32,823,824],{},[35,825,45],{},[47,827,45],{"encoding":49},[15,829,831],{"className":830,"ariaHidden":41},[54],[15,832,834,837],{"className":833},[58],[15,835],{"className":836,"style":299},[62],[15,838,45],{"className":839,"style":82},[67,68]," 的分布是什么」。",[510,842,843,515,846,1056,1057,1210,1211,1239,1240,811,1268,1296],{},[305,844,845],{},"第三层（反事实，Counterfactual）",[15,847,849,894],{"className":848,"translate":19},[18],[15,850,852],{"className":851},[23],[25,853,854],{"xmlns":27},[29,855,856,891],{},[32,857,858,860,862,869,871,881,883,889],{},[35,859,98],{},[39,861,102],{"stretchy":101},[863,864,865,867],"msub",{},[35,866,534],{},[35,868,539],{},[39,870,170],{},[872,873,874,876],"msup",{},[35,875,539],{},[39,877,880],{"mathvariant":878,"lspace":879,"rspace":879},"normal","0em","′",[39,882,42],{"separator":41},[872,884,885,887],{},[35,886,534],{},[39,888,880],{"mathvariant":878,"lspace":879,"rspace":879},[39,890,111],{"stretchy":101},[47,892,893],{"encoding":49},"P(y_x \\mid x', y')",[15,895,897,974],{"className":896,"ariaHidden":41},[54],[15,898,900,903,906,909,965,968,971],{"className":899},[58],[15,901],{"className":902,"style":124},[62],[15,904,98],{"className":905,"style":128},[67,68],[15,907,102],{"className":908},[132],[15,910,912,915],{"className":911},[67],[15,913,534],{"className":914,"style":563},[67,68],[15,916,919],{"className":917},[918],"msupsub",[15,920,924,956],{"className":921},[922,923],"vlist-t","vlist-t2",[15,925,928,951],{"className":926},[927],"vlist-r",[15,929,933],{"className":930,"style":932},[931],"vlist","height:0.1514em;",[15,934,936,941],{"style":935},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[15,937],{"className":938,"style":940},[939],"pstrut","height:2.7em;",[15,942,948],{"className":943},[944,945,946,947],"sizing","reset-size6","size3","mtight",[15,949,539],{"className":950},[67,68,947],[15,952,955],{"className":953},[954],"vlist-s","​",[15,957,959],{"className":958},[927],[15,960,963],{"className":961,"style":962},[931],"height:0.15em;",[15,964],{},[15,966],{"className":967,"style":199},[77],[15,969,170],{"className":970},[203],[15,972],{"className":973,"style":199},[77],[15,975,977,981,1015,1018,1021,1053],{"className":976},[58],[15,978],{"className":979,"style":980},[62],"height:1.0019em;vertical-align:-0.25em;",[15,982,984,987],{"className":983},[67],[15,985,539],{"className":986},[67,68],[15,988,990],{"className":989},[918],[15,991,993],{"className":992},[922],[15,994,996],{"className":995},[927],[15,997,1000],{"className":998,"style":999},[931],"height:0.7519em;",[15,1001,1003,1006],{"style":1002},"top:-3.063em;margin-right:0.05em;",[15,1004],{"className":1005,"style":940},[939],[15,1007,1009],{"className":1008},[944,945,946,947],[15,1010,1012],{"className":1011},[67,947],[15,1013,880],{"className":1014},[67,947],[15,1016,42],{"className":1017},[73],[15,1019],{"className":1020,"style":78},[77],[15,1022,1024,1027],{"className":1023},[67],[15,1025,534],{"className":1026,"style":563},[67,68],[15,1028,1030],{"className":1029},[918],[15,1031,1033],{"className":1032},[922],[15,1034,1036],{"className":1035},[927],[15,1037,1039],{"className":1038,"style":999},[931],[15,1040,1041,1044],{"style":1002},[15,1042],{"className":1043,"style":940},[939],[15,1045,1047],{"className":1046},[944,945,946,947],[15,1048,1050],{"className":1049},[67,947],[15,1051,880],{"className":1052},[67,947],[15,1054,111],{"className":1055},[148]," 的问题，即「已经观测到 ",[15,1058,1060,1094],{"className":1059,"translate":19},[18],[15,1061,1063],{"className":1062},[23],[25,1064,1065],{"xmlns":27},[29,1066,1067,1091],{},[32,1068,1069,1071,1073,1079,1081,1083,1085],{},[35,1070,37],{},[39,1072,602],{},[872,1074,1075,1077],{},[35,1076,539],{},[39,1078,880],{"mathvariant":878,"lspace":879,"rspace":879},[39,1080,42],{"separator":41},[35,1082,45],{},[39,1084,602],{},[872,1086,1087,1089],{},[35,1088,534],{},[39,1090,880],{"mathvariant":878,"lspace":879,"rspace":879},[47,1092,1093],{"encoding":49},"X=x', Y=y'",[15,1095,1097,1115,1172],{"className":1096,"ariaHidden":41},[54],[15,1098,1100,1103,1106,1109,1112],{"className":1099},[58],[15,1101],{"className":1102,"style":299},[62],[15,1104,37],{"className":1105,"style":69},[67,68],[15,1107],{"className":1108,"style":199},[77],[15,1110,602],{"className":1111},[203],[15,1113],{"className":1114,"style":199},[77],[15,1116,1118,1122,1154,1157,1160,1163,1166,1169],{"className":1117},[58],[15,1119],{"className":1120,"style":1121},[62],"height:0.9463em;vertical-align:-0.1944em;",[15,1123,1125,1128],{"className":1124},[67],[15,1126,539],{"className":1127},[67,68],[15,1129,1131],{"className":1130},[918],[15,1132,1134],{"className":1133},[922],[15,1135,1137],{"className":1136},[927],[15,1138,1140],{"className":1139,"style":999},[931],[15,1141,1142,1145],{"style":1002},[15,1143],{"className":1144,"style":940},[939],[15,1146,1148],{"className":1147},[944,945,946,947],[15,1149,1151],{"className":1150},[67,947],[15,1152,880],{"className":1153},[67,947],[15,1155,42],{"className":1156},[73],[15,1158],{"className":1159,"style":78},[77],[15,1161,45],{"className":1162,"style":82},[67,68],[15,1164],{"className":1165,"style":199},[77],[15,1167,602],{"className":1168},[203],[15,1170],{"className":1171,"style":199},[77],[15,1173,1175,1178],{"className":1174},[58],[15,1176],{"className":1177,"style":1121},[62],[15,1179,1181,1184],{"className":1180},[67],[15,1182,534],{"className":1183,"style":563},[67,68],[15,1185,1187],{"className":1186},[918],[15,1188,1190],{"className":1189},[922],[15,1191,1193],{"className":1192},[927],[15,1194,1196],{"className":1195,"style":999},[931],[15,1197,1198,1201],{"style":1002},[15,1199],{"className":1200,"style":940},[939],[15,1202,1204],{"className":1203},[944,945,946,947],[15,1205,1207],{"className":1206},[67,947],[15,1208,880],{"className":1209},[67,947]," 的这个个体，若当初 ",[15,1212,1214,1227],{"className":1213,"translate":19},[18],[15,1215,1217],{"className":1216},[23],[25,1218,1219],{"xmlns":27},[29,1220,1221,1225],{},[32,1222,1223],{},[35,1224,37],{},[47,1226,37],{"encoding":49},[15,1228,1230],{"className":1229,"ariaHidden":41},[54],[15,1231,1233,1236],{"className":1232},[58],[15,1234],{"className":1235,"style":299},[62],[15,1237,37],{"className":1238,"style":69},[67,68]," 被设为 ",[15,1241,1243,1256],{"className":1242,"translate":19},[18],[15,1244,1246],{"className":1245},[23],[25,1247,1248],{"xmlns":27},[29,1249,1250,1254],{},[32,1251,1252],{},[35,1253,539],{},[47,1255,539],{"encoding":49},[15,1257,1259],{"className":1258,"ariaHidden":41},[54],[15,1260,1262,1265],{"className":1261},[58],[15,1263],{"className":1264,"style":635},[62],[15,1266,539],{"className":1267},[67,68],[15,1269,1271,1284],{"className":1270,"translate":19},[18],[15,1272,1274],{"className":1273},[23],[25,1275,1276],{"xmlns":27},[29,1277,1278,1282],{},[32,1279,1280],{},[35,1281,45],{},[47,1283,45],{"encoding":49},[15,1285,1287],{"className":1286,"ariaHidden":41},[54],[15,1288,1290,1293],{"className":1289},[58],[15,1291],{"className":1292,"style":299},[62],[15,1294,45],{"className":1295,"style":82},[67,68]," 会取什么值」。",[11,1298,1299,1300,1303],{},"Pearl 证明了一个重要的否定性结论：",[305,1301,1302],{},"在一般情形下，仅凭第一层的信息（即观测分布本身），不足以唯一确定第二层或第三层的量","，除非引入额外的结构假设。这正是因果图、结构因果模型与结构方程存在的意义——它们是在观测分布之外，显式引入的「结构性知识」，使得第二、三层的问题在数学上可解。本文将依次、系统地展开这三个层层递进的形式化工具；随后把这一体系与潜在结果框架、传统结构方程模型等相邻传统作对照，并讨论其成立所依赖的假设与适用边界。",[1305,1306,1307],"h2",{"id":1307},"因果图",[1309,1310,1312],"h3",{"id":1311},"_11-有向无环图的形式化定义","1.1 有向无环图的形式化定义",[1314,1315,1316],"blockquote",{},[11,1317,1318,1321,1322,1400,1401,1582,1583,1661,1662,1825,1826,1962,1963,2033,2034,2104,2105,811,2108,2033,2177,2104,2246,2249],{},[305,1319,1320],{},"定义 1.1（有向图）"," 一个有向图是一个二元组 ",[15,1323,1325,1354],{"className":1324,"translate":19},[18],[15,1326,1328],{"className":1327},[23],[25,1329,1330],{"xmlns":27},[29,1331,1332,1351],{},[32,1333,1334,1337,1339,1341,1344,1346,1349],{},[35,1335,1336],{},"G",[39,1338,602],{},[39,1340,102],{"stretchy":101},[35,1342,1343],{},"V",[39,1345,42],{"separator":41},[35,1347,1348],{},"E",[39,1350,111],{"stretchy":101},[47,1352,1353],{"encoding":49},"G = (V, E)",[15,1355,1357,1375],{"className":1356,"ariaHidden":41},[54],[15,1358,1360,1363,1366,1369,1372],{"className":1359},[58],[15,1361],{"className":1362,"style":299},[62],[15,1364,1336],{"className":1365},[67,68],[15,1367],{"className":1368,"style":199},[77],[15,1370,602],{"className":1371},[203],[15,1373],{"className":1374,"style":199},[77],[15,1376,1378,1381,1384,1387,1390,1393,1397],{"className":1377},[58],[15,1379],{"className":1380,"style":124},[62],[15,1382,102],{"className":1383},[132],[15,1385,1343],{"className":1386,"style":82},[67,68],[15,1388,42],{"className":1389},[73],[15,1391],{"className":1392,"style":78},[77],[15,1394,1348],{"className":1395,"style":1396},[67,68],"margin-right:0.0576em;",[15,1398,111],{"className":1399},[148],"，其中 ",[15,1402,1404,1448],{"className":1403,"translate":19},[18],[15,1405,1407],{"className":1406},[23],[25,1408,1409],{"xmlns":27},[29,1410,1411,1445],{},[32,1412,1413,1415,1417,1420,1428,1430,1433,1435,1442],{},[35,1414,1343],{},[39,1416,602],{},[39,1418,1419],{"stretchy":101},"{",[863,1421,1422,1424],{},[35,1423,1343],{},[1425,1426,1427],"mn",{},"1",[39,1429,42],{"separator":41},[39,1431,1432],{},"…",[39,1434,42],{"separator":41},[863,1436,1437,1439],{},[35,1438,1343],{},[35,1440,1441],{},"n",[39,1443,1444],{"stretchy":101},"}",[47,1446,1447],{"encoding":49},"V = \\{V_1, \\dots, V_n\\}",[15,1449,1451,1469],{"className":1450,"ariaHidden":41},[54],[15,1452,1454,1457,1460,1463,1466],{"className":1453},[58],[15,1455],{"className":1456,"style":299},[62],[15,1458,1343],{"className":1459,"style":82},[67,68],[15,1461],{"className":1462,"style":199},[77],[15,1464,602],{"className":1465},[203],[15,1467],{"className":1468,"style":199},[77],[15,1470,1472,1475,1478,1520,1523,1526,1530,1533,1536,1539,1579],{"className":1471},[58],[15,1473],{"className":1474,"style":124},[62],[15,1476,1419],{"className":1477},[132],[15,1479,1481,1484],{"className":1480},[67],[15,1482,1343],{"className":1483,"style":82},[67,68],[15,1485,1487],{"className":1486},[918],[15,1488,1490,1512],{"className":1489},[922,923],[15,1491,1493,1509],{"className":1492},[927],[15,1494,1497],{"className":1495,"style":1496},[931],"height:0.3011em;",[15,1498,1500,1503],{"style":1499},"top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;",[15,1501],{"className":1502,"style":940},[939],[15,1504,1506],{"className":1505},[944,945,946,947],[15,1507,1427],{"className":1508},[67,947],[15,1510,955],{"className":1511},[954],[15,1513,1515],{"className":1514},[927],[15,1516,1518],{"className":1517,"style":962},[931],[15,1519],{},[15,1521,42],{"className":1522},[73],[15,1524],{"className":1525,"style":78},[77],[15,1527,1432],{"className":1528},[1529],"minner",[15,1531],{"className":1532,"style":78},[77],[15,1534,42],{"className":1535},[73],[15,1537],{"className":1538,"style":78},[77],[15,1540,1542,1545],{"className":1541},[67],[15,1543,1343],{"className":1544,"style":82},[67,68],[15,1546,1548],{"className":1547},[918],[15,1549,1551,1571],{"className":1550},[922,923],[15,1552,1554,1568],{"className":1553},[927],[15,1555,1557],{"className":1556,"style":932},[931],[15,1558,1559,1562],{"style":1499},[15,1560],{"className":1561,"style":940},[939],[15,1563,1565],{"className":1564},[944,945,946,947],[15,1566,1441],{"className":1567},[67,68,947],[15,1569,955],{"className":1570},[954],[15,1572,1574],{"className":1573},[927],[15,1575,1577],{"className":1576,"style":962},[931],[15,1578],{},[15,1580,1444],{"className":1581},[148]," 是节点（顶点）的有限集合，",[15,1584,1586,1610],{"className":1585,"translate":19},[18],[15,1587,1589],{"className":1588},[23],[25,1590,1591],{"xmlns":27},[29,1592,1593,1607],{},[32,1594,1595,1597,1600,1602,1605],{},[35,1596,1348],{},[39,1598,1599],{},"⊆",[35,1601,1343],{},[39,1603,1604],{},"×",[35,1606,1343],{},[47,1608,1609],{"encoding":49},"E \\subseteq V \\times V",[15,1611,1613,1632,1652],{"className":1612,"ariaHidden":41},[54],[15,1614,1616,1620,1623,1626,1629],{"className":1615},[58],[15,1617],{"className":1618,"style":1619},[62],"height:0.8193em;vertical-align:-0.136em;",[15,1621,1348],{"className":1622,"style":1396},[67,68],[15,1624],{"className":1625,"style":199},[77],[15,1627,1599],{"className":1628},[203],[15,1630],{"className":1631,"style":199},[77],[15,1633,1635,1639,1642,1645,1649],{"className":1634},[58],[15,1636],{"className":1637,"style":1638},[62],"height:0.7667em;vertical-align:-0.0833em;",[15,1640,1343],{"className":1641,"style":82},[67,68],[15,1643],{"className":1644,"style":82},[77],[15,1646,1604],{"className":1647},[1648],"mbin",[15,1650],{"className":1651,"style":82},[77],[15,1653,1655,1658],{"className":1654},[58],[15,1656],{"className":1657,"style":299},[62],[15,1659,1343],{"className":1660,"style":82},[67,68]," 是有向边的集合。若 ",[15,1663,1665,1702],{"className":1664,"translate":19},[18],[15,1666,1668],{"className":1667},[23],[25,1669,1670],{"xmlns":27},[29,1671,1672,1699],{},[32,1673,1674,1676,1683,1685,1692,1694,1697],{},[39,1675,102],{"stretchy":101},[863,1677,1678,1680],{},[35,1679,1343],{},[35,1681,1682],{},"i",[39,1684,42],{"separator":41},[863,1686,1687,1689],{},[35,1688,1343],{},[35,1690,1691],{},"j",[39,1693,111],{"stretchy":101},[39,1695,1696],{},"∈",[35,1698,1348],{},[47,1700,1701],{"encoding":49},"(V_i, V_j) \\in E",[15,1703,1705,1816],{"className":1704,"ariaHidden":41},[54],[15,1706,1708,1712,1715,1756,1759,1762,1804,1807,1810,1813],{"className":1707},[58],[15,1709],{"className":1710,"style":1711},[62],"height:1.0361em;vertical-align:-0.2861em;",[15,1713,102],{"className":1714},[132],[15,1716,1718,1721],{"className":1717},[67],[15,1719,1343],{"className":1720,"style":82},[67,68],[15,1722,1724],{"className":1723},[918],[15,1725,1727,1748],{"className":1726},[922,923],[15,1728,1730,1745],{"className":1729},[927],[15,1731,1734],{"className":1732,"style":1733},[931],"height:0.3117em;",[15,1735,1736,1739],{"style":1499},[15,1737],{"className":1738,"style":940},[939],[15,1740,1742],{"className":1741},[944,945,946,947],[15,1743,1682],{"className":1744},[67,68,947],[15,1746,955],{"className":1747},[954],[15,1749,1751],{"className":1750},[927],[15,1752,1754],{"className":1753,"style":962},[931],[15,1755],{},[15,1757,42],{"className":1758},[73],[15,1760],{"className":1761,"style":78},[77],[15,1763,1765,1768],{"className":1764},[67],[15,1766,1343],{"className":1767,"style":82},[67,68],[15,1769,1771],{"className":1770},[918],[15,1772,1774,1795],{"className":1773},[922,923],[15,1775,1777,1792],{"className":1776},[927],[15,1778,1780],{"className":1779,"style":1733},[931],[15,1781,1782,1785],{"style":1499},[15,1783],{"className":1784,"style":940},[939],[15,1786,1788],{"className":1787},[944,945,946,947],[15,1789,1691],{"className":1790,"style":1791},[67,68,947],"margin-right:0.0572em;",[15,1793,955],{"className":1794},[954],[15,1796,1798],{"className":1797},[927],[15,1799,1802],{"className":1800,"style":1801},[931],"height:0.2861em;",[15,1803],{},[15,1805,111],{"className":1806},[148],[15,1808],{"className":1809,"style":199},[77],[15,1811,1696],{"className":1812},[203],[15,1814],{"className":1815,"style":199},[77],[15,1817,1819,1822],{"className":1818},[58],[15,1820],{"className":1821,"style":299},[62],[15,1823,1348],{"className":1824,"style":1396},[67,68],"，记作 ",[15,1827,1829,1856],{"className":1828,"translate":19},[18],[15,1830,1832],{"className":1831},[23],[25,1833,1834],{"xmlns":27},[29,1835,1836,1853],{},[32,1837,1838,1844,1847],{},[863,1839,1840,1842],{},[35,1841,1343],{},[35,1843,1682],{},[39,1845,1846],{},"→",[863,1848,1849,1851],{},[35,1850,1343],{},[35,1852,1691],{},[47,1854,1855],{"encoding":49},"V_i \\to V_j",[15,1857,1859,1915],{"className":1858,"ariaHidden":41},[54],[15,1860,1862,1866,1906,1909,1912],{"className":1861},[58],[15,1863],{"className":1864,"style":1865},[62],"height:0.8333em;vertical-align:-0.15em;",[15,1867,1869,1872],{"className":1868},[67],[15,1870,1343],{"className":1871,"style":82},[67,68],[15,1873,1875],{"className":1874},[918],[15,1876,1878,1898],{"className":1877},[922,923],[15,1879,1881,1895],{"className":1880},[927],[15,1882,1884],{"className":1883,"style":1733},[931],[15,1885,1886,1889],{"style":1499},[15,1887],{"className":1888,"style":940},[939],[15,1890,1892],{"className":1891},[944,945,946,947],[15,1893,1682],{"className":1894},[67,68,947],[15,1896,955],{"className":1897},[954],[15,1899,1901],{"className":1900},[927],[15,1902,1904],{"className":1903,"style":962},[931],[15,1905],{},[15,1907],{"className":1908,"style":199},[77],[15,1910,1846],{"className":1911},[203],[15,1913],{"className":1914,"style":199},[77],[15,1916,1918,1922],{"className":1917},[58],[15,1919],{"className":1920,"style":1921},[62],"height:0.9694em;vertical-align:-0.2861em;",[15,1923,1925,1928],{"className":1924},[67],[15,1926,1343],{"className":1927,"style":82},[67,68],[15,1929,1931],{"className":1930},[918],[15,1932,1934,1954],{"className":1933},[922,923],[15,1935,1937,1951],{"className":1936},[927],[15,1938,1940],{"className":1939,"style":1733},[931],[15,1941,1942,1945],{"style":1499},[15,1943],{"className":1944,"style":940},[939],[15,1946,1948],{"className":1947},[944,945,946,947],[15,1949,1691],{"className":1950,"style":1791},[67,68,947],[15,1952,955],{"className":1953},[954],[15,1955,1957],{"className":1956},[927],[15,1958,1960],{"className":1959,"style":1801},[931],[15,1961],{},"，称 ",[15,1964,1966,1984],{"className":1965,"translate":19},[18],[15,1967,1969],{"className":1968},[23],[25,1970,1971],{"xmlns":27},[29,1972,1973,1981],{},[32,1974,1975],{},[863,1976,1977,1979],{},[35,1978,1343],{},[35,1980,1682],{},[47,1982,1983],{"encoding":49},"V_i",[15,1985,1987],{"className":1986,"ariaHidden":41},[54],[15,1988,1990,1993],{"className":1989},[58],[15,1991],{"className":1992,"style":1865},[62],[15,1994,1996,1999],{"className":1995},[67],[15,1997,1343],{"className":1998,"style":82},[67,68],[15,2000,2002],{"className":2001},[918],[15,2003,2005,2025],{"className":2004},[922,923],[15,2006,2008,2022],{"className":2007},[927],[15,2009,2011],{"className":2010,"style":1733},[931],[15,2012,2013,2016],{"style":1499},[15,2014],{"className":2015,"style":940},[939],[15,2017,2019],{"className":2018},[944,945,946,947],[15,2020,1682],{"className":2021},[67,68,947],[15,2023,955],{"className":2024},[954],[15,2026,2028],{"className":2027},[927],[15,2029,2031],{"className":2030,"style":962},[931],[15,2032],{}," 为 ",[15,2035,2037,2055],{"className":2036,"translate":19},[18],[15,2038,2040],{"className":2039},[23],[25,2041,2042],{"xmlns":27},[29,2043,2044,2052],{},[32,2045,2046],{},[863,2047,2048,2050],{},[35,2049,1343],{},[35,2051,1691],{},[47,2053,2054],{"encoding":49},"V_j",[15,2056,2058],{"className":2057,"ariaHidden":41},[54],[15,2059,2061,2064],{"className":2060},[58],[15,2062],{"className":2063,"style":1921},[62],[15,2065,2067,2070],{"className":2066},[67],[15,2068,1343],{"className":2069,"style":82},[67,68],[15,2071,2073],{"className":2072},[918],[15,2074,2076,2096],{"className":2075},[922,923],[15,2077,2079,2093],{"className":2078},[927],[15,2080,2082],{"className":2081,"style":1733},[931],[15,2083,2084,2087],{"style":1499},[15,2085],{"className":2086,"style":940},[939],[15,2088,2090],{"className":2089},[944,945,946,947],[15,2091,1691],{"className":2092,"style":1791},[67,68,947],[15,2094,955],{"className":2095},[954],[15,2097,2099],{"className":2098},[927],[15,2100,2102],{"className":2101,"style":1801},[931],[15,2103],{}," 的",[305,2106,2107],{},"父节点（parent）",[15,2109,2111,2128],{"className":2110,"translate":19},[18],[15,2112,2114],{"className":2113},[23],[25,2115,2116],{"xmlns":27},[29,2117,2118,2126],{},[32,2119,2120],{},[863,2121,2122,2124],{},[35,2123,1343],{},[35,2125,1691],{},[47,2127,2054],{"encoding":49},[15,2129,2131],{"className":2130,"ariaHidden":41},[54],[15,2132,2134,2137],{"className":2133},[58],[15,2135],{"className":2136,"style":1921},[62],[15,2138,2140,2143],{"className":2139},[67],[15,2141,1343],{"className":2142,"style":82},[67,68],[15,2144,2146],{"className":2145},[918],[15,2147,2149,2169],{"className":2148},[922,923],[15,2150,2152,2166],{"className":2151},[927],[15,2153,2155],{"className":2154,"style":1733},[931],[15,2156,2157,2160],{"style":1499},[15,2158],{"className":2159,"style":940},[939],[15,2161,2163],{"className":2162},[944,945,946,947],[15,2164,1691],{"className":2165,"style":1791},[67,68,947],[15,2167,955],{"className":2168},[954],[15,2170,2172],{"className":2171},[927],[15,2173,2175],{"className":2174,"style":1801},[931],[15,2176],{},[15,2178,2180,2197],{"className":2179,"translate":19},[18],[15,2181,2183],{"className":2182},[23],[25,2184,2185],{"xmlns":27},[29,2186,2187,2195],{},[32,2188,2189],{},[863,2190,2191,2193],{},[35,2192,1343],{},[35,2194,1682],{},[47,2196,1983],{"encoding":49},[15,2198,2200],{"className":2199,"ariaHidden":41},[54],[15,2201,2203,2206],{"className":2202},[58],[15,2204],{"className":2205,"style":1865},[62],[15,2207,2209,2212],{"className":2208},[67],[15,2210,1343],{"className":2211,"style":82},[67,68],[15,2213,2215],{"className":2214},[918],[15,2216,2218,2238],{"className":2217},[922,923],[15,2219,2221,2235],{"className":2220},[927],[15,2222,2224],{"className":2223,"style":1733},[931],[15,2225,2226,2229],{"style":1499},[15,2227],{"className":2228,"style":940},[939],[15,2230,2232],{"className":2231},[944,945,946,947],[15,2233,1682],{"className":2234},[67,68,947],[15,2236,955],{"className":2237},[954],[15,2239,2241],{"className":2240},[927],[15,2242,2244],{"className":2243,"style":962},[931],[15,2245],{},[305,2247,2248],{},"子节点（child）","。",[1314,2251,2252],{},[11,2253,2254,2257,2258,2286,2287,2356,2357,2426,2427,2430,2431,2770,2771,811,2801,431,2872,2960,2961,2964,2965,3098,3099,3153,3154,2249],{},[305,2255,2256],{},"定义 1.2（路径）"," 图 ",[15,2259,2261,2274],{"className":2260,"translate":19},[18],[15,2262,2264],{"className":2263},[23],[25,2265,2266],{"xmlns":27},[29,2267,2268,2272],{},[32,2269,2270],{},[35,2271,1336],{},[47,2273,1336],{"encoding":49},[15,2275,2277],{"className":2276,"ariaHidden":41},[54],[15,2278,2280,2283],{"className":2279},[58],[15,2281],{"className":2282,"style":299},[62],[15,2284,1336],{"className":2285},[67,68]," 中从 ",[15,2288,2290,2307],{"className":2289,"translate":19},[18],[15,2291,2293],{"className":2292},[23],[25,2294,2295],{"xmlns":27},[29,2296,2297,2305],{},[32,2298,2299],{},[863,2300,2301,2303],{},[35,2302,1343],{},[35,2304,1682],{},[47,2306,1983],{"encoding":49},[15,2308,2310],{"className":2309,"ariaHidden":41},[54],[15,2311,2313,2316],{"className":2312},[58],[15,2314],{"className":2315,"style":1865},[62],[15,2317,2319,2322],{"className":2318},[67],[15,2320,1343],{"className":2321,"style":82},[67,68],[15,2323,2325],{"className":2324},[918],[15,2326,2328,2348],{"className":2327},[922,923],[15,2329,2331,2345],{"className":2330},[927],[15,2332,2334],{"className":2333,"style":1733},[931],[15,2335,2336,2339],{"style":1499},[15,2337],{"className":2338,"style":940},[939],[15,2340,2342],{"className":2341},[944,945,946,947],[15,2343,1682],{"className":2344},[67,68,947],[15,2346,955],{"className":2347},[954],[15,2349,2351],{"className":2350},[927],[15,2352,2354],{"className":2353,"style":962},[931],[15,2355],{}," 到 ",[15,2358,2360,2377],{"className":2359,"translate":19},[18],[15,2361,2363],{"className":2362},[23],[25,2364,2365],{"xmlns":27},[29,2366,2367,2375],{},[32,2368,2369],{},[863,2370,2371,2373],{},[35,2372,1343],{},[35,2374,1691],{},[47,2376,2054],{"encoding":49},[15,2378,2380],{"className":2379,"ariaHidden":41},[54],[15,2381,2383,2386],{"className":2382},[58],[15,2384],{"className":2385,"style":1921},[62],[15,2387,2389,2392],{"className":2388},[67],[15,2390,1343],{"className":2391,"style":82},[67,68],[15,2393,2395],{"className":2394},[918],[15,2396,2398,2418],{"className":2397},[922,923],[15,2399,2401,2415],{"className":2400},[927],[15,2402,2404],{"className":2403,"style":1733},[931],[15,2405,2406,2409],{"style":1499},[15,2407],{"className":2408,"style":940},[939],[15,2410,2412],{"className":2411},[944,945,946,947],[15,2413,1691],{"className":2414,"style":1791},[67,68,947],[15,2416,955],{"className":2417},[954],[15,2419,2421],{"className":2420},[927],[15,2422,2424],{"className":2423,"style":1801},[931],[15,2425],{}," 的一条",[305,2428,2429],{},"路径","是一个节点序列 ",[15,2432,2434,2497],{"className":2433,"translate":19},[18],[15,2435,2437],{"className":2436},[23],[25,2438,2439],{"xmlns":27},[29,2440,2441,2494],{},[32,2442,2443,2446,2452,2454,2462,2464,2470,2472,2474,2476,2483,2485,2491],{},[39,2444,2445],{"stretchy":101},"⟨",[863,2447,2448,2450],{},[35,2449,1343],{},[35,2451,1682],{},[39,2453,602],{},[863,2455,2456,2459],{},[35,2457,2458],{},"U",[1425,2460,2461],{},"0",[39,2463,42],{"separator":41},[863,2465,2466,2468],{},[35,2467,2458],{},[1425,2469,1427],{},[39,2471,42],{"separator":41},[39,2473,1432],{},[39,2475,42],{"separator":41},[863,2477,2478,2480],{},[35,2479,2458],{},[35,2481,2482],{},"k",[39,2484,602],{},[863,2486,2487,2489],{},[35,2488,1343],{},[35,2490,1691],{},[39,2492,2493],{"stretchy":101},"⟩",[47,2495,2496],{"encoding":49},"\\langle V_i = U_0, U_1, \\dots, U_k = V_j\\rangle",[15,2498,2500,2558,2721],{"className":2499,"ariaHidden":41},[54],[15,2501,2503,2506,2509,2549,2552,2555],{"className":2502},[58],[15,2504],{"className":2505,"style":124},[62],[15,2507,2445],{"className":2508},[132],[15,2510,2512,2515],{"className":2511},[67],[15,2513,1343],{"className":2514,"style":82},[67,68],[15,2516,2518],{"className":2517},[918],[15,2519,2521,2541],{"className":2520},[922,923],[15,2522,2524,2538],{"className":2523},[927],[15,2525,2527],{"className":2526,"style":1733},[931],[15,2528,2529,2532],{"style":1499},[15,2530],{"className":2531,"style":940},[939],[15,2533,2535],{"className":2534},[944,945,946,947],[15,2536,1682],{"className":2537},[67,68,947],[15,2539,955],{"className":2540},[954],[15,2542,2544],{"className":2543},[927],[15,2545,2547],{"className":2546,"style":962},[931],[15,2548],{},[15,2550],{"className":2551,"style":199},[77],[15,2553,602],{"className":2554},[203],[15,2556],{"className":2557,"style":199},[77],[15,2559,2561,2564,2606,2609,2612,2652,2655,2658,2661,2664,2667,2670,2712,2715,2718],{"className":2560},[58],[15,2562],{"className":2563,"style":63},[62],[15,2565,2567,2571],{"className":2566},[67],[15,2568,2458],{"className":2569,"style":2570},[67,68],"margin-right:0.109em;",[15,2572,2574],{"className":2573},[918],[15,2575,2577,2598],{"className":2576},[922,923],[15,2578,2580,2595],{"className":2579},[927],[15,2581,2583],{"className":2582,"style":1496},[931],[15,2584,2586,2589],{"style":2585},"top:-2.55em;margin-left:-0.109em;margin-right:0.05em;",[15,2587],{"className":2588,"style":940},[939],[15,2590,2592],{"className":2591},[944,945,946,947],[15,2593,2461],{"className":2594},[67,947],[15,2596,955],{"className":2597},[954],[15,2599,2601],{"className":2600},[927],[15,2602,2604],{"className":2603,"style":962},[931],[15,2605],{},[15,2607,42],{"className":2608},[73],[15,2610],{"className":2611,"style":78},[77],[15,2613,2615,2618],{"className":2614},[67],[15,2616,2458],{"className":2617,"style":2570},[67,68],[15,2619,2621],{"className":2620},[918],[15,2622,2624,2644],{"className":2623},[922,923],[15,2625,2627,2641],{"className":2626},[927],[15,2628,2630],{"className":2629,"style":1496},[931],[15,2631,2632,2635],{"style":2585},[15,2633],{"className":2634,"style":940},[939],[15,2636,2638],{"className":2637},[944,945,946,947],[15,2639,1427],{"className":2640},[67,947],[15,2642,955],{"className":2643},[954],[15,2645,2647],{"className":2646},[927],[15,2648,2650],{"className":2649,"style":962},[931],[15,2651],{},[15,2653,42],{"className":2654},[73],[15,2656],{"className":2657,"style":78},[77],[15,2659,1432],{"className":2660},[1529],[15,2662],{"className":2663,"style":78},[77],[15,2665,42],{"className":2666},[73],[15,2668],{"className":2669,"style":78},[77],[15,2671,2673,2676],{"className":2672},[67],[15,2674,2458],{"className":2675,"style":2570},[67,68],[15,2677,2679],{"className":2678},[918],[15,2680,2682,2704],{"className":2681},[922,923],[15,2683,2685,2701],{"className":2684},[927],[15,2686,2689],{"className":2687,"style":2688},[931],"height:0.3361em;",[15,2690,2691,2694],{"style":2585},[15,2692],{"className":2693,"style":940},[939],[15,2695,2697],{"className":2696},[944,945,946,947],[15,2698,2482],{"className":2699,"style":2700},[67,68,947],"margin-right:0.0315em;",[15,2702,955],{"className":2703},[954],[15,2705,2707],{"className":2706},[927],[15,2708,2710],{"className":2709,"style":962},[931],[15,2711],{},[15,2713],{"className":2714,"style":199},[77],[15,2716,602],{"className":2717},[203],[15,2719],{"className":2720,"style":199},[77],[15,2722,2724,2727,2767],{"className":2723},[58],[15,2725],{"className":2726,"style":1711},[62],[15,2728,2730,2733],{"className":2729},[67],[15,2731,1343],{"className":2732,"style":82},[67,68],[15,2734,2736],{"className":2735},[918],[15,2737,2739,2759],{"className":2738},[922,923],[15,2740,2742,2756],{"className":2741},[927],[15,2743,2745],{"className":2744,"style":1733},[931],[15,2746,2747,2750],{"style":1499},[15,2748],{"className":2749,"style":940},[939],[15,2751,2753],{"className":2752},[944,945,946,947],[15,2754,1691],{"className":2755,"style":1791},[67,68,947],[15,2757,955],{"className":2758},[954],[15,2760,2762],{"className":2761},[927],[15,2763,2765],{"className":2764,"style":1801},[931],[15,2766],{},[15,2768,2493],{"className":2769},[148],"，使得对每个 ",[15,2772,2774,2788],{"className":2773,"translate":19},[18],[15,2775,2777],{"className":2776},[23],[25,2778,2779],{"xmlns":27},[29,2780,2781,2786],{},[32,2782,2783],{},[35,2784,2785],{},"t",[47,2787,2785],{"encoding":49},[15,2789,2791],{"className":2790,"ariaHidden":41},[54],[15,2792,2794,2798],{"className":2793},[58],[15,2795],{"className":2796,"style":2797},[62],"height:0.6151em;",[15,2799,2785],{"className":2800},[67,68],[15,2802,2804,2822],{"className":2803,"translate":19},[18],[15,2805,2807],{"className":2806},[23],[25,2808,2809],{"xmlns":27},[29,2810,2811,2819],{},[32,2812,2813],{},[863,2814,2815,2817],{},[35,2816,2458],{},[35,2818,2785],{},[47,2820,2821],{"encoding":49},"U_t",[15,2823,2825],{"className":2824,"ariaHidden":41},[54],[15,2826,2828,2831],{"className":2827},[58],[15,2829],{"className":2830,"style":1865},[62],[15,2832,2834,2837],{"className":2833},[67],[15,2835,2458],{"className":2836,"style":2570},[67,68],[15,2838,2840],{"className":2839},[918],[15,2841,2843,2864],{"className":2842},[922,923],[15,2844,2846,2861],{"className":2845},[927],[15,2847,2850],{"className":2848,"style":2849},[931],"height:0.2806em;",[15,2851,2852,2855],{"style":2585},[15,2853],{"className":2854,"style":940},[939],[15,2856,2858],{"className":2857},[944,945,946,947],[15,2859,2785],{"className":2860},[67,68,947],[15,2862,955],{"className":2863},[954],[15,2865,2867],{"className":2866},[927],[15,2868,2870],{"className":2869,"style":962},[931],[15,2871],{},[15,2873,2875,2900],{"className":2874,"translate":19},[18],[15,2876,2878],{"className":2877},[23],[25,2879,2880],{"xmlns":27},[29,2881,2882,2897],{},[32,2883,2884],{},[863,2885,2886,2888],{},[35,2887,2458],{},[32,2889,2890,2892,2895],{},[35,2891,2785],{},[39,2893,2894],{},"+",[1425,2896,1427],{},[47,2898,2899],{"encoding":49},"U_{t+1}",[15,2901,2903],{"className":2902,"ariaHidden":41},[54],[15,2904,2906,2910],{"className":2905},[58],[15,2907],{"className":2908,"style":2909},[62],"height:0.8917em;vertical-align:-0.2083em;",[15,2911,2913,2916],{"className":2912},[67],[15,2914,2458],{"className":2915,"style":2570},[67,68],[15,2917,2919],{"className":2918},[918],[15,2920,2922,2951],{"className":2921},[922,923],[15,2923,2925,2948],{"className":2924},[927],[15,2926,2928],{"className":2927,"style":1496},[931],[15,2929,2930,2933],{"style":2585},[15,2931],{"className":2932,"style":940},[939],[15,2934,2936],{"className":2935},[944,945,946,947],[15,2937,2939,2942,2945],{"className":2938},[67,947],[15,2940,2785],{"className":2941},[67,68,947],[15,2943,2894],{"className":2944},[1648,947],[15,2946,1427],{"className":2947},[67,947],[15,2949,955],{"className":2950},[954],[15,2952,2954],{"className":2953},[927],[15,2955,2958],{"className":2956,"style":2957},[931],"height:0.2083em;",[15,2959],{}," 之间存在一条边（不论方向）。若路径上所有边的方向都与路径前进方向一致，称为",[305,2962,2963],{},"有向路径","；若 ",[15,2966,2968,2994],{"className":2967,"translate":19},[18],[15,2969,2971],{"className":2970},[23],[25,2972,2973],{"xmlns":27},[29,2974,2975,2991],{},[32,2976,2977,2983,2985],{},[863,2978,2979,2981],{},[35,2980,2458],{},[1425,2982,2461],{},[39,2984,602],{},[863,2986,2987,2989],{},[35,2988,2458],{},[35,2990,2482],{},[47,2992,2993],{"encoding":49},"U_0 = U_k",[15,2995,2997,3052],{"className":2996,"ariaHidden":41},[54],[15,2998,3000,3003,3043,3046,3049],{"className":2999},[58],[15,3001],{"className":3002,"style":1865},[62],[15,3004,3006,3009],{"className":3005},[67],[15,3007,2458],{"className":3008,"style":2570},[67,68],[15,3010,3012],{"className":3011},[918],[15,3013,3015,3035],{"className":3014},[922,923],[15,3016,3018,3032],{"className":3017},[927],[15,3019,3021],{"className":3020,"style":1496},[931],[15,3022,3023,3026],{"style":2585},[15,3024],{"className":3025,"style":940},[939],[15,3027,3029],{"className":3028},[944,945,946,947],[15,3030,2461],{"className":3031},[67,947],[15,3033,955],{"className":3034},[954],[15,3036,3038],{"className":3037},[927],[15,3039,3041],{"className":3040,"style":962},[931],[15,3042],{},[15,3044],{"className":3045,"style":199},[77],[15,3047,602],{"className":3048},[203],[15,3050],{"className":3051,"style":199},[77],[15,3053,3055,3058],{"className":3054},[58],[15,3056],{"className":3057,"style":1865},[62],[15,3059,3061,3064],{"className":3060},[67],[15,3062,2458],{"className":3063,"style":2570},[67,68],[15,3065,3067],{"className":3066},[918],[15,3068,3070,3090],{"className":3069},[922,923],[15,3071,3073,3087],{"className":3072},[927],[15,3074,3076],{"className":3075,"style":2688},[931],[15,3077,3078,3081],{"style":2585},[15,3079],{"className":3080,"style":940},[939],[15,3082,3084],{"className":3083},[944,945,946,947],[15,3085,2482],{"className":3086,"style":2700},[67,68,947],[15,3088,955],{"className":3089},[954],[15,3091,3093],{"className":3092},[927],[15,3094,3096],{"className":3095,"style":962},[931],[15,3097],{}," 且 ",[15,3100,3102,3121],{"className":3101,"translate":19},[18],[15,3103,3105],{"className":3104},[23],[25,3106,3107],{"xmlns":27},[29,3108,3109,3118],{},[32,3110,3111,3113,3116],{},[35,3112,2482],{},[39,3114,3115],{},"≥",[1425,3117,1427],{},[47,3119,3120],{"encoding":49},"k \\geq 1",[15,3122,3124,3143],{"className":3123,"ariaHidden":41},[54],[15,3125,3127,3131,3134,3137,3140],{"className":3126},[58],[15,3128],{"className":3129,"style":3130},[62],"height:0.8304em;vertical-align:-0.136em;",[15,3132,2482],{"className":3133,"style":2700},[67,68],[15,3135],{"className":3136,"style":199},[77],[15,3138,3115],{"className":3139},[203],[15,3141],{"className":3142,"style":199},[77],[15,3144,3146,3150],{"className":3145},[58],[15,3147],{"className":3148,"style":3149},[62],"height:0.6444em;",[15,3151,1427],{"className":3152},[67],"，则称为一个",[305,3155,3156],{},"环（cycle）",[1314,3158,3159],{},[11,3160,3161,3164,3165,3193,3194,3222],{},[305,3162,3163],{},"定义 1.3（有向无环图，DAG）"," 若图 ",[15,3166,3168,3181],{"className":3167,"translate":19},[18],[15,3169,3171],{"className":3170},[23],[25,3172,3173],{"xmlns":27},[29,3174,3175,3179],{},[32,3176,3177],{},[35,3178,1336],{},[47,3180,1336],{"encoding":49},[15,3182,3184],{"className":3183,"ariaHidden":41},[54],[15,3185,3187,3190],{"className":3186},[58],[15,3188],{"className":3189,"style":299},[62],[15,3191,1336],{"className":3192},[67,68]," 中不存在任何环，则称 ",[15,3195,3197,3210],{"className":3196,"translate":19},[18],[15,3198,3200],{"className":3199},[23],[25,3201,3202],{"xmlns":27},[29,3203,3204,3208],{},[32,3205,3206],{},[35,3207,1336],{},[47,3209,1336],{"encoding":49},[15,3211,3213],{"className":3212,"ariaHidden":41},[54],[15,3214,3216,3219],{"className":3215},[58],[15,3217],{"className":3218,"style":299},[62],[15,3220,1336],{"className":3221},[67,68]," 为有向无环图。",[1314,3224,3225],{},[11,3226,3227,3230,3231,3305,3306,811,3461,3530,3531,2104,3600,3603,3604,3673,3674,3743],{},[305,3228,3229],{},"定义 1.4（因果图）"," 一个因果图是一个 DAG ",[15,3232,3234,3260],{"className":3233,"translate":19},[18],[15,3235,3237],{"className":3236},[23],[25,3238,3239],{"xmlns":27},[29,3240,3241,3257],{},[32,3242,3243,3245,3247,3249,3251,3253,3255],{},[35,3244,1336],{},[39,3246,602],{},[39,3248,102],{"stretchy":101},[35,3250,1343],{},[39,3252,42],{"separator":41},[35,3254,1348],{},[39,3256,111],{"stretchy":101},[47,3258,3259],{"encoding":49},"G=(V,E)",[15,3261,3263,3281],{"className":3262,"ariaHidden":41},[54],[15,3264,3266,3269,3272,3275,3278],{"className":3265},[58],[15,3267],{"className":3268,"style":299},[62],[15,3270,1336],{"className":3271},[67,68],[15,3273],{"className":3274,"style":199},[77],[15,3276,602],{"className":3277},[203],[15,3279],{"className":3280,"style":199},[77],[15,3282,3284,3287,3290,3293,3296,3299,3302],{"className":3283},[58],[15,3285],{"className":3286,"style":124},[62],[15,3288,102],{"className":3289},[132],[15,3291,1343],{"className":3292,"style":82},[67,68],[15,3294,42],{"className":3295},[73],[15,3297],{"className":3298,"style":78},[77],[15,3300,1348],{"className":3301,"style":1396},[67,68],[15,3303,111],{"className":3304},[148],"，附加如下语义解释：对任意 ",[15,3307,3309,3342],{"className":3308,"translate":19},[18],[15,3310,3312],{"className":3311},[23],[25,3313,3314],{"xmlns":27},[29,3315,3316,3340],{},[32,3317,3318,3320,3326,3328,3334,3336,3338],{},[39,3319,102],{"stretchy":101},[863,3321,3322,3324],{},[35,3323,1343],{},[35,3325,1682],{},[39,3327,42],{"separator":41},[863,3329,3330,3332],{},[35,3331,1343],{},[35,3333,1691],{},[39,3335,111],{"stretchy":101},[39,3337,1696],{},[35,3339,1348],{},[47,3341,1701],{"encoding":49},[15,3343,3345,3452],{"className":3344,"ariaHidden":41},[54],[15,3346,3348,3351,3354,3394,3397,3400,3440,3443,3446,3449],{"className":3347},[58],[15,3349],{"className":3350,"style":1711},[62],[15,3352,102],{"className":3353},[132],[15,3355,3357,3360],{"className":3356},[67],[15,3358,1343],{"className":3359,"style":82},[67,68],[15,3361,3363],{"className":3362},[918],[15,3364,3366,3386],{"className":3365},[922,923],[15,3367,3369,3383],{"className":3368},[927],[15,3370,3372],{"className":3371,"style":1733},[931],[15,3373,3374,3377],{"style":1499},[15,3375],{"className":3376,"style":940},[939],[15,3378,3380],{"className":3379},[944,945,946,947],[15,3381,1682],{"className":3382},[67,68,947],[15,3384,955],{"className":3385},[954],[15,3387,3389],{"className":3388},[927],[15,3390,3392],{"className":3391,"style":962},[931],[15,3393],{},[15,3395,42],{"className":3396},[73],[15,3398],{"className":3399,"style":78},[77],[15,3401,3403,3406],{"className":3402},[67],[15,3404,1343],{"className":3405,"style":82},[67,68],[15,3407,3409],{"className":3408},[918],[15,3410,3412,3432],{"className":3411},[922,923],[15,3413,3415,3429],{"className":3414},[927],[15,3416,3418],{"className":3417,"style":1733},[931],[15,3419,3420,3423],{"style":1499},[15,3421],{"className":3422,"style":940},[939],[15,3424,3426],{"className":3425},[944,945,946,947],[15,3427,1691],{"className":3428,"style":1791},[67,68,947],[15,3430,955],{"className":3431},[954],[15,3433,3435],{"className":3434},[927],[15,3436,3438],{"className":3437,"style":1801},[931],[15,3439],{},[15,3441,111],{"className":3442},[148],[15,3444],{"className":3445,"style":199},[77],[15,3447,1696],{"className":3448},[203],[15,3450],{"className":3451,"style":199},[77],[15,3453,3455,3458],{"className":3454},[58],[15,3456],{"className":3457,"style":299},[62],[15,3459,1348],{"className":3460,"style":1396},[67,68],[15,3462,3464,3481],{"className":3463,"translate":19},[18],[15,3465,3467],{"className":3466},[23],[25,3468,3469],{"xmlns":27},[29,3470,3471,3479],{},[32,3472,3473],{},[863,3474,3475,3477],{},[35,3476,1343],{},[35,3478,1682],{},[47,3480,1983],{"encoding":49},[15,3482,3484],{"className":3483,"ariaHidden":41},[54],[15,3485,3487,3490],{"className":3486},[58],[15,3488],{"className":3489,"style":1865},[62],[15,3491,3493,3496],{"className":3492},[67],[15,3494,1343],{"className":3495,"style":82},[67,68],[15,3497,3499],{"className":3498},[918],[15,3500,3502,3522],{"className":3501},[922,923],[15,3503,3505,3519],{"className":3504},[927],[15,3506,3508],{"className":3507,"style":1733},[931],[15,3509,3510,3513],{"style":1499},[15,3511],{"className":3512,"style":940},[939],[15,3514,3516],{"className":3515},[944,945,946,947],[15,3517,1682],{"className":3518},[67,68,947],[15,3520,955],{"className":3521},[954],[15,3523,3525],{"className":3524},[927],[15,3526,3528],{"className":3527,"style":962},[931],[15,3529],{}," 被假设为 ",[15,3532,3534,3551],{"className":3533,"translate":19},[18],[15,3535,3537],{"className":3536},[23],[25,3538,3539],{"xmlns":27},[29,3540,3541,3549],{},[32,3542,3543],{},[863,3544,3545,3547],{},[35,3546,1343],{},[35,3548,1691],{},[47,3550,2054],{"encoding":49},[15,3552,3554],{"className":3553,"ariaHidden":41},[54],[15,3555,3557,3560],{"className":3556},[58],[15,3558],{"className":3559,"style":1921},[62],[15,3561,3563,3566],{"className":3562},[67],[15,3564,1343],{"className":3565,"style":82},[67,68],[15,3567,3569],{"className":3568},[918],[15,3570,3572,3592],{"className":3571},[922,923],[15,3573,3575,3589],{"className":3574},[927],[15,3576,3578],{"className":3577,"style":1733},[931],[15,3579,3580,3583],{"style":1499},[15,3581],{"className":3582,"style":940},[939],[15,3584,3586],{"className":3585},[944,945,946,947],[15,3587,1691],{"className":3588,"style":1791},[67,68,947],[15,3590,955],{"className":3591},[954],[15,3593,3595],{"className":3594},[927],[15,3596,3598],{"className":3597,"style":1801},[931],[15,3599],{},[305,3601,3602],{},"直接原因（direct cause）","——即存在至少一种对其余变量的取值组合，使得改变 ",[15,3605,3607,3624],{"className":3606,"translate":19},[18],[15,3608,3610],{"className":3609},[23],[25,3611,3612],{"xmlns":27},[29,3613,3614,3622],{},[32,3615,3616],{},[863,3617,3618,3620],{},[35,3619,1343],{},[35,3621,1682],{},[47,3623,1983],{"encoding":49},[15,3625,3627],{"className":3626,"ariaHidden":41},[54],[15,3628,3630,3633],{"className":3629},[58],[15,3631],{"className":3632,"style":1865},[62],[15,3634,3636,3639],{"className":3635},[67],[15,3637,1343],{"className":3638,"style":82},[67,68],[15,3640,3642],{"className":3641},[918],[15,3643,3645,3665],{"className":3644},[922,923],[15,3646,3648,3662],{"className":3647},[927],[15,3649,3651],{"className":3650,"style":1733},[931],[15,3652,3653,3656],{"style":1499},[15,3654],{"className":3655,"style":940},[939],[15,3657,3659],{"className":3658},[944,945,946,947],[15,3660,1682],{"className":3661},[67,68,947],[15,3663,955],{"className":3664},[954],[15,3666,3668],{"className":3667},[927],[15,3669,3671],{"className":3670,"style":962},[931],[15,3672],{}," 会改变 ",[15,3675,3677,3694],{"className":3676,"translate":19},[18],[15,3678,3680],{"className":3679},[23],[25,3681,3682],{"xmlns":27},[29,3683,3684,3692],{},[32,3685,3686],{},[863,3687,3688,3690],{},[35,3689,1343],{},[35,3691,1691],{},[47,3693,2054],{"encoding":49},[15,3695,3697],{"className":3696,"ariaHidden":41},[54],[15,3698,3700,3703],{"className":3699},[58],[15,3701],{"className":3702,"style":1921},[62],[15,3704,3706,3709],{"className":3705},[67],[15,3707,1343],{"className":3708,"style":82},[67,68],[15,3710,3712],{"className":3711},[918],[15,3713,3715,3735],{"className":3714},[922,923],[15,3716,3718,3732],{"className":3717},[927],[15,3719,3721],{"className":3720,"style":1733},[931],[15,3722,3723,3726],{"style":1499},[15,3724],{"className":3725,"style":940},[939],[15,3727,3729],{"className":3728},[944,945,946,947],[15,3730,1691],{"className":3731,"style":1791},[67,68,947],[15,3733,955],{"className":3734},[954],[15,3736,3738],{"className":3737},[927],[15,3739,3741],{"className":3740,"style":1801},[931],[15,3742],{}," 的取值或分布。",[11,3745,3746,3747,3750],{},"需要强调：因果图的每一条边都是一个",[305,3748,3749],{},"不可从数据中验证的结构性假设","（除非借助特定的因果发现算法与额外假设），它来自领域知识、实验设计或时间先后关系等外部信息。这一点是因果图区别于「从数据拟合出的图模型」的本质特征。",[1314,3752,3753,4117,4128],{},[11,3754,3755,3758,3759,3868,3869,3897,3898,4112,4113,4116],{},[305,3756,3757],{},"例 1.1"," 设变量集合 ",[15,3760,3762,3801],{"className":3761,"translate":19},[18],[15,3763,3765],{"className":3764},[23],[25,3766,3767],{"xmlns":27},[29,3768,3769,3798],{},[32,3770,3771,3773,3775,3777,3780,3782,3785,3787,3789,3791,3793,3796],{},[35,3772,1343],{},[39,3774,602],{},[39,3776,1419],{"stretchy":101},[35,3778,3779],{},"S",[39,3781,42],{"separator":41},[35,3783,3784],{},"R",[39,3786,42],{"separator":41},[35,3788,3779],{},[35,3790,11],{},[39,3792,42],{"separator":41},[35,3794,3795],{},"W",[39,3797,1444],{"stretchy":101},[47,3799,3800],{"encoding":49},"V = \\{S, R, Sp, W\\}",[15,3802,3804,3822],{"className":3803,"ariaHidden":41},[54],[15,3805,3807,3810,3813,3816,3819],{"className":3806},[58],[15,3808],{"className":3809,"style":299},[62],[15,3811,1343],{"className":3812,"style":82},[67,68],[15,3814],{"className":3815,"style":199},[77],[15,3817,602],{"className":3818},[203],[15,3820],{"className":3821,"style":199},[77],[15,3823,3825,3828,3831,3834,3837,3840,3844,3847,3850,3853,3856,3859,3862,3865],{"className":3824},[58],[15,3826],{"className":3827,"style":124},[62],[15,3829,1419],{"className":3830},[132],[15,3832,3779],{"className":3833,"style":1396},[67,68],[15,3835,42],{"className":3836},[73],[15,3838],{"className":3839,"style":78},[77],[15,3841,3784],{"className":3842,"style":3843},[67,68],"margin-right:0.0077em;",[15,3845,42],{"className":3846},[73],[15,3848],{"className":3849,"style":78},[77],[15,3851,3779],{"className":3852,"style":1396},[67,68],[15,3854,11],{"className":3855},[67,68],[15,3857,42],{"className":3858},[73],[15,3860],{"className":3861,"style":78},[77],[15,3863,3795],{"className":3864,"style":128},[67,68],[15,3866,1444],{"className":3867},[148],"，分别代表季节（Season）、下雨（Rain）、洒水器开启（Sprinkler）、草坪潮湿（WetGrass）。因果图 ",[15,3870,3872,3885],{"className":3871,"translate":19},[18],[15,3873,3875],{"className":3874},[23],[25,3876,3877],{"xmlns":27},[29,3878,3879,3883],{},[32,3880,3881],{},[35,3882,1336],{},[47,3884,1336],{"encoding":49},[15,3886,3888],{"className":3887,"ariaHidden":41},[54],[15,3889,3891,3894],{"className":3890},[58],[15,3892],{"className":3893,"style":299},[62],[15,3895,1336],{"className":3896},[67,68]," 定义为：\n",[15,3899,3901,3962],{"className":3900,"translate":19},[18],[15,3902,3904],{"className":3903},[23],[25,3905,3906],{"xmlns":27},[29,3907,3908,3959],{},[32,3909,3910,3912,3914,3916,3918,3920,3922,3924,3927,3929,3931,3933,3935,3937,3939,3941,3943,3945,3947,3949,3951,3953,3955,3957],{},[35,3911,1348],{},[39,3913,602],{},[39,3915,1419],{"stretchy":101},[35,3917,3779],{},[39,3919,1846],{},[35,3921,3784],{},[39,3923,42],{"separator":41},[238,3925,3926],{}," ",[35,3928,3779],{},[39,3930,1846],{},[35,3932,3779],{},[35,3934,11],{},[39,3936,42],{"separator":41},[238,3938,3926],{},[35,3940,3784],{},[39,3942,1846],{},[35,3944,3795],{},[39,3946,42],{"separator":41},[238,3948,3926],{},[35,3950,3779],{},[35,3952,11],{},[39,3954,1846],{},[35,3956,3795],{},[39,3958,1444],{"stretchy":101},[47,3960,3961],{"encoding":49},"E = \\{S \\to R,\\ S \\to Sp,\\ R \\to W,\\ Sp \\to W\\}",[15,3963,3965,3983,4004,4034,4067,4100],{"className":3964,"ariaHidden":41},[54],[15,3966,3968,3971,3974,3977,3980],{"className":3967},[58],[15,3969],{"className":3970,"style":299},[62],[15,3972,1348],{"className":3973,"style":1396},[67,68],[15,3975],{"className":3976,"style":199},[77],[15,3978,602],{"className":3979},[203],[15,3981],{"className":3982,"style":199},[77],[15,3984,3986,3989,3992,3995,3998,4001],{"className":3985},[58],[15,3987],{"className":3988,"style":124},[62],[15,3990,1419],{"className":3991},[132],[15,3993,3779],{"className":3994,"style":1396},[67,68],[15,3996],{"className":3997,"style":199},[77],[15,3999,1846],{"className":4000},[203],[15,4002],{"className":4003,"style":199},[77],[15,4005,4007,4010,4013,4016,4019,4022,4025,4028,4031],{"className":4006},[58],[15,4008],{"className":4009,"style":63},[62],[15,4011,3784],{"className":4012,"style":3843},[67,68],[15,4014,42],{"className":4015},[73],[15,4017,3926],{"className":4018},[77],[15,4020],{"className":4021,"style":78},[77],[15,4023,3779],{"className":4024,"style":1396},[67,68],[15,4026],{"className":4027,"style":199},[77],[15,4029,1846],{"className":4030},[203],[15,4032],{"className":4033,"style":199},[77],[15,4035,4037,4040,4043,4046,4049,4052,4055,4058,4061,4064],{"className":4036},[58],[15,4038],{"className":4039,"style":63},[62],[15,4041,3779],{"className":4042,"style":1396},[67,68],[15,4044,11],{"className":4045},[67,68],[15,4047,42],{"className":4048},[73],[15,4050,3926],{"className":4051},[77],[15,4053],{"className":4054,"style":78},[77],[15,4056,3784],{"className":4057,"style":3843},[67,68],[15,4059],{"className":4060,"style":199},[77],[15,4062,1846],{"className":4063},[203],[15,4065],{"className":4066,"style":199},[77],[15,4068,4070,4073,4076,4079,4082,4085,4088,4091,4094,4097],{"className":4069},[58],[15,4071],{"className":4072,"style":63},[62],[15,4074,3795],{"className":4075,"style":128},[67,68],[15,4077,42],{"className":4078},[73],[15,4080,3926],{"className":4081},[77],[15,4083],{"className":4084,"style":78},[77],[15,4086,3779],{"className":4087,"style":1396},[67,68],[15,4089,11],{"className":4090},[67,68],[15,4092],{"className":4093,"style":199},[77],[15,4095,1846],{"className":4096},[203],[15,4098],{"className":4099,"style":199},[77],[15,4101,4103,4106,4109],{"className":4102},[58],[15,4104],{"className":4105,"style":124},[62],[15,4107,3795],{"className":4108,"style":128},[67,68],[15,4110,1444],{"className":4111},[148],"\n此图断言：季节直接影响降雨与洒水器的开启概率；降雨与洒水器开启都直接影响草坪是否潮湿；而季节对草坪潮湿的影响完全通过降雨与洒水器这两条中介路径传递，不存在季节直接作用于草坪的边。这后一点——",[305,4114,4115],{},"某条边不存在","——与图中已画出的边同样重要，是因果图的核心信息量所在。整张图的形状如下：",[4118,4119,4124],"pre",{"className":4120,"code":4122,"language":4123},[4121],"language-text","           ┌──────────→ R ──────────┐\n           │                        ↓\n      S ───┤                        W\n           │                        ↑\n           └──────────→ Sp ─────────┘\n","text",[4125,4126,4122],"code",{"__ignoreMap":4127},"",[11,4129,4130,4131,4159,4160,4188],{},"其中季节 ",[15,4132,4134,4147],{"className":4133,"translate":19},[18],[15,4135,4137],{"className":4136},[23],[25,4138,4139],{"xmlns":27},[29,4140,4141,4145],{},[32,4142,4143],{},[35,4144,3779],{},[47,4146,3779],{"encoding":49},[15,4148,4150],{"className":4149,"ariaHidden":41},[54],[15,4151,4153,4156],{"className":4152},[58],[15,4154],{"className":4155,"style":299},[62],[15,4157,3779],{"className":4158,"style":1396},[67,68]," 是整套机制的源头，草坪潮湿 ",[15,4161,4163,4176],{"className":4162,"translate":19},[18],[15,4164,4166],{"className":4165},[23],[25,4167,4168],{"xmlns":27},[29,4169,4170,4174],{},[32,4171,4172],{},[35,4173,3795],{},[47,4175,3795],{"encoding":49},[15,4177,4179],{"className":4178,"ariaHidden":41},[54],[15,4180,4182,4185],{"className":4181},[58],[15,4183],{"className":4184,"style":299},[62],[15,4186,3795],{"className":4187,"style":128},[67,68]," 是两条中介路径的汇合点。",[1309,4190,4192],{"id":4191},"_12-三种基本连接结构及其统计含义","1.2 三种基本连接结构及其统计含义",[11,4194,4195,4196,811,4253,4281,4282,4323],{},"任意路径都可以分解为若干长度为 2 的子路径（即三节点结构），因此理解全图的依赖关系，可以归约为理解三种基本三节点结构。设三个节点 ",[15,4197,4199,4222],{"className":4198,"translate":19},[18],[15,4200,4202],{"className":4201},[23],[25,4203,4204],{"xmlns":27},[29,4205,4206,4219],{},[32,4207,4208,4210,4212,4215,4217],{},[35,4209,37],{},[39,4211,42],{"separator":41},[35,4213,4214],{},"Z",[39,4216,42],{"separator":41},[35,4218,45],{},[47,4220,4221],{"encoding":49},"X, Z, Y",[15,4223,4225],{"className":4224,"ariaHidden":41},[54],[15,4226,4228,4231,4234,4237,4240,4244,4247,4250],{"className":4227},[58],[15,4229],{"className":4230,"style":63},[62],[15,4232,37],{"className":4233,"style":69},[67,68],[15,4235,42],{"className":4236},[73],[15,4238],{"className":4239,"style":78},[77],[15,4241,4214],{"className":4242,"style":4243},[67,68],"margin-right:0.0715em;",[15,4245,42],{"className":4246},[73],[15,4248],{"className":4249,"style":78},[77],[15,4251,45],{"className":4252,"style":82},[67,68],[15,4254,4256,4269],{"className":4255,"translate":19},[18],[15,4257,4259],{"className":4258},[23],[25,4260,4261],{"xmlns":27},[29,4262,4263,4267],{},[32,4264,4265],{},[35,4266,4214],{},[47,4268,4214],{"encoding":49},[15,4270,4272],{"className":4271,"ariaHidden":41},[54],[15,4273,4275,4278],{"className":4274},[58],[15,4276],{"className":4277,"style":299},[62],[15,4279,4214],{"className":4280,"style":4243},[67,68]," 位于 ",[15,4283,4285,4302],{"className":4284,"translate":19},[18],[15,4286,4288],{"className":4287},[23],[25,4289,4290],{"xmlns":27},[29,4291,4292,4300],{},[32,4293,4294,4296,4298],{},[35,4295,37],{},[39,4297,42],{"separator":41},[35,4299,45],{},[47,4301,50],{"encoding":49},[15,4303,4305],{"className":4304,"ariaHidden":41},[54],[15,4306,4308,4311,4314,4317,4320],{"className":4307},[58],[15,4309],{"className":4310,"style":63},[62],[15,4312,37],{"className":4313,"style":69},[67,68],[15,4315,42],{"className":4316},[73],[15,4318],{"className":4319,"style":78},[77],[15,4321,45],{"className":4322,"style":82},[67,68]," 之间的路径上。三种结构图示如下：",[4118,4325,4328],{"className":4326,"code":4327,"language":4123},[4121],"   链      X ──→ Z ──→ Y\n\n   叉      X ←── Z ──→ Y\n\n   对撞    X ──→ Z ←── Y\n",[4125,4329,4327],{"__ignoreMap":4127},[11,4331,4332,4335,4336],{},[305,4333,4334],{},"结构一：链（Chain）"," ",[15,4337,4339,4361],{"className":4338,"translate":19},[18],[15,4340,4342],{"className":4341},[23],[25,4343,4344],{"xmlns":27},[29,4345,4346,4358],{},[32,4347,4348,4350,4352,4354,4356],{},[35,4349,37],{},[39,4351,1846],{},[35,4353,4214],{},[39,4355,1846],{},[35,4357,45],{},[47,4359,4360],{"encoding":49},"X \\to Z \\to Y",[15,4362,4364,4382,4400],{"className":4363,"ariaHidden":41},[54],[15,4365,4367,4370,4373,4376,4379],{"className":4366},[58],[15,4368],{"className":4369,"style":299},[62],[15,4371,37],{"className":4372,"style":69},[67,68],[15,4374],{"className":4375,"style":199},[77],[15,4377,1846],{"className":4378},[203],[15,4380],{"className":4381,"style":199},[77],[15,4383,4385,4388,4391,4394,4397],{"className":4384},[58],[15,4386],{"className":4387,"style":299},[62],[15,4389,4214],{"className":4390,"style":4243},[67,68],[15,4392],{"className":4393,"style":199},[77],[15,4395,1846],{"className":4396},[203],[15,4398],{"className":4399,"style":199},[77],[15,4401,4403,4406],{"className":4402},[58],[15,4404],{"className":4405,"style":299},[62],[15,4407,45],{"className":4408,"style":82},[67,68],[1314,4410,4411],{},[11,4412,4413,4416,4417,4533,4534,4633,4634,4662],{},[305,4414,4415],{},"命题 1.1"," 在链式结构下，若结构方程满足一般位置条件（无退化取消），则 ",[15,4418,4420,4447],{"className":4419,"translate":19},[18],[15,4421,4423],{"className":4422},[23],[25,4424,4425],{"xmlns":27},[29,4426,4427,4444],{},[32,4428,4429,4431,4434,4436,4438,4440,4442],{},[35,4430,37],{},[39,4432,4433],{},"⊥̸",[238,4435,240],{},[238,4437,240],{},[238,4439,240],{},[39,4441,236],{},[35,4443,45],{},[47,4445,4446],{"encoding":49},"X \\not\\perp\\!\\!\\!\\perp Y",[15,4448,4450,4512,4524],{"className":4449,"ariaHidden":41},[54],[15,4451,4453,4457,4460,4463,4496,4500,4503,4506,4509],{"className":4452},[58],[15,4454],{"className":4455,"style":4456},[62],"height:0.8889em;vertical-align:-0.1944em;",[15,4458,37],{"className":4459,"style":69},[67,68],[15,4461],{"className":4462,"style":199},[77],[15,4464,4466],{"className":4465},[203],[15,4467,4470],{"className":4468},[67,4469],"vbox",[15,4471,4474],{"className":4472},[4473],"thinbox",[15,4475,4478,4481,4492],{"className":4476},[4477],"rlap",[15,4479],{"className":4480,"style":4456},[62],[15,4482,4485],{"className":4483},[4484],"inner",[15,4486,4488],{"className":4487},[67],[15,4489,4491],{"className":4490},[203],"",[15,4493],{"className":4494},[4495],"fix",[15,4497],{"className":4498},[77,4499],"nobreak",[15,4501,236],{"className":4502},[203],[15,4504],{"className":4505,"style":274},[77],[15,4507],{"className":4508,"style":274},[77],[15,4510],{"className":4511,"style":274},[77],[15,4513,4515,4518,4521],{"className":4514},[58],[15,4516],{"className":4517,"style":261},[62],[15,4519,236],{"className":4520},[203],[15,4522],{"className":4523,"style":199},[77],[15,4525,4527,4530],{"className":4526},[58],[15,4528],{"className":4529,"style":299},[62],[15,4531,45],{"className":4532,"style":82},[67,68],"（边际不独立），但 ",[15,4535,4537,4567],{"className":4536,"translate":19},[18],[15,4538,4540],{"className":4539},[23],[25,4541,4542],{"xmlns":27},[29,4543,4544,4564],{},[32,4545,4546,4548,4550,4552,4554,4556,4558,4560,4562],{},[35,4547,37],{},[39,4549,236],{},[238,4551,240],{},[238,4553,240],{},[238,4555,240],{},[39,4557,236],{},[35,4559,45],{},[39,4561,170],{},[35,4563,4214],{},[47,4565,4566],{"encoding":49},"X \\perp\\!\\!\\!\\perp Y \\mid Z",[15,4568,4570,4594,4606,4624],{"className":4569,"ariaHidden":41},[54],[15,4571,4573,4576,4579,4582,4585,4588,4591],{"className":4572},[58],[15,4574],{"className":4575,"style":261},[62],[15,4577,37],{"className":4578,"style":69},[67,68],[15,4580],{"className":4581,"style":199},[77],[15,4583,236],{"className":4584},[203],[15,4586],{"className":4587,"style":274},[77],[15,4589],{"className":4590,"style":274},[77],[15,4592],{"className":4593,"style":274},[77],[15,4595,4597,4600,4603],{"className":4596},[58],[15,4598],{"className":4599,"style":261},[62],[15,4601,236],{"className":4602},[203],[15,4604],{"className":4605,"style":199},[77],[15,4607,4609,4612,4615,4618,4621],{"className":4608},[58],[15,4610],{"className":4611,"style":124},[62],[15,4613,45],{"className":4614,"style":82},[67,68],[15,4616],{"className":4617,"style":199},[77],[15,4619,170],{"className":4620},[203],[15,4622],{"className":4623,"style":199},[77],[15,4625,4627,4630],{"className":4626},[58],[15,4628],{"className":4629,"style":299},[62],[15,4631,4214],{"className":4632,"style":4243},[67,68],"（给定 ",[15,4635,4637,4650],{"className":4636,"translate":19},[18],[15,4638,4640],{"className":4639},[23],[25,4641,4642],{"xmlns":27},[29,4643,4644,4648],{},[32,4645,4646],{},[35,4647,4214],{},[47,4649,4214],{"encoding":49},[15,4651,4653],{"className":4652,"ariaHidden":41},[54],[15,4654,4656,4659],{"className":4655},[58],[15,4657],{"className":4658,"style":299},[62],[15,4660,4214],{"className":4661,"style":4243},[67,68]," 时条件独立）。",[11,4664,4665,505,4669,4697,4698,4726,4727,4755,4756,4784,4785,4813,4814,4842],{},[4666,4667,4668],"em",{},"直观证明",[15,4670,4672,4685],{"className":4671,"translate":19},[18],[15,4673,4675],{"className":4674},[23],[25,4676,4677],{"xmlns":27},[29,4678,4679,4683],{},[32,4680,4681],{},[35,4682,37],{},[47,4684,37],{"encoding":49},[15,4686,4688],{"className":4687,"ariaHidden":41},[54],[15,4689,4691,4694],{"className":4690},[58],[15,4692],{"className":4693,"style":299},[62],[15,4695,37],{"className":4696,"style":69},[67,68]," 对 ",[15,4699,4701,4714],{"className":4700,"translate":19},[18],[15,4702,4704],{"className":4703},[23],[25,4705,4706],{"xmlns":27},[29,4707,4708,4712],{},[32,4709,4710],{},[35,4711,45],{},[47,4713,45],{"encoding":49},[15,4715,4717],{"className":4716,"ariaHidden":41},[54],[15,4718,4720,4723],{"className":4719},[58],[15,4721],{"className":4722,"style":299},[62],[15,4724,45],{"className":4725,"style":82},[67,68]," 的全部影响必须经过 ",[15,4728,4730,4743],{"className":4729,"translate":19},[18],[15,4731,4733],{"className":4732},[23],[25,4734,4735],{"xmlns":27},[29,4736,4737,4741],{},[32,4738,4739],{},[35,4740,4214],{},[47,4742,4214],{"encoding":49},[15,4744,4746],{"className":4745,"ariaHidden":41},[54],[15,4747,4749,4752],{"className":4748},[58],[15,4750],{"className":4751,"style":299},[62],[15,4753,4214],{"className":4754,"style":4243},[67,68]," 传递。一旦 ",[15,4757,4759,4772],{"className":4758,"translate":19},[18],[15,4760,4762],{"className":4761},[23],[25,4763,4764],{"xmlns":27},[29,4765,4766,4770],{},[32,4767,4768],{},[35,4769,4214],{},[47,4771,4214],{"encoding":49},[15,4773,4775],{"className":4774,"ariaHidden":41},[54],[15,4776,4778,4781],{"className":4777},[58],[15,4779],{"className":4780,"style":299},[62],[15,4782,4214],{"className":4783,"style":4243},[67,68]," 的取值被固定，",[15,4786,4788,4801],{"className":4787,"translate":19},[18],[15,4789,4791],{"className":4790},[23],[25,4792,4793],{"xmlns":27},[29,4794,4795,4799],{},[32,4796,4797],{},[35,4798,37],{},[47,4800,37],{"encoding":49},[15,4802,4804],{"className":4803,"ariaHidden":41},[54],[15,4805,4807,4810],{"className":4806},[58],[15,4808],{"className":4809,"style":299},[62],[15,4811,37],{"className":4812,"style":69},[67,68]," 就丧失了改变 ",[15,4815,4817,4830],{"className":4816,"translate":19},[18],[15,4818,4820],{"className":4819},[23],[25,4821,4822],{"xmlns":27},[29,4823,4824,4828],{},[32,4825,4826],{},[35,4827,45],{},[47,4829,45],{"encoding":49},[15,4831,4833],{"className":4832,"ariaHidden":41},[54],[15,4834,4836,4839],{"className":4835},[58],[15,4837],{"className":4838,"style":299},[62],[15,4840,45],{"className":4841,"style":82},[67,68]," 分布的任何「渠道」，因此二者在此条件下不再携带彼此的信息。",[1314,4844,4845],{},[11,4846,4847,4850],{},[305,4848,4849],{},"例 1.2"," 吸烟（Smoking）→ 焦油沉积（Tar）→ 肺癌（Cancer）。边际地看，吸烟与肺癌高度相关；但若将研究对象限定为「焦油沉积水平完全相同的人群」，则在这一子群体内，是否吸烟与是否患癌不再相关——因为吸烟致癌的全部机制已经被「焦油沉积」这一中介变量所概括。",[11,4852,4853,4856,4857,4860],{},[305,4854,4855],{},"需要强调这里隐含的假设","：上述结论真正成立的前提，是「焦油沉积」与「肺癌」之间不存在未观测的共同原因。这一点值得仔细分辨——它并不是「在数据中按焦油分层」，而是在说「若外部把焦油水平固定住，吸烟对肺癌就不再有效应」。二者只有在特定假设下才一致：一旦焦油与肺癌之间存在未观测的共同原因，条件化焦油反而会在中介与结果之间引入新的对撞偏差（其机制正是下文结构三）。因此例 1.2 应被理解为一个",[305,4858,4859],{},"理想化的机制分解","，而非一条可以在真实流行病学数据上直接执行的结论——这也正是 3.4 节中介分析必须依赖更强假设的原因。",[11,4862,4863,4335,4866],{},[305,4864,4865],{},"结构二：叉（Fork），共同原因结构",[15,4867,4869,4892],{"className":4868,"translate":19},[18],[15,4870,4872],{"className":4871},[23],[25,4873,4874],{"xmlns":27},[29,4875,4876,4889],{},[32,4877,4878,4880,4883,4885,4887],{},[35,4879,37],{},[39,4881,4882],{},"←",[35,4884,4214],{},[39,4886,1846],{},[35,4888,45],{},[47,4890,4891],{"encoding":49},"X \\leftarrow Z \\to Y",[15,4893,4895,4913,4931],{"className":4894,"ariaHidden":41},[54],[15,4896,4898,4901,4904,4907,4910],{"className":4897},[58],[15,4899],{"className":4900,"style":299},[62],[15,4902,37],{"className":4903,"style":69},[67,68],[15,4905],{"className":4906,"style":199},[77],[15,4908,4882],{"className":4909},[203],[15,4911],{"className":4912,"style":199},[77],[15,4914,4916,4919,4922,4925,4928],{"className":4915},[58],[15,4917],{"className":4918,"style":299},[62],[15,4920,4214],{"className":4921,"style":4243},[67,68],[15,4923],{"className":4924,"style":199},[77],[15,4926,1846],{"className":4927},[203],[15,4929],{"className":4930,"style":199},[77],[15,4932,4934,4937],{"className":4933},[58],[15,4935],{"className":4936,"style":299},[62],[15,4938,45],{"className":4939,"style":82},[67,68],[1314,4941,4942],{},[11,4943,4944,4947,4948,4533,5054,2249],{},[305,4945,4946],{},"命题 1.2"," 在叉式结构下，",[15,4949,4951,4976],{"className":4950,"translate":19},[18],[15,4952,4954],{"className":4953},[23],[25,4955,4956],{"xmlns":27},[29,4957,4958,4974],{},[32,4959,4960,4962,4964,4966,4968,4970,4972],{},[35,4961,37],{},[39,4963,4433],{},[238,4965,240],{},[238,4967,240],{},[238,4969,240],{},[39,4971,236],{},[35,4973,45],{},[47,4975,4446],{"encoding":49},[15,4977,4979,5033,5045],{"className":4978,"ariaHidden":41},[54],[15,4980,4982,4985,4988,4991,5018,5021,5024,5027,5030],{"className":4981},[58],[15,4983],{"className":4984,"style":4456},[62],[15,4986,37],{"className":4987,"style":69},[67,68],[15,4989],{"className":4990,"style":199},[77],[15,4992,4994],{"className":4993},[203],[15,4995,4997],{"className":4996},[67,4469],[15,4998,5000],{"className":4999},[4473],[15,5001,5003,5006,5015],{"className":5002},[4477],[15,5004],{"className":5005,"style":4456},[62],[15,5007,5009],{"className":5008},[4484],[15,5010,5012],{"className":5011},[67],[15,5013,4491],{"className":5014},[203],[15,5016],{"className":5017},[4495],[15,5019],{"className":5020},[77,4499],[15,5022,236],{"className":5023},[203],[15,5025],{"className":5026,"style":274},[77],[15,5028],{"className":5029,"style":274},[77],[15,5031],{"className":5032,"style":274},[77],[15,5034,5036,5039,5042],{"className":5035},[58],[15,5037],{"className":5038,"style":261},[62],[15,5040,236],{"className":5041},[203],[15,5043],{"className":5044,"style":199},[77],[15,5046,5048,5051],{"className":5047},[58],[15,5049],{"className":5050,"style":299},[62],[15,5052,45],{"className":5053,"style":82},[67,68],[15,5055,5057,5086],{"className":5056,"translate":19},[18],[15,5058,5060],{"className":5059},[23],[25,5061,5062],{"xmlns":27},[29,5063,5064,5084],{},[32,5065,5066,5068,5070,5072,5074,5076,5078,5080,5082],{},[35,5067,37],{},[39,5069,236],{},[238,5071,240],{},[238,5073,240],{},[238,5075,240],{},[39,5077,236],{},[35,5079,45],{},[39,5081,170],{},[35,5083,4214],{},[47,5085,4566],{"encoding":49},[15,5087,5089,5113,5125,5143],{"className":5088,"ariaHidden":41},[54],[15,5090,5092,5095,5098,5101,5104,5107,5110],{"className":5091},[58],[15,5093],{"className":5094,"style":261},[62],[15,5096,37],{"className":5097,"style":69},[67,68],[15,5099],{"className":5100,"style":199},[77],[15,5102,236],{"className":5103},[203],[15,5105],{"className":5106,"style":274},[77],[15,5108],{"className":5109,"style":274},[77],[15,5111],{"className":5112,"style":274},[77],[15,5114,5116,5119,5122],{"className":5115},[58],[15,5117],{"className":5118,"style":261},[62],[15,5120,236],{"className":5121},[203],[15,5123],{"className":5124,"style":199},[77],[15,5126,5128,5131,5134,5137,5140],{"className":5127},[58],[15,5129],{"className":5130,"style":124},[62],[15,5132,45],{"className":5133,"style":82},[67,68],[15,5135],{"className":5136,"style":199},[77],[15,5138,170],{"className":5139},[203],[15,5141],{"className":5142,"style":199},[77],[15,5144,5146,5149],{"className":5145},[58],[15,5147],{"className":5148,"style":299},[62],[15,5150,4214],{"className":5151,"style":4243},[67,68],[1314,5153,5154],{},[11,5155,5156,5159,5160,5197,5198,5235,5236,5273,5274,811,5277,5305,5306,2249],{},[305,5157,5158],{},"例 1.3"," 气温（Temperature）→ 冰淇淋销量（IceCream），气温 → 溺水人数（Drowning）。",[15,5161,5163,5179],{"className":5162,"translate":19},[18],[15,5164,5166],{"className":5165},[23],[25,5167,5168],{"xmlns":27},[29,5169,5170,5176],{},[32,5171,5172,5174],{},[35,5173,37],{},[39,5175,602],{},[47,5177,5178],{"encoding":49},"X=",[15,5180,5182],{"className":5181,"ariaHidden":41},[54],[15,5183,5185,5188,5191,5194],{"className":5184},[58],[15,5186],{"className":5187,"style":299},[62],[15,5189,37],{"className":5190,"style":69},[67,68],[15,5192],{"className":5193,"style":199},[77],[15,5195,602],{"className":5196},[203]," 冰淇淋销量，",[15,5199,5201,5217],{"className":5200,"translate":19},[18],[15,5202,5204],{"className":5203},[23],[25,5205,5206],{"xmlns":27},[29,5207,5208,5214],{},[32,5209,5210,5212],{},[35,5211,45],{},[39,5213,602],{},[47,5215,5216],{"encoding":49},"Y=",[15,5218,5220],{"className":5219,"ariaHidden":41},[54],[15,5221,5223,5226,5229,5232],{"className":5222},[58],[15,5224],{"className":5225,"style":299},[62],[15,5227,45],{"className":5228,"style":82},[67,68],[15,5230],{"className":5231,"style":199},[77],[15,5233,602],{"className":5234},[203]," 溺水人数，二者在夏季同步上升，边际相关系数显著为正；但若将数据按气温分层（即条件化 ",[15,5237,5239,5255],{"className":5238,"translate":19},[18],[15,5240,5242],{"className":5241},[23],[25,5243,5244],{"xmlns":27},[29,5245,5246,5252],{},[32,5247,5248,5250],{},[35,5249,4214],{},[39,5251,602],{},[47,5253,5254],{"encoding":49},"Z=",[15,5256,5258],{"className":5257,"ariaHidden":41},[54],[15,5259,5261,5264,5267,5270],{"className":5260},[58],[15,5262],{"className":5263,"style":299},[62],[15,5265,4214],{"className":5266,"style":4243},[67,68],[15,5268],{"className":5269,"style":199},[77],[15,5271,602],{"className":5272},[203],"气温），在每一层内部冰淇淋销量与溺水人数不再相关。这类由共同原因导致的边际关联，称为",[305,5275,5276],{},"虚假关联（spurious association）",[15,5278,5280,5293],{"className":5279,"translate":19},[18],[15,5281,5283],{"className":5282},[23],[25,5284,5285],{"xmlns":27},[29,5286,5287,5291],{},[32,5288,5289],{},[35,5290,4214],{},[47,5292,4214],{"encoding":49},[15,5294,5296],{"className":5295,"ariaHidden":41},[54],[15,5297,5299,5302],{"className":5298},[58],[15,5300],{"className":5301,"style":299},[62],[15,5303,4214],{"className":5304,"style":4243},[67,68]," 称为",[305,5307,5308],{},"混杂因子（confounder）",[11,5310,5311,4335,5314],{},[305,5312,5313],{},"结构三：对撞（Collider）",[15,5315,5317,5339],{"className":5316,"translate":19},[18],[15,5318,5320],{"className":5319},[23],[25,5321,5322],{"xmlns":27},[29,5323,5324,5336],{},[32,5325,5326,5328,5330,5332,5334],{},[35,5327,37],{},[39,5329,1846],{},[35,5331,4214],{},[39,5333,4882],{},[35,5335,45],{},[47,5337,5338],{"encoding":49},"X \\to Z \\leftarrow Y",[15,5340,5342,5360,5378],{"className":5341,"ariaHidden":41},[54],[15,5343,5345,5348,5351,5354,5357],{"className":5344},[58],[15,5346],{"className":5347,"style":299},[62],[15,5349,37],{"className":5350,"style":69},[67,68],[15,5352],{"className":5353,"style":199},[77],[15,5355,1846],{"className":5356},[203],[15,5358],{"className":5359,"style":199},[77],[15,5361,5363,5366,5369,5372,5375],{"className":5362},[58],[15,5364],{"className":5365,"style":299},[62],[15,5367,4214],{"className":5368,"style":4243},[67,68],[15,5370],{"className":5371,"style":199},[77],[15,5373,4882],{"className":5374},[203],[15,5376],{"className":5377,"style":199},[77],[15,5379,5381,5384],{"className":5380},[58],[15,5382],{"className":5383,"style":299},[62],[15,5385,45],{"className":5386,"style":82},[67,68],[1314,5388,5389],{},[11,5390,5391,5394,5395,5436,5437,5513,5514,4633,5643,5671,5672,5700],{},[305,5392,5393],{},"命题 1.3（对撞偏差，Collider Bias）"," 在对撞结构下，若 ",[15,5396,5398,5415],{"className":5397,"translate":19},[18],[15,5399,5401],{"className":5400},[23],[25,5402,5403],{"xmlns":27},[29,5404,5405,5413],{},[32,5406,5407,5409,5411],{},[35,5408,37],{},[39,5410,42],{"separator":41},[35,5412,45],{},[47,5414,50],{"encoding":49},[15,5416,5418],{"className":5417,"ariaHidden":41},[54],[15,5419,5421,5424,5427,5430,5433],{"className":5420},[58],[15,5422],{"className":5423,"style":63},[62],[15,5425,37],{"className":5426,"style":69},[67,68],[15,5428,42],{"className":5429},[73],[15,5431],{"className":5432,"style":78},[77],[15,5434,45],{"className":5435,"style":82},[67,68]," 无其他连接路径，则 ",[15,5438,5440,5465],{"className":5439,"translate":19},[18],[15,5441,5443],{"className":5442},[23],[25,5444,5445],{"xmlns":27},[29,5446,5447,5463],{},[32,5448,5449,5451,5453,5455,5457,5459,5461],{},[35,5450,37],{},[39,5452,236],{},[238,5454,240],{},[238,5456,240],{},[238,5458,240],{},[39,5460,236],{},[35,5462,45],{},[47,5464,251],{"encoding":49},[15,5466,5468,5492,5504],{"className":5467,"ariaHidden":41},[54],[15,5469,5471,5474,5477,5480,5483,5486,5489],{"className":5470},[58],[15,5472],{"className":5473,"style":261},[62],[15,5475,37],{"className":5476,"style":69},[67,68],[15,5478],{"className":5479,"style":199},[77],[15,5481,236],{"className":5482},[203],[15,5484],{"className":5485,"style":274},[77],[15,5487],{"className":5488,"style":274},[77],[15,5490],{"className":5491,"style":274},[77],[15,5493,5495,5498,5501],{"className":5494},[58],[15,5496],{"className":5497,"style":261},[62],[15,5499,236],{"className":5500},[203],[15,5502],{"className":5503,"style":199},[77],[15,5505,5507,5510],{"className":5506},[58],[15,5508],{"className":5509,"style":299},[62],[15,5511,45],{"className":5512,"style":82},[67,68],"（边际独立）；但 ",[15,5515,5517,5547],{"className":5516,"translate":19},[18],[15,5518,5520],{"className":5519},[23],[25,5521,5522],{"xmlns":27},[29,5523,5524,5544],{},[32,5525,5526,5528,5530,5532,5534,5536,5538,5540,5542],{},[35,5527,37],{},[39,5529,4433],{},[238,5531,240],{},[238,5533,240],{},[238,5535,240],{},[39,5537,236],{},[35,5539,45],{},[39,5541,170],{},[35,5543,4214],{},[47,5545,5546],{"encoding":49},"X \\not\\perp\\!\\!\\!\\perp Y \\mid Z",[15,5548,5550,5604,5616,5634],{"className":5549,"ariaHidden":41},[54],[15,5551,5553,5556,5559,5562,5589,5592,5595,5598,5601],{"className":5552},[58],[15,5554],{"className":5555,"style":4456},[62],[15,5557,37],{"className":5558,"style":69},[67,68],[15,5560],{"className":5561,"style":199},[77],[15,5563,5565],{"className":5564},[203],[15,5566,5568],{"className":5567},[67,4469],[15,5569,5571],{"className":5570},[4473],[15,5572,5574,5577,5586],{"className":5573},[4477],[15,5575],{"className":5576,"style":4456},[62],[15,5578,5580],{"className":5579},[4484],[15,5581,5583],{"className":5582},[67],[15,5584,4491],{"className":5585},[203],[15,5587],{"className":5588},[4495],[15,5590],{"className":5591},[77,4499],[15,5593,236],{"className":5594},[203],[15,5596],{"className":5597,"style":274},[77],[15,5599],{"className":5600,"style":274},[77],[15,5602],{"className":5603,"style":274},[77],[15,5605,5607,5610,5613],{"className":5606},[58],[15,5608],{"className":5609,"style":261},[62],[15,5611,236],{"className":5612},[203],[15,5614],{"className":5615,"style":199},[77],[15,5617,5619,5622,5625,5628,5631],{"className":5618},[58],[15,5620],{"className":5621,"style":124},[62],[15,5623,45],{"className":5624,"style":82},[67,68],[15,5626],{"className":5627,"style":199},[77],[15,5629,170],{"className":5630},[203],[15,5632],{"className":5633,"style":199},[77],[15,5635,5637,5640],{"className":5636},[58],[15,5638],{"className":5639,"style":299},[62],[15,5641,4214],{"className":5642,"style":4243},[67,68],[15,5644,5646,5659],{"className":5645,"translate":19},[18],[15,5647,5649],{"className":5648},[23],[25,5650,5651],{"xmlns":27},[29,5652,5653,5657],{},[32,5654,5655],{},[35,5656,4214],{},[47,5658,4214],{"encoding":49},[15,5660,5662],{"className":5661,"ariaHidden":41},[54],[15,5663,5665,5668],{"className":5664},[58],[15,5666],{"className":5667,"style":299},[62],[15,5669,4214],{"className":5670,"style":4243},[67,68],"，即便只是给定 ",[15,5673,5675,5688],{"className":5674,"translate":19},[18],[15,5676,5678],{"className":5677},[23],[25,5679,5680],{"xmlns":27},[29,5681,5682,5686],{},[32,5683,5684],{},[35,5685,4214],{},[47,5687,4214],{"encoding":49},[15,5689,5691],{"className":5690,"ariaHidden":41},[54],[15,5692,5694,5697],{"className":5693},[58],[15,5695],{"className":5696,"style":299},[62],[15,5698,4214],{"className":5699,"style":4243},[67,68]," 的后代变量，也会产生条件不独立）。",[11,5702,5703,5705,5706,5800,5801,5854,5855,5907,5908,6000,6001,6029,6030,6058,6059,6100,6101,6129,6130,6158,6159,6187,6188,6216,6217,6245],{},[4666,5704,4668],{},"：不失一般性设 ",[15,5707,5709,5742],{"className":5708,"translate":19},[18],[15,5710,5712],{"className":5711},[23],[25,5713,5714],{"xmlns":27},[29,5715,5716,5739],{},[32,5717,5718,5720,5722,5725,5727,5729,5731,5733,5735,5737],{},[35,5719,4214],{},[39,5721,602],{},[35,5723,5724],{},"f",[39,5726,102],{"stretchy":101},[35,5728,37],{},[39,5730,42],{"separator":41},[35,5732,45],{},[39,5734,42],{"separator":41},[35,5736,2458],{},[39,5738,111],{"stretchy":101},[47,5740,5741],{"encoding":49},"Z = f(X, Y, U)",[15,5743,5745,5763],{"className":5744,"ariaHidden":41},[54],[15,5746,5748,5751,5754,5757,5760],{"className":5747},[58],[15,5749],{"className":5750,"style":299},[62],[15,5752,4214],{"className":5753,"style":4243},[67,68],[15,5755],{"className":5756,"style":199},[77],[15,5758,602],{"className":5759},[203],[15,5761],{"className":5762,"style":199},[77],[15,5764,5766,5769,5773,5776,5779,5782,5785,5788,5791,5794,5797],{"className":5765},[58],[15,5767],{"className":5768,"style":124},[62],[15,5770,5724],{"className":5771,"style":5772},[67,68],"margin-right:0.1076em;",[15,5774,102],{"className":5775},[132],[15,5777,37],{"className":5778,"style":69},[67,68],[15,5780,42],{"className":5781},[73],[15,5783],{"className":5784,"style":78},[77],[15,5786,45],{"className":5787,"style":82},[67,68],[15,5789,42],{"className":5790},[73],[15,5792],{"className":5793,"style":78},[77],[15,5795,2458],{"className":5796,"style":2570},[67,68],[15,5798,111],{"className":5799},[148],"。给定 ",[15,5802,5804,5823],{"className":5803,"translate":19},[18],[15,5805,5807],{"className":5806},[23],[25,5808,5809],{"xmlns":27},[29,5810,5811,5820],{},[32,5812,5813,5815,5817],{},[35,5814,4214],{},[39,5816,602],{},[35,5818,5819],{},"z",[47,5821,5822],{"encoding":49},"Z = z",[15,5824,5826,5844],{"className":5825,"ariaHidden":41},[54],[15,5827,5829,5832,5835,5838,5841],{"className":5828},[58],[15,5830],{"className":5831,"style":299},[62],[15,5833,4214],{"className":5834,"style":4243},[67,68],[15,5836],{"className":5837,"style":199},[77],[15,5839,602],{"className":5840},[203],[15,5842],{"className":5843,"style":199},[77],[15,5845,5847,5850],{"className":5846},[58],[15,5848],{"className":5849,"style":635},[62],[15,5851,5819],{"className":5852,"style":5853},[67,68],"margin-right:0.044em;"," 这一约束，相当于把 ",[15,5856,5858,5880],{"className":5857,"translate":19},[18],[15,5859,5861],{"className":5860},[23],[25,5862,5863],{"xmlns":27},[29,5864,5865,5877],{},[32,5866,5867,5869,5871,5873,5875],{},[39,5868,102],{"stretchy":101},[35,5870,37],{},[39,5872,42],{"separator":41},[35,5874,45],{},[39,5876,111],{"stretchy":101},[47,5878,5879],{"encoding":49},"(X,Y)",[15,5881,5883],{"className":5882,"ariaHidden":41},[54],[15,5884,5886,5889,5892,5895,5898,5901,5904],{"className":5885},[58],[15,5887],{"className":5888,"style":124},[62],[15,5890,102],{"className":5891},[132],[15,5893,37],{"className":5894,"style":69},[67,68],[15,5896,42],{"className":5897},[73],[15,5899],{"className":5900,"style":78},[77],[15,5902,45],{"className":5903,"style":82},[67,68],[15,5905,111],{"className":5906},[148]," 的取值限制在满足 ",[15,5909,5911,5943],{"className":5910,"translate":19},[18],[15,5912,5914],{"className":5913},[23],[25,5915,5916],{"xmlns":27},[29,5917,5918,5940],{},[32,5919,5920,5922,5924,5926,5928,5930,5932,5934,5936,5938],{},[35,5921,5724],{},[39,5923,102],{"stretchy":101},[35,5925,37],{},[39,5927,42],{"separator":41},[35,5929,45],{},[39,5931,42],{"separator":41},[35,5933,2458],{},[39,5935,111],{"stretchy":101},[39,5937,602],{},[35,5939,5819],{},[47,5941,5942],{"encoding":49},"f(X,Y,U)=z",[15,5944,5946,5991],{"className":5945,"ariaHidden":41},[54],[15,5947,5949,5952,5955,5958,5961,5964,5967,5970,5973,5976,5979,5982,5985,5988],{"className":5948},[58],[15,5950],{"className":5951,"style":124},[62],[15,5953,5724],{"className":5954,"style":5772},[67,68],[15,5956,102],{"className":5957},[132],[15,5959,37],{"className":5960,"style":69},[67,68],[15,5962,42],{"className":5963},[73],[15,5965],{"className":5966,"style":78},[77],[15,5968,45],{"className":5969,"style":82},[67,68],[15,5971,42],{"className":5972},[73],[15,5974],{"className":5975,"style":78},[77],[15,5977,2458],{"className":5978,"style":2570},[67,68],[15,5980,111],{"className":5981},[148],[15,5983],{"className":5984,"style":199},[77],[15,5986,602],{"className":5987},[203],[15,5989],{"className":5990,"style":199},[77],[15,5992,5994,5997],{"className":5993},[58],[15,5995],{"className":5996,"style":635},[62],[15,5998,5819],{"className":5999,"style":5853},[67,68]," 的一个子流形上。在这个子流形上，",[15,6002,6004,6017],{"className":6003,"translate":19},[18],[15,6005,6007],{"className":6006},[23],[25,6008,6009],{"xmlns":27},[29,6010,6011,6015],{},[32,6012,6013],{},[35,6014,37],{},[47,6016,37],{"encoding":49},[15,6018,6020],{"className":6019,"ariaHidden":41},[54],[15,6021,6023,6026],{"className":6022},[58],[15,6024],{"className":6025,"style":299},[62],[15,6027,37],{"className":6028,"style":69},[67,68]," 的取值会反向约束 ",[15,6031,6033,6046],{"className":6032,"translate":19},[18],[15,6034,6036],{"className":6035},[23],[25,6037,6038],{"xmlns":27},[29,6039,6040,6044],{},[32,6041,6042],{},[35,6043,45],{},[47,6045,45],{"encoding":49},[15,6047,6049],{"className":6048,"ariaHidden":41},[54],[15,6050,6052,6055],{"className":6051},[58],[15,6053],{"className":6054,"style":299},[62],[15,6056,45],{"className":6057,"style":82},[67,68]," 的可能取值范围——即便 ",[15,6060,6062,6079],{"className":6061,"translate":19},[18],[15,6063,6065],{"className":6064},[23],[25,6066,6067],{"xmlns":27},[29,6068,6069,6077],{},[32,6070,6071,6073,6075],{},[35,6072,37],{},[39,6074,42],{"separator":41},[35,6076,45],{},[47,6078,50],{"encoding":49},[15,6080,6082],{"className":6081,"ariaHidden":41},[54],[15,6083,6085,6088,6091,6094,6097],{"className":6084},[58],[15,6086],{"className":6087,"style":63},[62],[15,6089,37],{"className":6090,"style":69},[67,68],[15,6092,42],{"className":6093},[73],[15,6095],{"className":6096,"style":78},[77],[15,6098,45],{"className":6099,"style":82},[67,68]," 在无约束时相互独立，在此子流形上二者一般不再独立。这一现象与「解释消除（explaining away）」直觉一致：已知 ",[15,6102,6104,6117],{"className":6103,"translate":19},[18],[15,6105,6107],{"className":6106},[23],[25,6108,6109],{"xmlns":27},[29,6110,6111,6115],{},[32,6112,6113],{},[35,6114,4214],{},[47,6116,4214],{"encoding":49},[15,6118,6120],{"className":6119,"ariaHidden":41},[54],[15,6121,6123,6126],{"className":6122},[58],[15,6124],{"className":6125,"style":299},[62],[15,6127,4214],{"className":6128,"style":4243},[67,68]," 发生，若又得知 ",[15,6131,6133,6146],{"className":6132,"translate":19},[18],[15,6134,6136],{"className":6135},[23],[25,6137,6138],{"xmlns":27},[29,6139,6140,6144],{},[32,6141,6142],{},[35,6143,37],{},[47,6145,37],{"encoding":49},[15,6147,6149],{"className":6148,"ariaHidden":41},[54],[15,6150,6152,6155],{"className":6151},[58],[15,6153],{"className":6154,"style":299},[62],[15,6156,37],{"className":6157,"style":69},[67,68]," 是导致 ",[15,6160,6162,6175],{"className":6161,"translate":19},[18],[15,6163,6165],{"className":6164},[23],[25,6166,6167],{"xmlns":27},[29,6168,6169,6173],{},[32,6170,6171],{},[35,6172,4214],{},[47,6174,4214],{"encoding":49},[15,6176,6178],{"className":6177,"ariaHidden":41},[54],[15,6179,6181,6184],{"className":6180},[58],[15,6182],{"className":6183,"style":299},[62],[15,6185,4214],{"className":6186,"style":4243},[67,68]," 的原因，则 ",[15,6189,6191,6204],{"className":6190,"translate":19},[18],[15,6192,6194],{"className":6193},[23],[25,6195,6196],{"xmlns":27},[29,6197,6198,6202],{},[32,6199,6200],{},[35,6201,45],{},[47,6203,45],{"encoding":49},[15,6205,6207],{"className":6206,"ariaHidden":41},[54],[15,6208,6210,6213],{"className":6209},[58],[15,6211],{"className":6212,"style":299},[62],[15,6214,45],{"className":6215,"style":82},[67,68]," 作为 ",[15,6218,6220,6233],{"className":6219,"translate":19},[18],[15,6221,6223],{"className":6222},[23],[25,6224,6225],{"xmlns":27},[29,6226,6227,6231],{},[32,6228,6229],{},[35,6230,4214],{},[47,6232,4214],{"encoding":49},[15,6234,6236],{"className":6235,"ariaHidden":41},[54],[15,6237,6239,6242],{"className":6238},[58],[15,6240],{"className":6241,"style":299},[62],[15,6243,4214],{"className":6244,"style":4243},[67,68]," 的另一原因的「责任」会被相应降低。",[1314,6247,6248],{},[11,6249,6250,6253,6254,6331,6332,6335,6336,6339],{},[305,6251,6252],{},"例 1.4"," 才华（Talent）→ 明星身份（Celebrity）← 美貌（Beauty）。设才华与美貌在总体人群中独立同分布，互不相关。若将研究样本限定为「已成为明星的人」（即条件化 ",[15,6255,6257,6280],{"className":6256,"translate":19},[18],[15,6258,6260],{"className":6259},[23],[25,6261,6262],{"xmlns":27},[29,6263,6264,6277],{},[32,6265,6266,6268,6270,6273,6275],{},[35,6267,4214],{},[39,6269,602],{},[238,6271,6272],{},"Celebrity",[39,6274,602],{},[1425,6276,1427],{},[47,6278,6279],{"encoding":49},"Z=\\text{Celebrity}=1",[15,6281,6283,6301,6322],{"className":6282,"ariaHidden":41},[54],[15,6284,6286,6289,6292,6295,6298],{"className":6285},[58],[15,6287],{"className":6288,"style":299},[62],[15,6290,4214],{"className":6291,"style":4243},[67,68],[15,6293],{"className":6294,"style":199},[77],[15,6296,602],{"className":6297},[203],[15,6299],{"className":6300,"style":199},[77],[15,6302,6304,6307,6313,6316,6319],{"className":6303},[58],[15,6305],{"className":6306,"style":4456},[62],[15,6308,6310],{"className":6309},[67,4123],[15,6311,6272],{"className":6312},[67],[15,6314],{"className":6315,"style":199},[77],[15,6317,602],{"className":6318},[203],[15,6320],{"className":6321,"style":199},[77],[15,6323,6325,6328],{"className":6324},[58],[15,6326],{"className":6327,"style":3149},[62],[15,6329,1427],{"className":6330},[67],"），则在这一子群体中，才华与美貌会呈现出",[305,6333,6334],{},"负相关","——因为一个才华一般的人若能成为明星，多半是靠美貌弥补，反之亦然。这一负相关是样本选择造成的统计假象，并非二者之间存在任何真实的因果联系。这类偏差在流行病学中亦称",[305,6337,6338],{},"伯克森悖论（Berkson's Paradox）","，也是众多观测性研究中「选择偏差」的图论根源。",[1309,6341,6343],{"id":6342},"_13-d-分离路径阻断的一般判据","1.3 d-分离：路径阻断的一般判据",[11,6345,6346],{},"三种基本结构可统一为一个可在任意复杂 DAG 上递归判定的一般规则。",[1314,6348,6349,6612,6831],{},[11,6350,6351,6354,6355,6406,6407,2033,6436,431,6464,6492,6493,6521,6522,4335,6550,6553,6554,6582,6583,6611],{},[305,6352,6353],{},"定义 1.5（路径的阻断）"," 设 ",[15,6356,6358,6376],{"className":6357,"translate":19},[18],[15,6359,6361],{"className":6360},[23],[25,6362,6363],{"xmlns":27},[29,6364,6365,6373],{},[32,6366,6367,6369,6371],{},[35,6368,3779],{},[39,6370,1599],{},[35,6372,1343],{},[47,6374,6375],{"encoding":49},"S \\subseteq V",[15,6377,6379,6397],{"className":6378,"ariaHidden":41},[54],[15,6380,6382,6385,6388,6391,6394],{"className":6381},[58],[15,6383],{"className":6384,"style":1619},[62],[15,6386,3779],{"className":6387,"style":1396},[67,68],[15,6389],{"className":6390,"style":199},[77],[15,6392,1599],{"className":6393},[203],[15,6395],{"className":6396,"style":199},[77],[15,6398,6400,6403],{"className":6399},[58],[15,6401],{"className":6402,"style":299},[62],[15,6404,1343],{"className":6405,"style":82},[67,68]," 为一组已条件化的节点集合，",[15,6408,6410,6423],{"className":6409,"translate":19},[18],[15,6411,6413],{"className":6412},[23],[25,6414,6415],{"xmlns":27},[29,6416,6417,6421],{},[32,6418,6419],{},[35,6420,11],{},[47,6422,11],{"encoding":49},[15,6424,6426],{"className":6425,"ariaHidden":41},[54],[15,6427,6429,6433],{"className":6428},[58],[15,6430],{"className":6431,"style":6432},[62],"height:0.625em;vertical-align:-0.1944em;",[15,6434,11],{"className":6435},[67,68],[15,6437,6439,6452],{"className":6438,"translate":19},[18],[15,6440,6442],{"className":6441},[23],[25,6443,6444],{"xmlns":27},[29,6445,6446,6450],{},[32,6447,6448],{},[35,6449,37],{},[47,6451,37],{"encoding":49},[15,6453,6455],{"className":6454,"ariaHidden":41},[54],[15,6456,6458,6461],{"className":6457},[58],[15,6459],{"className":6460,"style":299},[62],[15,6462,37],{"className":6463,"style":69},[67,68],[15,6465,6467,6480],{"className":6466,"translate":19},[18],[15,6468,6470],{"className":6469},[23],[25,6471,6472],{"xmlns":27},[29,6473,6474,6478],{},[32,6475,6476],{},[35,6477,45],{},[47,6479,45],{"encoding":49},[15,6481,6483],{"className":6482,"ariaHidden":41},[54],[15,6484,6486,6489],{"className":6485},[58],[15,6487],{"className":6488,"style":299},[62],[15,6490,45],{"className":6491,"style":82},[67,68]," 之间的一条路径。称 ",[15,6494,6496,6509],{"className":6495,"translate":19},[18],[15,6497,6499],{"className":6498},[23],[25,6500,6501],{"xmlns":27},[29,6502,6503,6507],{},[32,6504,6505],{},[35,6506,11],{},[47,6508,11],{"encoding":49},[15,6510,6512],{"className":6511,"ariaHidden":41},[54],[15,6513,6515,6518],{"className":6514},[58],[15,6516],{"className":6517,"style":6432},[62],[15,6519,11],{"className":6520},[67,68]," 被 ",[15,6523,6525,6538],{"className":6524,"translate":19},[18],[15,6526,6528],{"className":6527},[23],[25,6529,6530],{"xmlns":27},[29,6531,6532,6536],{},[32,6533,6534],{},[35,6535,3779],{},[47,6537,3779],{"encoding":49},[15,6539,6541],{"className":6540,"ariaHidden":41},[54],[15,6542,6544,6547],{"className":6543},[58],[15,6545],{"className":6546,"style":299},[62],[15,6548,3779],{"className":6549,"style":1396},[67,68],[305,6551,6552],{},"阻断","，当且仅当 ",[15,6555,6557,6570],{"className":6556,"translate":19},[18],[15,6558,6560],{"className":6559},[23],[25,6561,6562],{"xmlns":27},[29,6563,6564,6568],{},[32,6565,6566],{},[35,6567,11],{},[47,6569,11],{"encoding":49},[15,6571,6573],{"className":6572,"ariaHidden":41},[54],[15,6574,6576,6579],{"className":6575},[58],[15,6577],{"className":6578,"style":6432},[62],[15,6580,11],{"className":6581},[67,68]," 上至少存在一个节点 ",[15,6584,6586,6599],{"className":6585,"translate":19},[18],[15,6587,6589],{"className":6588},[23],[25,6590,6591],{"xmlns":27},[29,6592,6593,6597],{},[32,6594,6595],{},[35,6596,4214],{},[47,6598,4214],{"encoding":49},[15,6600,6602],{"className":6601,"ariaHidden":41},[54],[15,6603,6605,6608],{"className":6604},[58],[15,6606],{"className":6607,"style":299},[62],[15,6609,4214],{"className":6610,"style":4243},[67,68]," 满足下列条件之一：",[11,6613,6614,6615,6667,6668,6696,6697,6725,6726,6778,6779,6830],{},"(i) ",[15,6616,6618,6636],{"className":6617,"translate":19},[18],[15,6619,6621],{"className":6620},[23],[25,6622,6623],{"xmlns":27},[29,6624,6625,6633],{},[32,6626,6627,6629,6631],{},[35,6628,4214],{},[39,6630,1696],{},[35,6632,3779],{},[47,6634,6635],{"encoding":49},"Z \\in S",[15,6637,6639,6658],{"className":6638,"ariaHidden":41},[54],[15,6640,6642,6646,6649,6652,6655],{"className":6641},[58],[15,6643],{"className":6644,"style":6645},[62],"height:0.7224em;vertical-align:-0.0391em;",[15,6647,4214],{"className":6648,"style":4243},[67,68],[15,6650],{"className":6651,"style":199},[77],[15,6653,1696],{"className":6654},[203],[15,6656],{"className":6657,"style":199},[77],[15,6659,6661,6664],{"className":6660},[58],[15,6662],{"className":6663,"style":299},[62],[15,6665,3779],{"className":6666,"style":1396},[67,68],"，且 ",[15,6669,6671,6684],{"className":6670,"translate":19},[18],[15,6672,6674],{"className":6673},[23],[25,6675,6676],{"xmlns":27},[29,6677,6678,6682],{},[32,6679,6680],{},[35,6681,4214],{},[47,6683,4214],{"encoding":49},[15,6685,6687],{"className":6686,"ariaHidden":41},[54],[15,6688,6690,6693],{"className":6689},[58],[15,6691],{"className":6692,"style":299},[62],[15,6694,4214],{"className":6695,"style":4243},[67,68]," 在 ",[15,6698,6700,6713],{"className":6699,"translate":19},[18],[15,6701,6703],{"className":6702},[23],[25,6704,6705],{"xmlns":27},[29,6706,6707,6711],{},[32,6708,6709],{},[35,6710,11],{},[47,6712,11],{"encoding":49},[15,6714,6716],{"className":6715,"ariaHidden":41},[54],[15,6717,6719,6722],{"className":6718},[58],[15,6720],{"className":6721,"style":6432},[62],[15,6723,11],{"className":6724},[67,68]," 上构成链结构（",[15,6727,6729,6747],{"className":6728,"translate":19},[18],[15,6730,6732],{"className":6731},[23],[25,6733,6734],{"xmlns":27},[29,6735,6736,6744],{},[32,6737,6738,6740,6742],{},[39,6739,1846],{},[35,6741,4214],{},[39,6743,1846],{},[47,6745,6746],{"encoding":49},"\\to Z \\to",[15,6748,6750,6763],{"className":6749,"ariaHidden":41},[54],[15,6751,6753,6757,6760],{"className":6752},[58],[15,6754],{"className":6755,"style":6756},[62],"height:0.3669em;",[15,6758,1846],{"className":6759},[203],[15,6761],{"className":6762,"style":199},[77],[15,6764,6766,6769,6772,6775],{"className":6765},[58],[15,6767],{"className":6768,"style":299},[62],[15,6770,4214],{"className":6771,"style":4243},[67,68],[15,6773],{"className":6774,"style":199},[77],[15,6776,1846],{"className":6777},[203],"）或叉结构（",[15,6780,6782,6800],{"className":6781,"translate":19},[18],[15,6783,6785],{"className":6784},[23],[25,6786,6787],{"xmlns":27},[29,6788,6789,6797],{},[32,6790,6791,6793,6795],{},[39,6792,4882],{},[35,6794,4214],{},[39,6796,1846],{},[47,6798,6799],{"encoding":49},"\\leftarrow Z \\to",[15,6801,6803,6815],{"className":6802,"ariaHidden":41},[54],[15,6804,6806,6809,6812],{"className":6805},[58],[15,6807],{"className":6808,"style":6756},[62],[15,6810,4882],{"className":6811},[203],[15,6813],{"className":6814,"style":199},[77],[15,6816,6818,6821,6824,6827],{"className":6817},[58],[15,6819],{"className":6820,"style":299},[62],[15,6822,4214],{"className":6823,"style":4243},[67,68],[15,6825],{"className":6826,"style":199},[77],[15,6828,1846],{"className":6829},[203],"）；",[11,6832,6833,6834,6696,6862,6890,6891,6942,6943,6971,6972,2249],{},"(ii) ",[15,6835,6837,6850],{"className":6836,"translate":19},[18],[15,6838,6840],{"className":6839},[23],[25,6841,6842],{"xmlns":27},[29,6843,6844,6848],{},[32,6845,6846],{},[35,6847,4214],{},[47,6849,4214],{"encoding":49},[15,6851,6853],{"className":6852,"ariaHidden":41},[54],[15,6854,6856,6859],{"className":6855},[58],[15,6857],{"className":6858,"style":299},[62],[15,6860,4214],{"className":6861,"style":4243},[67,68],[15,6863,6865,6878],{"className":6864,"translate":19},[18],[15,6866,6868],{"className":6867},[23],[25,6869,6870],{"xmlns":27},[29,6871,6872,6876],{},[32,6873,6874],{},[35,6875,11],{},[47,6877,11],{"encoding":49},[15,6879,6881],{"className":6880,"ariaHidden":41},[54],[15,6882,6884,6887],{"className":6883},[58],[15,6885],{"className":6886,"style":6432},[62],[15,6888,11],{"className":6889},[67,68]," 上构成对撞结构（",[15,6892,6894,6912],{"className":6893,"translate":19},[18],[15,6895,6897],{"className":6896},[23],[25,6898,6899],{"xmlns":27},[29,6900,6901,6909],{},[32,6902,6903,6905,6907],{},[39,6904,1846],{},[35,6906,4214],{},[39,6908,4882],{},[47,6910,6911],{"encoding":49},"\\to Z \\leftarrow",[15,6913,6915,6927],{"className":6914,"ariaHidden":41},[54],[15,6916,6918,6921,6924],{"className":6917},[58],[15,6919],{"className":6920,"style":6756},[62],[15,6922,1846],{"className":6923},[203],[15,6925],{"className":6926,"style":199},[77],[15,6928,6930,6933,6936,6939],{"className":6929},[58],[15,6931],{"className":6932,"style":299},[62],[15,6934,4214],{"className":6935,"style":4243},[67,68],[15,6937],{"className":6938,"style":199},[77],[15,6940,4882],{"className":6941},[203],"），且 ",[15,6944,6946,6959],{"className":6945,"translate":19},[18],[15,6947,6949],{"className":6948},[23],[25,6950,6951],{"xmlns":27},[29,6952,6953,6957],{},[32,6954,6955],{},[35,6956,4214],{},[47,6958,4214],{"encoding":49},[15,6960,6962],{"className":6961,"ariaHidden":41},[54],[15,6963,6965,6968],{"className":6964},[58],[15,6966],{"className":6967,"style":299},[62],[15,6969,4214],{"className":6970,"style":4243},[67,68]," 本身及其**全部后代（descendants）**都不属于 ",[15,6973,6975,6988],{"className":6974,"translate":19},[18],[15,6976,6978],{"className":6977},[23],[25,6979,6980],{"xmlns":27},[29,6981,6982,6986],{},[32,6983,6984],{},[35,6985,3779],{},[47,6987,3779],{"encoding":49},[15,6989,6991],{"className":6990,"ariaHidden":41},[54],[15,6992,6994,6997],{"className":6993},[58],[15,6995],{"className":6996,"style":299},[62],[15,6998,3779],{"className":6999,"style":1396},[67,68],[1314,7001,7002],{},[11,7003,7004,7007,7008,431,7036,7064,7065,7068,7069,7097,7098,431,7126,7154,7155,7183,7184,1825,7187,2249],{},[305,7005,7006],{},"定义 1.6（d-分离）"," 若 ",[15,7009,7011,7024],{"className":7010,"translate":19},[18],[15,7012,7014],{"className":7013},[23],[25,7015,7016],{"xmlns":27},[29,7017,7018,7022],{},[32,7019,7020],{},[35,7021,37],{},[47,7023,37],{"encoding":49},[15,7025,7027],{"className":7026,"ariaHidden":41},[54],[15,7028,7030,7033],{"className":7029},[58],[15,7031],{"className":7032,"style":299},[62],[15,7034,37],{"className":7035,"style":69},[67,68],[15,7037,7039,7052],{"className":7038,"translate":19},[18],[15,7040,7042],{"className":7041},[23],[25,7043,7044],{"xmlns":27},[29,7045,7046,7050],{},[32,7047,7048],{},[35,7049,45],{},[47,7051,45],{"encoding":49},[15,7053,7055],{"className":7054,"ariaHidden":41},[54],[15,7056,7058,7061],{"className":7057},[58],[15,7059],{"className":7060,"style":299},[62],[15,7062,45],{"className":7063,"style":82},[67,68]," 之间的",[305,7066,7067],{},"每一条","路径都被 ",[15,7070,7072,7085],{"className":7071,"translate":19},[18],[15,7073,7075],{"className":7074},[23],[25,7076,7077],{"xmlns":27},[29,7078,7079,7083],{},[32,7080,7081],{},[35,7082,3779],{},[47,7084,3779],{"encoding":49},[15,7086,7088],{"className":7087,"ariaHidden":41},[54],[15,7089,7091,7094],{"className":7090},[58],[15,7092],{"className":7093,"style":299},[62],[15,7095,3779],{"className":7096,"style":1396},[67,68]," 阻断，则称 ",[15,7099,7101,7114],{"className":7100,"translate":19},[18],[15,7102,7104],{"className":7103},[23],[25,7105,7106],{"xmlns":27},[29,7107,7108,7112],{},[32,7109,7110],{},[35,7111,37],{},[47,7113,37],{"encoding":49},[15,7115,7117],{"className":7116,"ariaHidden":41},[54],[15,7118,7120,7123],{"className":7119},[58],[15,7121],{"className":7122,"style":299},[62],[15,7124,37],{"className":7125,"style":69},[67,68],[15,7127,7129,7142],{"className":7128,"translate":19},[18],[15,7130,7132],{"className":7131},[23],[25,7133,7134],{"xmlns":27},[29,7135,7136,7140],{},[32,7137,7138],{},[35,7139,45],{},[47,7141,45],{"encoding":49},[15,7143,7145],{"className":7144,"ariaHidden":41},[54],[15,7146,7148,7151],{"className":7147},[58],[15,7149],{"className":7150,"style":299},[62],[15,7152,45],{"className":7153,"style":82},[67,68]," 在给定 ",[15,7156,7158,7171],{"className":7157,"translate":19},[18],[15,7159,7161],{"className":7160},[23],[25,7162,7163],{"xmlns":27},[29,7164,7165,7169],{},[32,7166,7167],{},[35,7168,3779],{},[47,7170,3779],{"encoding":49},[15,7172,7174],{"className":7173,"ariaHidden":41},[54],[15,7175,7177,7180],{"className":7176},[58],[15,7178],{"className":7179,"style":299},[62],[15,7181,3779],{"className":7182,"style":1396},[67,68]," 时 ",[305,7185,7186],{},"d-分离",[15,7188,7190,7232],{"className":7189,"translate":19},[18],[15,7191,7193],{"className":7192},[23],[25,7194,7195],{"xmlns":27},[29,7196,7197,7229],{},[32,7198,7199,7201,7203,7205,7207,7209,7211,7217,7219,7221,7223],{},[39,7200,102],{"stretchy":101},[35,7202,37],{},[39,7204,236],{},[238,7206,240],{},[238,7208,240],{},[238,7210,240],{},[863,7212,7213,7215],{},[39,7214,236],{},[35,7216,696],{},[35,7218,45],{},[39,7220,170],{},[35,7222,3779],{},[863,7224,7225,7227],{},[39,7226,111],{"stretchy":101},[35,7228,1336],{},[47,7230,7231],{"encoding":49},"(X \\perp\\!\\!\\!\\perp_d Y \\mid S)_G",[15,7233,7235,7262,7313,7331],{"className":7234,"ariaHidden":41},[54],[15,7236,7238,7241,7244,7247,7250,7253,7256,7259],{"className":7237},[58],[15,7239],{"className":7240,"style":124},[62],[15,7242,102],{"className":7243},[132],[15,7245,37],{"className":7246,"style":69},[67,68],[15,7248],{"className":7249,"style":199},[77],[15,7251,236],{"className":7252},[203],[15,7254],{"className":7255,"style":274},[77],[15,7257],{"className":7258,"style":274},[77],[15,7260],{"className":7261,"style":274},[77],[15,7263,7265,7269,7310],{"className":7264},[58],[15,7266],{"className":7267,"style":7268},[62],"height:0.8444em;vertical-align:-0.15em;",[15,7270,7272,7275],{"className":7271},[203],[15,7273,236],{"className":7274},[203],[15,7276,7278],{"className":7277},[918],[15,7279,7281,7302],{"className":7280},[922,923],[15,7282,7284,7299],{"className":7283},[927],[15,7285,7287],{"className":7286,"style":2688},[931],[15,7288,7290,7293],{"style":7289},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[15,7291],{"className":7292,"style":940},[939],[15,7294,7296],{"className":7295},[944,945,946,947],[15,7297,696],{"className":7298},[67,68,947],[15,7300,955],{"className":7301},[954],[15,7303,7305],{"className":7304},[927],[15,7306,7308],{"className":7307,"style":962},[931],[15,7309],{},[15,7311],{"className":7312,"style":199},[77],[15,7314,7316,7319,7322,7325,7328],{"className":7315},[58],[15,7317],{"className":7318,"style":124},[62],[15,7320,45],{"className":7321,"style":82},[67,68],[15,7323],{"className":7324,"style":199},[77],[15,7326,170],{"className":7327},[203],[15,7329],{"className":7330,"style":199},[77],[15,7332,7334,7337,7340],{"className":7333},[58],[15,7335],{"className":7336,"style":124},[62],[15,7338,3779],{"className":7339,"style":1396},[67,68],[15,7341,7343,7346],{"className":7342},[148],[15,7344,111],{"className":7345},[148],[15,7347,7349],{"className":7348},[918],[15,7350,7352,7373],{"className":7351},[922,923],[15,7353,7355,7370],{"className":7354},[927],[15,7356,7359],{"className":7357,"style":7358},[931],"height:0.3283em;",[15,7360,7361,7364],{"style":7289},[15,7362],{"className":7363,"style":940},[939],[15,7365,7367],{"className":7366},[944,945,946,947],[15,7368,1336],{"className":7369},[67,68,947],[15,7371,955],{"className":7372},[954],[15,7374,7376],{"className":7375},[927],[15,7377,7379],{"className":7378,"style":962},[931],[15,7380],{},[1314,7382,7383],{},[11,7384,7385,7388,7389,7417,7418,7446,7447,7777,7778,7781,7782,7810,7811,7839,7840,7843,7844,7872,7873,2249],{},[305,7386,7387],{},"定理 1.1（图 - 分布对应定理，Verma & Pearl, 1988）"," 设分布 ",[15,7390,7392,7405],{"className":7391,"translate":19},[18],[15,7393,7395],{"className":7394},[23],[25,7396,7397],{"xmlns":27},[29,7398,7399,7403],{},[32,7400,7401],{},[35,7402,98],{},[47,7404,98],{"encoding":49},[15,7406,7408],{"className":7407,"ariaHidden":41},[54],[15,7409,7411,7414],{"className":7410},[58],[15,7412],{"className":7413,"style":299},[62],[15,7415,98],{"className":7416,"style":128},[67,68]," 由与 DAG ",[15,7419,7421,7434],{"className":7420,"translate":19},[18],[15,7422,7424],{"className":7423},[23],[25,7425,7426],{"xmlns":27},[29,7427,7428,7432],{},[32,7429,7430],{},[35,7431,1336],{},[47,7433,1336],{"encoding":49},[15,7435,7437],{"className":7436,"ariaHidden":41},[54],[15,7438,7440,7443],{"className":7439},[58],[15,7441],{"className":7442,"style":299},[62],[15,7444,1336],{"className":7445},[67,68]," 相容的 SCM 生成（见第二部分马尔可夫性假设）。则：\n",[15,7448,7450,7526],{"className":7449,"translate":19},[18],[15,7451,7453],{"className":7452},[23],[25,7454,7455],{"xmlns":27},[29,7456,7457,7523],{},[32,7458,7459,7461,7463,7465,7467,7469,7471,7477,7479,7481,7483,7489,7492,7495,7497,7499,7501,7503,7505,7507,7509,7511,7513,7515,7518,7520],{},[39,7460,102],{"stretchy":101},[35,7462,37],{},[39,7464,236],{},[238,7466,240],{},[238,7468,240],{},[238,7470,240],{},[863,7472,7473,7475],{},[39,7474,236],{},[35,7476,696],{},[35,7478,45],{},[39,7480,170],{},[35,7482,3779],{},[863,7484,7485,7487],{},[39,7486,111],{"stretchy":101},[35,7488,1336],{},[238,7490,7491],{},"  ",[39,7493,7494],{},"⟹",[238,7496,7491],{},[35,7498,37],{},[39,7500,236],{},[238,7502,240],{},[238,7504,240],{},[238,7506,240],{},[39,7508,236],{},[35,7510,45],{},[39,7512,170],{},[35,7514,3779],{},[238,7516,7517],{}," 在 ",[35,7519,98],{},[238,7521,7522],{}," 中成立",[47,7524,7525],{"encoding":49},"(X \\perp\\!\\!\\!\\perp_d Y \\mid S)_G \\implies X \\perp\\!\\!\\!\\perp Y \\mid S \\text{ 在 } P \\text{ 中成立}",[15,7527,7529,7556,7605,7623,7687,7711,7723,7741],{"className":7528,"ariaHidden":41},[54],[15,7530,7532,7535,7538,7541,7544,7547,7550,7553],{"className":7531},[58],[15,7533],{"className":7534,"style":124},[62],[15,7536,102],{"className":7537},[132],[15,7539,37],{"className":7540,"style":69},[67,68],[15,7542],{"className":7543,"style":199},[77],[15,7545,236],{"className":7546},[203],[15,7548],{"className":7549,"style":274},[77],[15,7551],{"className":7552,"style":274},[77],[15,7554],{"className":7555,"style":274},[77],[15,7557,7559,7562,7602],{"className":7558},[58],[15,7560],{"className":7561,"style":7268},[62],[15,7563,7565,7568],{"className":7564},[203],[15,7566,236],{"className":7567},[203],[15,7569,7571],{"className":7570},[918],[15,7572,7574,7594],{"className":7573},[922,923],[15,7575,7577,7591],{"className":7576},[927],[15,7578,7580],{"className":7579,"style":2688},[931],[15,7581,7582,7585],{"style":7289},[15,7583],{"className":7584,"style":940},[939],[15,7586,7588],{"className":7587},[944,945,946,947],[15,7589,696],{"className":7590},[67,68,947],[15,7592,955],{"className":7593},[954],[15,7595,7597],{"className":7596},[927],[15,7598,7600],{"className":7599,"style":962},[931],[15,7601],{},[15,7603],{"className":7604,"style":199},[77],[15,7606,7608,7611,7614,7617,7620],{"className":7607},[58],[15,7609],{"className":7610,"style":124},[62],[15,7612,45],{"className":7613,"style":82},[67,68],[15,7615],{"className":7616,"style":199},[77],[15,7618,170],{"className":7619},[203],[15,7621],{"className":7622,"style":199},[77],[15,7624,7626,7629,7632,7672,7675,7678,7681,7684],{"className":7625},[58],[15,7627],{"className":7628,"style":124},[62],[15,7630,3779],{"className":7631,"style":1396},[67,68],[15,7633,7635,7638],{"className":7634},[148],[15,7636,111],{"className":7637},[148],[15,7639,7641],{"className":7640},[918],[15,7642,7644,7664],{"className":7643},[922,923],[15,7645,7647,7661],{"className":7646},[927],[15,7648,7650],{"className":7649,"style":7358},[931],[15,7651,7652,7655],{"style":7289},[15,7653],{"className":7654,"style":940},[939],[15,7656,7658],{"className":7657},[944,945,946,947],[15,7659,1336],{"className":7660},[67,68,947],[15,7662,955],{"className":7663},[954],[15,7665,7667],{"className":7666},[927],[15,7668,7670],{"className":7669,"style":962},[931],[15,7671],{},[15,7673],{"className":7674,"style":199},[77],[15,7676],{"className":7677,"style":199},[77],[15,7679,7494],{"className":7680},[203],[15,7682],{"className":7683,"style":199},[77],[15,7685],{"className":7686,"style":199},[77],[15,7688,7690,7693,7696,7699,7702,7705,7708],{"className":7689},[58],[15,7691],{"className":7692,"style":261},[62],[15,7694,37],{"className":7695,"style":69},[67,68],[15,7697],{"className":7698,"style":199},[77],[15,7700,236],{"className":7701},[203],[15,7703],{"className":7704,"style":274},[77],[15,7706],{"className":7707,"style":274},[77],[15,7709],{"className":7710,"style":274},[77],[15,7712,7714,7717,7720],{"className":7713},[58],[15,7715],{"className":7716,"style":261},[62],[15,7718,236],{"className":7719},[203],[15,7721],{"className":7722,"style":199},[77],[15,7724,7726,7729,7732,7735,7738],{"className":7725},[58],[15,7727],{"className":7728,"style":124},[62],[15,7730,45],{"className":7731,"style":82},[67,68],[15,7733],{"className":7734,"style":199},[77],[15,7736,170],{"className":7737},[203],[15,7739],{"className":7740,"style":199},[77],[15,7742,7744,7747,7750,7764,7767],{"className":7743},[58],[15,7745],{"className":7746,"style":299},[62],[15,7748,3779],{"className":7749,"style":1396},[67,68],[15,7751,7753,7756,7761],{"className":7752},[67,4123],[15,7754,3926],{"className":7755},[67],[15,7757,7760],{"className":7758},[67,7759],"cjk_fallback","在",[15,7762,3926],{"className":7763},[67],[15,7765,98],{"className":7766,"style":128},[67,68],[15,7768,7770,7773],{"className":7769},[67,4123],[15,7771,3926],{"className":7772},[67],[15,7774,7776],{"className":7775},[67,7759],"中成立","\n即 d-分离是概率独立性的",[305,7779,7780],{},"充分条件","。若进一步假设 ",[15,7783,7785,7798],{"className":7784,"translate":19},[18],[15,7786,7788],{"className":7787},[23],[25,7789,7790],{"xmlns":27},[29,7791,7792,7796],{},[32,7793,7794],{},[35,7795,98],{},[47,7797,98],{"encoding":49},[15,7799,7801],{"className":7800,"ariaHidden":41},[54],[15,7802,7804,7807],{"className":7803},[58],[15,7805],{"className":7806,"style":299},[62],[15,7808,98],{"className":7809,"style":128},[67,68]," 相对于 ",[15,7812,7814,7827],{"className":7813,"translate":19},[18],[15,7815,7817],{"className":7816},[23],[25,7818,7819],{"xmlns":27},[29,7820,7821,7825],{},[32,7822,7823],{},[35,7824,1336],{},[47,7826,1336],{"encoding":49},[15,7828,7830],{"className":7829,"ariaHidden":41},[54],[15,7831,7833,7836],{"className":7832},[58],[15,7834],{"className":7835,"style":299},[62],[15,7837,1336],{"className":7838},[67,68]," 满足",[305,7841,7842],{},"忠实性（faithfulness）","——即 ",[15,7845,7847,7860],{"className":7846,"translate":19},[18],[15,7848,7850],{"className":7849},[23],[25,7851,7852],{"xmlns":27},[29,7853,7854,7858],{},[32,7855,7856],{},[35,7857,98],{},[47,7859,98],{"encoding":49},[15,7861,7863],{"className":7862,"ariaHidden":41},[54],[15,7864,7866,7869],{"className":7865},[58],[15,7867],{"className":7868,"style":299},[62],[15,7870,98],{"className":7871,"style":128},[67,68]," 中不存在的独立性都不是偶然的参数取消所致——则该蕴含关系可加强为",[305,7874,7875],{},"当且仅当",[11,7877,7878,7879,7907,7908,7911,7912,2249],{},"这一定理的实践意义极为重大：它把「该不该在回归分析中控制某个变量」这一问题，从一个凭经验拍脑袋的决策，转化为一个在图上可机械判定的组合问题。控制混杂因子（叉结构中的 ",[15,7880,7882,7895],{"className":7881,"translate":19},[18],[15,7883,7885],{"className":7884},[23],[25,7886,7887],{"xmlns":27},[29,7888,7889,7893],{},[32,7890,7891],{},[35,7892,4214],{},[47,7894,4214],{"encoding":49},[15,7896,7898],{"className":7897,"ariaHidden":41},[54],[15,7899,7901,7904],{"className":7900},[58],[15,7902],{"className":7903,"style":299},[62],[15,7905,4214],{"className":7906,"style":4243},[67,68],"）能够正确地消除虚假关联；但控制对撞因子（或对撞因子的后代）却会人为",[305,7909,7910],{},"制造","虚假关联——这正是所谓「越多变量控制越严谨」这一朴素直觉在因果推断框架下失效的根本原因，实践中称为",[305,7913,7914],{},"对撞偏差引发的过度控制谬误（overcontrol bias）",[1309,7916,7918],{"id":7917},"_14-因果图的来源因果发现","1.4 因果图的来源：因果发现",[11,7920,7921],{},"定义 1.4 之后我们强调过：图中的每一条边都是不可从数据中验证的结构性假设。但一个自然的问题是——这些假设究竟从哪里来？实践中主要有四个来源：",[7923,7924,7925,7931,8046,8209],"ol",{},[510,7926,7927,7930],{},[305,7928,7929],{},"领域知识与物理机制","：电路中的欧姆定律、燃烧过程中的氧化反应，机制本身规定了方向；",[510,7932,7933,7936,7937,7965,7966,365,7994,8045],{},[305,7934,7935],{},"时间先后","：若 ",[15,7938,7940,7953],{"className":7939,"translate":19},[18],[15,7941,7943],{"className":7942},[23],[25,7944,7945],{"xmlns":27},[29,7946,7947,7951],{},[32,7948,7949],{},[35,7950,37],{},[47,7952,37],{"encoding":49},[15,7954,7956],{"className":7955,"ariaHidden":41},[54],[15,7957,7959,7962],{"className":7958},[58],[15,7960],{"className":7961,"style":299},[62],[15,7963,37],{"className":7964,"style":69},[67,68]," 在时间上先于 ",[15,7967,7969,7982],{"className":7968,"translate":19},[18],[15,7970,7972],{"className":7971},[23],[25,7973,7974],{"xmlns":27},[29,7975,7976,7980],{},[32,7977,7978],{},[35,7979,45],{},[47,7981,45],{"encoding":49},[15,7983,7985],{"className":7984,"ariaHidden":41},[54],[15,7986,7988,7991],{"className":7987},[58],[15,7989],{"className":7990,"style":299},[62],[15,7992,45],{"className":7993,"style":82},[67,68],[15,7995,7997,8015],{"className":7996,"translate":19},[18],[15,7998,8000],{"className":7999},[23],[25,8001,8002],{"xmlns":27},[29,8003,8004,8012],{},[32,8005,8006,8008,8010],{},[35,8007,45],{},[39,8009,1846],{},[35,8011,37],{},[47,8013,8014],{"encoding":49},"Y \\to X",[15,8016,8018,8036],{"className":8017,"ariaHidden":41},[54],[15,8019,8021,8024,8027,8030,8033],{"className":8020},[58],[15,8022],{"className":8023,"style":299},[62],[15,8025,45],{"className":8026,"style":82},[67,68],[15,8028],{"className":8029,"style":199},[77],[15,8031,1846],{"className":8032},[203],[15,8034],{"className":8035,"style":199},[77],[15,8037,8039,8042],{"className":8038},[58],[15,8040],{"className":8041,"style":299},[62],[15,8043,37],{"className":8044,"style":69},[67,68]," 被排除；但反向并不自动成立，因为共同原因仍可能同时影响二者；",[510,8047,8048,505,8051,8122,8123,8151,8152,4697,8180,8208],{},[305,8049,8050],{},"实验干预",[15,8052,8054,8080],{"className":8053,"translate":19},[18],[15,8055,8057],{"className":8056},[23],[25,8058,8059],{"xmlns":27},[29,8060,8061,8077],{},[32,8062,8063,8065,8067,8069,8071,8073,8075],{},[35,8064,696],{},[35,8066,699],{},[39,8068,102],{"stretchy":101},[35,8070,37],{},[39,8072,602],{},[35,8074,539],{},[39,8076,111],{"stretchy":101},[47,8078,8079],{"encoding":49},"do(X=x)",[15,8081,8083,8110],{"className":8082,"ariaHidden":41},[54],[15,8084,8086,8089,8092,8095,8098,8101,8104,8107],{"className":8085},[58],[15,8087],{"className":8088,"style":124},[62],[15,8090,696],{"className":8091},[67,68],[15,8093,699],{"className":8094},[67,68],[15,8096,102],{"className":8097},[132],[15,8099,37],{"className":8100,"style":69},[67,68],[15,8102],{"className":8103,"style":199},[77],[15,8105,602],{"className":8106},[203],[15,8108],{"className":8109,"style":199},[77],[15,8111,8113,8116,8119],{"className":8112},[58],[15,8114],{"className":8115,"style":124},[62],[15,8117,539],{"className":8118},[67,68],[15,8120,111],{"className":8121},[148]," 会切断 ",[15,8124,8126,8139],{"className":8125,"translate":19},[18],[15,8127,8129],{"className":8128},[23],[25,8130,8131],{"xmlns":27},[29,8132,8133,8137],{},[32,8134,8135],{},[35,8136,37],{},[47,8138,37],{"encoding":49},[15,8140,8142],{"className":8141,"ariaHidden":41},[54],[15,8143,8145,8148],{"className":8144},[58],[15,8146],{"className":8147,"style":299},[62],[15,8149,37],{"className":8150,"style":69},[67,68]," 的全部入边，直接暴露 ",[15,8153,8155,8168],{"className":8154,"translate":19},[18],[15,8156,8158],{"className":8157},[23],[25,8159,8160],{"xmlns":27},[29,8161,8162,8166],{},[32,8163,8164],{},[35,8165,37],{},[47,8167,37],{"encoding":49},[15,8169,8171],{"className":8170,"ariaHidden":41},[54],[15,8172,8174,8177],{"className":8173},[58],[15,8175],{"className":8176,"style":299},[62],[15,8178,37],{"className":8179,"style":69},[67,68],[15,8181,8183,8196],{"className":8182,"translate":19},[18],[15,8184,8186],{"className":8185},[23],[25,8187,8188],{"xmlns":27},[29,8189,8190,8194],{},[32,8191,8192],{},[35,8193,45],{},[47,8195,45],{"encoding":49},[15,8197,8199],{"className":8198,"ariaHidden":41},[54],[15,8200,8202,8205],{"className":8201},[58],[15,8203],{"className":8204,"style":299},[62],[15,8206,45],{"className":8207,"style":82},[67,68]," 的作用方向，是最可靠的来源；",[510,8210,8211,8214],{},[305,8212,8213],{},"因果发现算法","：在额外假设下，由观测数据自动推断图的结构。",[11,8216,8217,8218,2249],{},"第 4 条值得展开，因为它常被误解为「从数据中读出因果」，而其真实含义恰恰相反——",[305,8219,8220],{},"它是关于「在何种假设下，数据中的哪些部分能够约束图」的一组定理",[11,8222,8223,8224,8227,8228,8283],{},"首先要承认一个否定性结论：",[305,8225,8226],{},"仅凭观测分布，我们至多只能确定图所属的一个马尔可夫等价类（Markov equivalence class），而非图本身","。以三个变量 ",[15,8229,8231,8253],{"className":8230,"translate":19},[18],[15,8232,8234],{"className":8233},[23],[25,8235,8236],{"xmlns":27},[29,8237,8238,8250],{},[32,8239,8240,8242,8244,8246,8248],{},[35,8241,37],{},[39,8243,42],{"separator":41},[35,8245,45],{},[39,8247,42],{"separator":41},[35,8249,4214],{},[47,8251,8252],{"encoding":49},"X, Y, Z",[15,8254,8256],{"className":8255,"ariaHidden":41},[54],[15,8257,8259,8262,8265,8268,8271,8274,8277,8280],{"className":8258},[58],[15,8260],{"className":8261,"style":63},[62],[15,8263,37],{"className":8264,"style":69},[67,68],[15,8266,42],{"className":8267},[73],[15,8269],{"className":8270,"style":78},[77],[15,8272,45],{"className":8273,"style":82},[67,68],[15,8275,42],{"className":8276},[73],[15,8278],{"className":8279,"style":78},[77],[15,8281,4214],{"className":8282,"style":4243},[67,68]," 为例，下面三个 DAG",[4118,8285,8288],{"className":8286,"code":8287,"language":4123},[4121],"   X ──→ Y ──→ Z        X ←── Y ──→ Z        X ←── Y ←── Z\n",[4125,8289,8287],{"__ignoreMap":4127},[11,8291,8292,8293,8399,8400,431,8507,8606,8607,8680,8681,8757,8758,2249],{},"所蕴含的条件独立关系完全相同：三者都蕴含 ",[15,8294,8296,8321],{"className":8295,"translate":19},[18],[15,8297,8299],{"className":8298},[23],[25,8300,8301],{"xmlns":27},[29,8302,8303,8319],{},[32,8304,8305,8307,8309,8311,8313,8315,8317],{},[35,8306,37],{},[39,8308,4433],{},[238,8310,240],{},[238,8312,240],{},[238,8314,240],{},[39,8316,236],{},[35,8318,45],{},[47,8320,4446],{"encoding":49},[15,8322,8324,8378,8390],{"className":8323,"ariaHidden":41},[54],[15,8325,8327,8330,8333,8336,8363,8366,8369,8372,8375],{"className":8326},[58],[15,8328],{"className":8329,"style":4456},[62],[15,8331,37],{"className":8332,"style":69},[67,68],[15,8334],{"className":8335,"style":199},[77],[15,8337,8339],{"className":8338},[203],[15,8340,8342],{"className":8341},[67,4469],[15,8343,8345],{"className":8344},[4473],[15,8346,8348,8351,8360],{"className":8347},[4477],[15,8349],{"className":8350,"style":4456},[62],[15,8352,8354],{"className":8353},[4484],[15,8355,8357],{"className":8356},[67],[15,8358,4491],{"className":8359},[203],[15,8361],{"className":8362},[4495],[15,8364],{"className":8365},[77,4499],[15,8367,236],{"className":8368},[203],[15,8370],{"className":8371,"style":274},[77],[15,8373],{"className":8374,"style":274},[77],[15,8376],{"className":8377,"style":274},[77],[15,8379,8381,8384,8387],{"className":8380},[58],[15,8382],{"className":8383,"style":261},[62],[15,8385,236],{"className":8386},[203],[15,8388],{"className":8389,"style":199},[77],[15,8391,8393,8396],{"className":8392},[58],[15,8394],{"className":8395,"style":299},[62],[15,8397,45],{"className":8398,"style":82},[67,68],"、",[15,8401,8403,8429],{"className":8402,"translate":19},[18],[15,8404,8406],{"className":8405},[23],[25,8407,8408],{"xmlns":27},[29,8409,8410,8426],{},[32,8411,8412,8414,8416,8418,8420,8422,8424],{},[35,8413,45],{},[39,8415,4433],{},[238,8417,240],{},[238,8419,240],{},[238,8421,240],{},[39,8423,236],{},[35,8425,4214],{},[47,8427,8428],{"encoding":49},"Y \\not\\perp\\!\\!\\!\\perp Z",[15,8430,8432,8486,8498],{"className":8431,"ariaHidden":41},[54],[15,8433,8435,8438,8441,8444,8471,8474,8477,8480,8483],{"className":8434},[58],[15,8436],{"className":8437,"style":4456},[62],[15,8439,45],{"className":8440,"style":82},[67,68],[15,8442],{"className":8443,"style":199},[77],[15,8445,8447],{"className":8446},[203],[15,8448,8450],{"className":8449},[67,4469],[15,8451,8453],{"className":8452},[4473],[15,8454,8456,8459,8468],{"className":8455},[4477],[15,8457],{"className":8458,"style":4456},[62],[15,8460,8462],{"className":8461},[4484],[15,8463,8465],{"className":8464},[67],[15,8466,4491],{"className":8467},[203],[15,8469],{"className":8470},[4495],[15,8472],{"className":8473},[77,4499],[15,8475,236],{"className":8476},[203],[15,8478],{"className":8479,"style":274},[77],[15,8481],{"className":8482,"style":274},[77],[15,8484],{"className":8485,"style":274},[77],[15,8487,8489,8492,8495],{"className":8488},[58],[15,8490],{"className":8491,"style":261},[62],[15,8493,236],{"className":8494},[203],[15,8496],{"className":8497,"style":199},[77],[15,8499,8501,8504],{"className":8500},[58],[15,8502],{"className":8503,"style":299},[62],[15,8505,4214],{"className":8506,"style":4243},[67,68],[15,8508,8510,8540],{"className":8509,"translate":19},[18],[15,8511,8513],{"className":8512},[23],[25,8514,8515],{"xmlns":27},[29,8516,8517,8537],{},[32,8518,8519,8521,8523,8525,8527,8529,8531,8533,8535],{},[35,8520,37],{},[39,8522,236],{},[238,8524,240],{},[238,8526,240],{},[238,8528,240],{},[39,8530,236],{},[35,8532,4214],{},[39,8534,170],{},[35,8536,45],{},[47,8538,8539],{"encoding":49},"X \\perp\\!\\!\\!\\perp Z \\mid Y",[15,8541,8543,8567,8579,8597],{"className":8542,"ariaHidden":41},[54],[15,8544,8546,8549,8552,8555,8558,8561,8564],{"className":8545},[58],[15,8547],{"className":8548,"style":261},[62],[15,8550,37],{"className":8551,"style":69},[67,68],[15,8553],{"className":8554,"style":199},[77],[15,8556,236],{"className":8557},[203],[15,8559],{"className":8560,"style":274},[77],[15,8562],{"className":8563,"style":274},[77],[15,8565],{"className":8566,"style":274},[77],[15,8568,8570,8573,8576],{"className":8569},[58],[15,8571],{"className":8572,"style":261},[62],[15,8574,236],{"className":8575},[203],[15,8577],{"className":8578,"style":199},[77],[15,8580,8582,8585,8588,8591,8594],{"className":8581},[58],[15,8583],{"className":8584,"style":124},[62],[15,8586,4214],{"className":8587,"style":4243},[67,68],[15,8589],{"className":8590,"style":199},[77],[15,8592,170],{"className":8593},[203],[15,8595],{"className":8596,"style":199},[77],[15,8598,8600,8603],{"className":8599},[58],[15,8601],{"className":8602,"style":299},[62],[15,8604,45],{"className":8605,"style":82},[67,68],"，因此在任何与之相容的分布下，三者产生的数据在统计上无法区分。而第四个图，即对撞结构 ",[15,8608,8610,8632],{"className":8609,"translate":19},[18],[15,8611,8613],{"className":8612},[23],[25,8614,8615],{"xmlns":27},[29,8616,8617,8629],{},[32,8618,8619,8621,8623,8625,8627],{},[35,8620,37],{},[39,8622,1846],{},[35,8624,45],{},[39,8626,4882],{},[35,8628,4214],{},[47,8630,8631],{"encoding":49},"X \\to Y \\leftarrow Z",[15,8633,8635,8653,8671],{"className":8634,"ariaHidden":41},[54],[15,8636,8638,8641,8644,8647,8650],{"className":8637},[58],[15,8639],{"className":8640,"style":299},[62],[15,8642,37],{"className":8643,"style":69},[67,68],[15,8645],{"className":8646,"style":199},[77],[15,8648,1846],{"className":8649},[203],[15,8651],{"className":8652,"style":199},[77],[15,8654,8656,8659,8662,8665,8668],{"className":8655},[58],[15,8657],{"className":8658,"style":299},[62],[15,8660,45],{"className":8661,"style":82},[67,68],[15,8663],{"className":8664,"style":199},[77],[15,8666,4882],{"className":8667},[203],[15,8669],{"className":8670,"style":199},[77],[15,8672,8674,8677],{"className":8673},[58],[15,8675],{"className":8676,"style":299},[62],[15,8678,4214],{"className":8679,"style":4243},[67,68],"，蕴含的是边际独立 ",[15,8682,8684,8709],{"className":8683,"translate":19},[18],[15,8685,8687],{"className":8686},[23],[25,8688,8689],{"xmlns":27},[29,8690,8691,8707],{},[32,8692,8693,8695,8697,8699,8701,8703,8705],{},[35,8694,37],{},[39,8696,236],{},[238,8698,240],{},[238,8700,240],{},[238,8702,240],{},[39,8704,236],{},[35,8706,45],{},[47,8708,251],{"encoding":49},[15,8710,8712,8736,8748],{"className":8711,"ariaHidden":41},[54],[15,8713,8715,8718,8721,8724,8727,8730,8733],{"className":8714},[58],[15,8716],{"className":8717,"style":261},[62],[15,8719,37],{"className":8720,"style":69},[67,68],[15,8722],{"className":8723,"style":199},[77],[15,8725,236],{"className":8726},[203],[15,8728],{"className":8729,"style":274},[77],[15,8731],{"className":8732,"style":274},[77],[15,8734],{"className":8735,"style":274},[77],[15,8737,8739,8742,8745],{"className":8738},[58],[15,8740],{"className":8741,"style":261},[62],[15,8743,236],{"className":8744},[203],[15,8746],{"className":8747,"style":199},[77],[15,8749,8751,8754],{"className":8750},[58],[15,8752],{"className":8753,"style":299},[62],[15,8755,45],{"className":8756,"style":82},[67,68],"，与前三个不同，因此",[305,8759,8760],{},"它可以被数据认出来",[11,8762,8763,8764,8767,8768,2249],{},"这一观察可以推广为一个一般结论：",[305,8765,8766],{},"观测分布唯一确定的是图的骨架（skeleton，忽略方向的边集）以及所有的对撞结构（v-结构），其余边的方向原则上不可识别","。这解释了为什么因果发现算法的输出往往不是一个 DAG，而是一张带有部分无向边的",[305,8769,8770],{},"本质图（CPDAG，亦称 pattern）",[11,8772,8773],{},"要在此基础上进一步定向，必须引入超出分布本身的假设，主要有三条路线：",[507,8775,8776,8835,8841],{},[510,8777,8778,8781,8782,8834],{},[305,8779,8780],{},"约束式方法（constraint-based）","：以忠实性假设为前提，反复检验条件独立关系并据此定向，代表算法为 PC。若允许存在未观测的混杂变量，则须改用 FCI，其输出（PAG）以双向边 ",[15,8783,8785,8804],{"className":8784,"translate":19},[18],[15,8786,8788],{"className":8787},[23],[25,8789,8790],{"xmlns":27},[29,8791,8792,8801],{},[32,8793,8794,8796,8799],{},[35,8795,37],{},[39,8797,8798],{},"↔",[35,8800,45],{},[47,8802,8803],{"encoding":49},"X \\leftrightarrow Y",[15,8805,8807,8825],{"className":8806,"ariaHidden":41},[54],[15,8808,8810,8813,8816,8819,8822],{"className":8809},[58],[15,8811],{"className":8812,"style":299},[62],[15,8814,37],{"className":8815,"style":69},[67,68],[15,8817],{"className":8818,"style":199},[77],[15,8820,8798],{"className":8821},[203],[15,8823],{"className":8824,"style":199},[77],[15,8826,8828,8831],{"className":8827},[58],[15,8829],{"className":8830,"style":299},[62],[15,8832,45],{"className":8833,"style":82},[67,68]," 显式标示「二者之间存在未观测的共同原因」。",[510,8836,8837,8840],{},[305,8838,8839],{},"评分式方法（score-based）","：为每个 DAG 或等价类定义评分（如 BIC、贝叶斯后验），在等价类空间上做搜索，代表算法为 GES。它与约束式方法一样，仍然只能恢复到马尔可夫等价类。",[510,8842,8843,8846,8847,3098,8939,9016,9017,9068,9069,9119,9120,9123,9124,9152],{},[305,8844,8845],{},"函数式方法（functional \u002F additive noise）","：假设结构方程取加性噪声形式 ",[15,8848,8850,8881],{"className":8849,"translate":19},[18],[15,8851,8853],{"className":8852},[23],[25,8854,8855],{"xmlns":27},[29,8856,8857,8878],{},[32,8858,8859,8861,8864,8866,8868,8870,8872,8874,8876],{},[35,8860,45],{},[39,8862,8863],{},":",[39,8865,602],{},[35,8867,5724],{},[39,8869,102],{"stretchy":101},[35,8871,37],{},[39,8873,111],{"stretchy":101},[39,8875,2894],{},[35,8877,2458],{},[47,8879,8880],{"encoding":49},"Y := f(X) + U",[15,8882,8884,8903,8930],{"className":8883,"ariaHidden":41},[54],[15,8885,8887,8890,8893,8896,8900],{"className":8886},[58],[15,8888],{"className":8889,"style":299},[62],[15,8891,45],{"className":8892,"style":82},[67,68],[15,8894],{"className":8895,"style":199},[77],[15,8897,8899],{"className":8898},[203],":=",[15,8901],{"className":8902,"style":199},[77],[15,8904,8906,8909,8912,8915,8918,8921,8924,8927],{"className":8905},[58],[15,8907],{"className":8908,"style":124},[62],[15,8910,5724],{"className":8911,"style":5772},[67,68],[15,8913,102],{"className":8914},[132],[15,8916,37],{"className":8917,"style":69},[67,68],[15,8919,111],{"className":8920},[148],[15,8922],{"className":8923,"style":82},[77],[15,8925,2894],{"className":8926},[1648],[15,8928],{"className":8929,"style":82},[77],[15,8931,8933,8936],{"className":8932},[58],[15,8934],{"className":8935,"style":299},[62],[15,8937,2458],{"className":8938,"style":2570},[67,68],[15,8940,8942,8968],{"className":8941,"translate":19},[18],[15,8943,8945],{"className":8944},[23],[25,8946,8947],{"xmlns":27},[29,8948,8949,8965],{},[32,8950,8951,8953,8955,8957,8959,8961,8963],{},[35,8952,37],{},[39,8954,236],{},[238,8956,240],{},[238,8958,240],{},[238,8960,240],{},[39,8962,236],{},[35,8964,2458],{},[47,8966,8967],{"encoding":49},"X \\perp\\!\\!\\!\\perp U",[15,8969,8971,8995,9007],{"className":8970,"ariaHidden":41},[54],[15,8972,8974,8977,8980,8983,8986,8989,8992],{"className":8973},[58],[15,8975],{"className":8976,"style":261},[62],[15,8978,37],{"className":8979,"style":69},[67,68],[15,8981],{"className":8982,"style":199},[77],[15,8984,236],{"className":8985},[203],[15,8987],{"className":8988,"style":274},[77],[15,8990],{"className":8991,"style":274},[77],[15,8993],{"className":8994,"style":274},[77],[15,8996,8998,9001,9004],{"className":8997},[58],[15,8999],{"className":9000,"style":261},[62],[15,9002,236],{"className":9003},[203],[15,9005],{"className":9006,"style":199},[77],[15,9008,9010,9013],{"className":9009},[58],[15,9011],{"className":9012,"style":299},[62],[15,9014,2458],{"className":9015,"style":2570},[67,68],"。此时「",[15,9018,9020,9038],{"className":9019,"translate":19},[18],[15,9021,9023],{"className":9022},[23],[25,9024,9025],{"xmlns":27},[29,9026,9027,9035],{},[32,9028,9029,9031,9033],{},[35,9030,37],{},[39,9032,1846],{},[35,9034,45],{},[47,9036,9037],{"encoding":49},"X \\to Y",[15,9039,9041,9059],{"className":9040,"ariaHidden":41},[54],[15,9042,9044,9047,9050,9053,9056],{"className":9043},[58],[15,9045],{"className":9046,"style":299},[62],[15,9048,37],{"className":9049,"style":69},[67,68],[15,9051],{"className":9052,"style":199},[77],[15,9054,1846],{"className":9055},[203],[15,9057],{"className":9058,"style":199},[77],[15,9060,9062,9065],{"className":9061},[58],[15,9063],{"className":9064,"style":299},[62],[15,9066,45],{"className":9067,"style":82},[67,68],"」与「",[15,9070,9072,9089],{"className":9071,"translate":19},[18],[15,9073,9075],{"className":9074},[23],[25,9076,9077],{"xmlns":27},[29,9078,9079,9087],{},[32,9080,9081,9083,9085],{},[35,9082,45],{},[39,9084,1846],{},[35,9086,37],{},[47,9088,8014],{"encoding":49},[15,9090,9092,9110],{"className":9091,"ariaHidden":41},[54],[15,9093,9095,9098,9101,9104,9107],{"className":9094},[58],[15,9096],{"className":9097,"style":299},[62],[15,9099,45],{"className":9100,"style":82},[67,68],[15,9102],{"className":9103,"style":199},[77],[15,9105,1846],{"className":9106},[203],[15,9108],{"className":9109,"style":199},[77],[15,9111,9113,9116],{"className":9112},[58],[15,9114],{"className":9115,"style":299},[62],[15,9117,37],{"className":9118,"style":69},[67,68],"」两个模型一般",[305,9121,9122],{},"不能互相拟合","——反向模型的噪声项会与输入相关，除非 ",[15,9125,9127,9140],{"className":9126,"translate":19},[18],[15,9128,9130],{"className":9129},[23],[25,9131,9132],{"xmlns":27},[29,9133,9134,9138],{},[32,9135,9136],{},[35,9137,5724],{},[47,9139,5724],{"encoding":49},[15,9141,9143],{"className":9142,"ariaHidden":41},[54],[15,9144,9146,9149],{"className":9145},[58],[15,9147],{"className":9148,"style":4456},[62],[15,9150,5724],{"className":9151,"style":5772},[67,68]," 为线性且噪声为高斯。于是方向变得可识别，线性非高斯情形下即得到 LiNGAM 家族算法。代价是引入了比忠实性更强的函数类假设，且判定结果对该假设相当敏感。",[11,9154,9155,9156,9159],{},"综上，因果发现把「边从哪来」这一问题从纯粹的先验判断，部分地转化为「在给定假设下可被数据检验」的问题；但",[305,9157,9158],{},"这些假设本身（忠实性、无隐变量、函数类）仍然无法从数据中获得","。这与本文的核心立场一致：数据只能在结构给定的前提下发挥作用，结构本身必须来自数据之外。",[1314,9161,9162],{},[11,9163,9164,9167,9168,431,9196,9224,9225,431,9253,9281,9282,9359,9360,9432],{},[305,9165,9166],{},"例 1.5"," 若已知 ",[15,9169,9171,9184],{"className":9170,"translate":19},[18],[15,9172,9174],{"className":9173},[23],[25,9175,9176],{"xmlns":27},[29,9177,9178,9182],{},[32,9179,9180],{},[35,9181,37],{},[47,9183,37],{"encoding":49},[15,9185,9187],{"className":9186,"ariaHidden":41},[54],[15,9188,9190,9193],{"className":9189},[58],[15,9191],{"className":9192,"style":299},[62],[15,9194,37],{"className":9195,"style":69},[67,68],[15,9197,9199,9212],{"className":9198,"translate":19},[18],[15,9200,9202],{"className":9201},[23],[25,9203,9204],{"xmlns":27},[29,9205,9206,9210],{},[32,9207,9208],{},[35,9209,45],{},[47,9211,45],{"encoding":49},[15,9213,9215],{"className":9214,"ariaHidden":41},[54],[15,9216,9218,9221],{"className":9217},[58],[15,9219],{"className":9220,"style":299},[62],[15,9222,45],{"className":9223,"style":82},[67,68]," 依赖、",[15,9226,9228,9241],{"className":9227,"translate":19},[18],[15,9229,9231],{"className":9230},[23],[25,9232,9233],{"xmlns":27},[29,9234,9235,9239],{},[32,9236,9237],{},[35,9238,45],{},[47,9240,45],{"encoding":49},[15,9242,9244],{"className":9243,"ariaHidden":41},[54],[15,9245,9247,9250],{"className":9246},[58],[15,9248],{"className":9249,"style":299},[62],[15,9251,45],{"className":9252,"style":82},[67,68],[15,9254,9256,9269],{"className":9255,"translate":19},[18],[15,9257,9259],{"className":9258},[23],[25,9260,9261],{"xmlns":27},[29,9262,9263,9267],{},[32,9264,9265],{},[35,9266,4214],{},[47,9268,4214],{"encoding":49},[15,9270,9272],{"className":9271,"ariaHidden":41},[54],[15,9273,9275,9278],{"className":9274},[58],[15,9276],{"className":9277,"style":299},[62],[15,9279,4214],{"className":9280,"style":4243},[67,68]," 依赖，而又观测到 ",[15,9283,9285,9311],{"className":9284,"translate":19},[18],[15,9286,9288],{"className":9287},[23],[25,9289,9290],{"xmlns":27},[29,9291,9292,9308],{},[32,9293,9294,9296,9298,9300,9302,9304,9306],{},[35,9295,37],{},[39,9297,236],{},[238,9299,240],{},[238,9301,240],{},[238,9303,240],{},[39,9305,236],{},[35,9307,4214],{},[47,9309,9310],{"encoding":49},"X \\perp\\!\\!\\!\\perp Z",[15,9312,9314,9338,9350],{"className":9313,"ariaHidden":41},[54],[15,9315,9317,9320,9323,9326,9329,9332,9335],{"className":9316},[58],[15,9318],{"className":9319,"style":261},[62],[15,9321,37],{"className":9322,"style":69},[67,68],[15,9324],{"className":9325,"style":199},[77],[15,9327,236],{"className":9328},[203],[15,9330],{"className":9331,"style":274},[77],[15,9333],{"className":9334,"style":274},[77],[15,9336],{"className":9337,"style":274},[77],[15,9339,9341,9344,9347],{"className":9340},[58],[15,9342],{"className":9343,"style":261},[62],[15,9345,236],{"className":9346},[203],[15,9348],{"className":9349,"style":199},[77],[15,9351,9353,9356],{"className":9352},[58],[15,9354],{"className":9355,"style":299},[62],[15,9357,4214],{"className":9358,"style":4243},[67,68],"，则与之相容的三节点结构只剩下对撞 ",[15,9361,9363,9384],{"className":9362,"translate":19},[18],[15,9364,9366],{"className":9365},[23],[25,9367,9368],{"xmlns":27},[29,9369,9370,9382],{},[32,9371,9372,9374,9376,9378,9380],{},[35,9373,37],{},[39,9375,1846],{},[35,9377,45],{},[39,9379,4882],{},[35,9381,4214],{},[47,9383,8631],{"encoding":49},[15,9385,9387,9405,9423],{"className":9386,"ariaHidden":41},[54],[15,9388,9390,9393,9396,9399,9402],{"className":9389},[58],[15,9391],{"className":9392,"style":299},[62],[15,9394,37],{"className":9395,"style":69},[67,68],[15,9397],{"className":9398,"style":199},[77],[15,9400,1846],{"className":9401},[203],[15,9403],{"className":9404,"style":199},[77],[15,9406,9408,9411,9414,9417,9420],{"className":9407},[58],[15,9409],{"className":9410,"style":299},[62],[15,9412,45],{"className":9413,"style":82},[67,68],[15,9415],{"className":9416,"style":199},[77],[15,9418,4882],{"className":9419},[203],[15,9421],{"className":9422,"style":199},[77],[15,9424,9426,9429],{"className":9425},[58],[15,9427],{"className":9428,"style":299},[62],[15,9430,4214],{"className":9431,"style":4243},[67,68],"。这是因果发现中最基本的一条定向规则，也是「共同原因」与「因果链」两族结构唯一能被数据区分开的地方。",[1305,9434,9435],{"id":9435},"结构因果模型",[11,9437,9438,9439,9442],{},"因果图给出的是变量间依赖关系的",[305,9440,9441],{},"定性拓扑","，尚不包含足以计算具体数值的信息。要将因果图提升为可定量计算的生成模型，需要引入结构因果模型。",[1309,9444,9446],{"id":9445},"_21-scm-的形式化定义","2.1 SCM 的形式化定义",[1314,9448,9449,9571],{},[11,9450,9451,9454,9455,9570],{},[305,9452,9453],{},"定义 2.1（结构因果模型）"," 一个结构因果模型是一个四元组\n",[15,9456,9458,9500],{"className":9457,"translate":19},[18],[15,9459,9461],{"className":9460},[23],[25,9462,9463],{"xmlns":27},[29,9464,9465,9497],{},[32,9466,9467,9470,9472,9474,9476,9478,9480,9482,9485,9487,9489,9491,9493,9495],{},[35,9468,9469],{},"M",[39,9471,602],{},[39,9473,2445],{"stretchy":101},[35,9475,2458],{},[39,9477,42],{"separator":41},[35,9479,1343],{},[39,9481,42],{"separator":41},[35,9483,9484],{},"F",[39,9486,42],{"separator":41},[35,9488,98],{},[39,9490,102],{"stretchy":101},[35,9492,2458],{},[39,9494,111],{"stretchy":101},[39,9496,2493],{"stretchy":101},[47,9498,9499],{"encoding":49},"M = \\langle U, V, F, P(U) \\rangle",[15,9501,9503,9521],{"className":9502,"ariaHidden":41},[54],[15,9504,9506,9509,9512,9515,9518],{"className":9505},[58],[15,9507],{"className":9508,"style":299},[62],[15,9510,9469],{"className":9511,"style":2570},[67,68],[15,9513],{"className":9514,"style":199},[77],[15,9516,602],{"className":9517},[203],[15,9519],{"className":9520,"style":199},[77],[15,9522,9524,9527,9530,9533,9536,9539,9542,9545,9548,9551,9554,9557,9560,9563,9566],{"className":9523},[58],[15,9525],{"className":9526,"style":124},[62],[15,9528,2445],{"className":9529},[132],[15,9531,2458],{"className":9532,"style":2570},[67,68],[15,9534,42],{"className":9535},[73],[15,9537],{"className":9538,"style":78},[77],[15,9540,1343],{"className":9541,"style":82},[67,68],[15,9543,42],{"className":9544},[73],[15,9546],{"className":9547,"style":78},[77],[15,9549,9484],{"className":9550,"style":128},[67,68],[15,9552,42],{"className":9553},[73],[15,9555],{"className":9556,"style":78},[77],[15,9558,98],{"className":9559,"style":128},[67,68],[15,9561,102],{"className":9562},[132],[15,9564,2458],{"className":9565,"style":2570},[67,68],[15,9567,9569],{"className":9568},[148],")⟩","\n其中：",[507,9572,9573,9753,9930,10982],{},[510,9574,9575,9748,9749,9752],{},[15,9576,9578,9617],{"className":9577,"translate":19},[18],[15,9579,9581],{"className":9580},[23],[25,9582,9583],{"xmlns":27},[29,9584,9585,9614],{},[32,9586,9587,9589,9591,9593,9599,9601,9603,9605,9612],{},[35,9588,2458],{},[39,9590,602],{},[39,9592,1419],{"stretchy":101},[863,9594,9595,9597],{},[35,9596,2458],{},[1425,9598,1427],{},[39,9600,42],{"separator":41},[39,9602,1432],{},[39,9604,42],{"separator":41},[863,9606,9607,9609],{},[35,9608,2458],{},[35,9610,9611],{},"m",[39,9613,1444],{"stretchy":101},[47,9615,9616],{"encoding":49},"U = \\{U_1, \\dots, U_m\\}",[15,9618,9620,9638],{"className":9619,"ariaHidden":41},[54],[15,9621,9623,9626,9629,9632,9635],{"className":9622},[58],[15,9624],{"className":9625,"style":299},[62],[15,9627,2458],{"className":9628,"style":2570},[67,68],[15,9630],{"className":9631,"style":199},[77],[15,9633,602],{"className":9634},[203],[15,9636],{"className":9637,"style":199},[77],[15,9639,9641,9644,9647,9687,9690,9693,9696,9699,9702,9705,9745],{"className":9640},[58],[15,9642],{"className":9643,"style":124},[62],[15,9645,1419],{"className":9646},[132],[15,9648,9650,9653],{"className":9649},[67],[15,9651,2458],{"className":9652,"style":2570},[67,68],[15,9654,9656],{"className":9655},[918],[15,9657,9659,9679],{"className":9658},[922,923],[15,9660,9662,9676],{"className":9661},[927],[15,9663,9665],{"className":9664,"style":1496},[931],[15,9666,9667,9670],{"style":2585},[15,9668],{"className":9669,"style":940},[939],[15,9671,9673],{"className":9672},[944,945,946,947],[15,9674,1427],{"className":9675},[67,947],[15,9677,955],{"className":9678},[954],[15,9680,9682],{"className":9681},[927],[15,9683,9685],{"className":9684,"style":962},[931],[15,9686],{},[15,9688,42],{"className":9689},[73],[15,9691],{"className":9692,"style":78},[77],[15,9694,1432],{"className":9695},[1529],[15,9697],{"className":9698,"style":78},[77],[15,9700,42],{"className":9701},[73],[15,9703],{"className":9704,"style":78},[77],[15,9706,9708,9711],{"className":9707},[67],[15,9709,2458],{"className":9710,"style":2570},[67,68],[15,9712,9714],{"className":9713},[918],[15,9715,9717,9737],{"className":9716},[922,923],[15,9718,9720,9734],{"className":9719},[927],[15,9721,9723],{"className":9722,"style":932},[931],[15,9724,9725,9728],{"style":2585},[15,9726],{"className":9727,"style":940},[939],[15,9729,9731],{"className":9730},[944,945,946,947],[15,9732,9611],{"className":9733},[67,68,947],[15,9735,955],{"className":9736},[954],[15,9738,9740],{"className":9739},[927],[15,9741,9743],{"className":9742,"style":962},[931],[15,9744],{},[15,9746,1444],{"className":9747},[148]," 是 ",[305,9750,9751],{},"外生变量（exogenous variables）"," 集合，代表模型边界之外、不由模型内部机制解释的随机扰动源；",[510,9754,9755,9748,9926,9929],{},[15,9756,9758,9795],{"className":9757,"translate":19},[18],[15,9759,9761],{"className":9760},[23],[25,9762,9763],{"xmlns":27},[29,9764,9765,9793],{},[32,9766,9767,9769,9771,9773,9779,9781,9783,9785,9791],{},[35,9768,1343],{},[39,9770,602],{},[39,9772,1419],{"stretchy":101},[863,9774,9775,9777],{},[35,9776,1343],{},[1425,9778,1427],{},[39,9780,42],{"separator":41},[39,9782,1432],{},[39,9784,42],{"separator":41},[863,9786,9787,9789],{},[35,9788,1343],{},[35,9790,1441],{},[39,9792,1444],{"stretchy":101},[47,9794,1447],{"encoding":49},[15,9796,9798,9816],{"className":9797,"ariaHidden":41},[54],[15,9799,9801,9804,9807,9810,9813],{"className":9800},[58],[15,9802],{"className":9803,"style":299},[62],[15,9805,1343],{"className":9806,"style":82},[67,68],[15,9808],{"className":9809,"style":199},[77],[15,9811,602],{"className":9812},[203],[15,9814],{"className":9815,"style":199},[77],[15,9817,9819,9822,9825,9865,9868,9871,9874,9877,9880,9883,9923],{"className":9818},[58],[15,9820],{"className":9821,"style":124},[62],[15,9823,1419],{"className":9824},[132],[15,9826,9828,9831],{"className":9827},[67],[15,9829,1343],{"className":9830,"style":82},[67,68],[15,9832,9834],{"className":9833},[918],[15,9835,9837,9857],{"className":9836},[922,923],[15,9838,9840,9854],{"className":9839},[927],[15,9841,9843],{"className":9842,"style":1496},[931],[15,9844,9845,9848],{"style":1499},[15,9846],{"className":9847,"style":940},[939],[15,9849,9851],{"className":9850},[944,945,946,947],[15,9852,1427],{"className":9853},[67,947],[15,9855,955],{"className":9856},[954],[15,9858,9860],{"className":9859},[927],[15,9861,9863],{"className":9862,"style":962},[931],[15,9864],{},[15,9866,42],{"className":9867},[73],[15,9869],{"className":9870,"style":78},[77],[15,9872,1432],{"className":9873},[1529],[15,9875],{"className":9876,"style":78},[77],[15,9878,42],{"className":9879},[73],[15,9881],{"className":9882,"style":78},[77],[15,9884,9886,9889],{"className":9885},[67],[15,9887,1343],{"className":9888,"style":82},[67,68],[15,9890,9892],{"className":9891},[918],[15,9893,9895,9915],{"className":9894},[922,923],[15,9896,9898,9912],{"className":9897},[927],[15,9899,9901],{"className":9900,"style":932},[931],[15,9902,9903,9906],{"style":1499},[15,9904],{"className":9905,"style":940},[939],[15,9907,9909],{"className":9908},[944,945,946,947],[15,9910,1441],{"className":9911},[67,68,947],[15,9913,955],{"className":9914},[954],[15,9916,9918],{"className":9917},[927],[15,9919,9921],{"className":9920,"style":962},[931],[15,9922],{},[15,9924,1444],{"className":9925},[148],[305,9927,9928],{},"内生变量（endogenous variables）"," 集合，是模型所关心、由模型内部机制决定的变量；",[510,9931,9932,9748,10105,10108,10109,10179,10180,10600,10601,10678,10679,10748,10749,10818,10819,10911,10912,10981],{},[15,9933,9935,9973],{"className":9934,"translate":19},[18],[15,9936,9938],{"className":9937},[23],[25,9939,9940],{"xmlns":27},[29,9941,9942,9970],{},[32,9943,9944,9946,9948,9950,9956,9958,9960,9962,9968],{},[35,9945,9484],{},[39,9947,602],{},[39,9949,1419],{"stretchy":101},[863,9951,9952,9954],{},[35,9953,5724],{},[1425,9955,1427],{},[39,9957,42],{"separator":41},[39,9959,1432],{},[39,9961,42],{"separator":41},[863,9963,9964,9966],{},[35,9965,5724],{},[35,9967,1441],{},[39,9969,1444],{"stretchy":101},[47,9971,9972],{"encoding":49},"F = \\{f_1, \\dots, f_n\\}",[15,9974,9976,9994],{"className":9975,"ariaHidden":41},[54],[15,9977,9979,9982,9985,9988,9991],{"className":9978},[58],[15,9980],{"className":9981,"style":299},[62],[15,9983,9484],{"className":9984,"style":128},[67,68],[15,9986],{"className":9987,"style":199},[77],[15,9989,602],{"className":9990},[203],[15,9992],{"className":9993,"style":199},[77],[15,9995,9997,10000,10003,10044,10047,10050,10053,10056,10059,10062,10102],{"className":9996},[58],[15,9998],{"className":9999,"style":124},[62],[15,10001,1419],{"className":10002},[132],[15,10004,10006,10009],{"className":10005},[67],[15,10007,5724],{"className":10008,"style":5772},[67,68],[15,10010,10012],{"className":10011},[918],[15,10013,10015,10036],{"className":10014},[922,923],[15,10016,10018,10033],{"className":10017},[927],[15,10019,10021],{"className":10020,"style":1496},[931],[15,10022,10024,10027],{"style":10023},"top:-2.55em;margin-left:-0.1076em;margin-right:0.05em;",[15,10025],{"className":10026,"style":940},[939],[15,10028,10030],{"className":10029},[944,945,946,947],[15,10031,1427],{"className":10032},[67,947],[15,10034,955],{"className":10035},[954],[15,10037,10039],{"className":10038},[927],[15,10040,10042],{"className":10041,"style":962},[931],[15,10043],{},[15,10045,42],{"className":10046},[73],[15,10048],{"className":10049,"style":78},[77],[15,10051,1432],{"className":10052},[1529],[15,10054],{"className":10055,"style":78},[77],[15,10057,42],{"className":10058},[73],[15,10060],{"className":10061,"style":78},[77],[15,10063,10065,10068],{"className":10064},[67],[15,10066,5724],{"className":10067,"style":5772},[67,68],[15,10069,10071],{"className":10070},[918],[15,10072,10074,10094],{"className":10073},[922,923],[15,10075,10077,10091],{"className":10076},[927],[15,10078,10080],{"className":10079,"style":932},[931],[15,10081,10082,10085],{"style":10023},[15,10083],{"className":10084,"style":940},[939],[15,10086,10088],{"className":10087},[944,945,946,947],[15,10089,1441],{"className":10090},[67,68,947],[15,10092,955],{"className":10093},[954],[15,10095,10097],{"className":10096},[927],[15,10098,10100],{"className":10099,"style":962},[931],[15,10101],{},[15,10103,1444],{"className":10104},[148],[305,10106,10107],{},"结构方程（structural equations）"," 集合，每个 ",[15,10110,10112,10130],{"className":10111,"translate":19},[18],[15,10113,10115],{"className":10114},[23],[25,10116,10117],{"xmlns":27},[29,10118,10119,10127],{},[32,10120,10121],{},[863,10122,10123,10125],{},[35,10124,5724],{},[35,10126,1682],{},[47,10128,10129],{"encoding":49},"f_i",[15,10131,10133],{"className":10132,"ariaHidden":41},[54],[15,10134,10136,10139],{"className":10135},[58],[15,10137],{"className":10138,"style":4456},[62],[15,10140,10142,10145],{"className":10141},[67],[15,10143,5724],{"className":10144,"style":5772},[67,68],[15,10146,10148],{"className":10147},[918],[15,10149,10151,10171],{"className":10150},[922,923],[15,10152,10154,10168],{"className":10153},[927],[15,10155,10157],{"className":10156,"style":1733},[931],[15,10158,10159,10162],{"style":10023},[15,10160],{"className":10161,"style":940},[939],[15,10163,10165],{"className":10164},[944,945,946,947],[15,10166,1682],{"className":10167},[67,68,947],[15,10169,955],{"className":10170},[954],[15,10172,10174],{"className":10173},[927],[15,10175,10177],{"className":10176,"style":962},[931],[15,10178],{}," 是一个确定性函数\n",[15,10181,10183,10266],{"className":10182,"translate":19},[18],[15,10184,10186],{"className":10185},[23],[25,10187,10188],{"xmlns":27},[29,10189,10190,10263],{},[32,10191,10192,10198,10200,10202,10208,10210,10221,10223,10229,10231,10233,10236,10246,10248,10250,10253,10255,10261],{},[863,10193,10194,10196],{},[35,10195,1343],{},[35,10197,1682],{},[39,10199,8863],{},[39,10201,602],{},[863,10203,10204,10206],{},[35,10205,5724],{},[35,10207,1682],{},[39,10209,102],{"stretchy":101},[863,10211,10212,10219],{},[32,10213,10214,10216],{},[35,10215,98],{"mathvariant":878},[35,10217,10218],{"mathvariant":878},"a",[35,10220,1682],{},[39,10222,42],{"separator":41},[863,10224,10225,10227],{},[35,10226,2458],{},[35,10228,1682],{},[39,10230,111],{"stretchy":101},[39,10232,42],{"separator":41},[77,10234],{"width":10235},"2em",[863,10237,10238,10244],{},[32,10239,10240,10242],{},[35,10241,98],{"mathvariant":878},[35,10243,10218],{"mathvariant":878},[35,10245,1682],{},[39,10247,1599],{},[35,10249,1343],{},[39,10251,10252],{},"∖",[39,10254,1419],{"stretchy":101},[863,10256,10257,10259],{},[35,10258,1343],{},[35,10260,1682],{},[39,10262,1444],{"stretchy":101},[47,10264,10265],{"encoding":49},"V_i := f_i(\\mathrm{Pa}_i, U_i), \\qquad \\mathrm{Pa}_i \\subseteq V \\setminus \\{V_i\\}",[15,10267,10269,10324,10530,10548],{"className":10268,"ariaHidden":41},[54],[15,10270,10272,10275,10315,10318,10321],{"className":10271},[58],[15,10273],{"className":10274,"style":1865},[62],[15,10276,10278,10281],{"className":10277},[67],[15,10279,1343],{"className":10280,"style":82},[67,68],[15,10282,10284],{"className":10283},[918],[15,10285,10287,10307],{"className":10286},[922,923],[15,10288,10290,10304],{"className":10289},[927],[15,10291,10293],{"className":10292,"style":1733},[931],[15,10294,10295,10298],{"style":1499},[15,10296],{"className":10297,"style":940},[939],[15,10299,10301],{"className":10300},[944,945,946,947],[15,10302,1682],{"className":10303},[67,68,947],[15,10305,955],{"className":10306},[954],[15,10308,10310],{"className":10309},[927],[15,10311,10313],{"className":10312,"style":962},[931],[15,10314],{},[15,10316],{"className":10317,"style":199},[77],[15,10319,8899],{"className":10320},[203],[15,10322],{"className":10323,"style":199},[77],[15,10325,10327,10330,10370,10373,10419,10422,10425,10465,10468,10471,10475,10478,10521,10524,10527],{"className":10326},[58],[15,10328],{"className":10329,"style":124},[62],[15,10331,10333,10336],{"className":10332},[67],[15,10334,5724],{"className":10335,"style":5772},[67,68],[15,10337,10339],{"className":10338},[918],[15,10340,10342,10362],{"className":10341},[922,923],[15,10343,10345,10359],{"className":10344},[927],[15,10346,10348],{"className":10347,"style":1733},[931],[15,10349,10350,10353],{"style":10023},[15,10351],{"className":10352,"style":940},[939],[15,10354,10356],{"className":10355},[944,945,946,947],[15,10357,1682],{"className":10358},[67,68,947],[15,10360,955],{"className":10361},[954],[15,10363,10365],{"className":10364},[927],[15,10366,10368],{"className":10367,"style":962},[931],[15,10369],{},[15,10371,102],{"className":10372},[132],[15,10374,10376,10384],{"className":10375},[67],[15,10377,10379],{"className":10378},[67],[15,10380,10383],{"className":10381},[67,10382],"mathrm","Pa",[15,10385,10387],{"className":10386},[918],[15,10388,10390,10411],{"className":10389},[922,923],[15,10391,10393,10408],{"className":10392},[927],[15,10394,10396],{"className":10395,"style":1733},[931],[15,10397,10399,10402],{"style":10398},"top:-2.55em;margin-right:0.05em;",[15,10400],{"className":10401,"style":940},[939],[15,10403,10405],{"className":10404},[944,945,946,947],[15,10406,1682],{"className":10407},[67,68,947],[15,10409,955],{"className":10410},[954],[15,10412,10414],{"className":10413},[927],[15,10415,10417],{"className":10416,"style":962},[931],[15,10418],{},[15,10420,42],{"className":10421},[73],[15,10423],{"className":10424,"style":78},[77],[15,10426,10428,10431],{"className":10427},[67],[15,10429,2458],{"className":10430,"style":2570},[67,68],[15,10432,10434],{"className":10433},[918],[15,10435,10437,10457],{"className":10436},[922,923],[15,10438,10440,10454],{"className":10439},[927],[15,10441,10443],{"className":10442,"style":1733},[931],[15,10444,10445,10448],{"style":2585},[15,10446],{"className":10447,"style":940},[939],[15,10449,10451],{"className":10450},[944,945,946,947],[15,10452,1682],{"className":10453},[67,68,947],[15,10455,955],{"className":10456},[954],[15,10458,10460],{"className":10459},[927],[15,10461,10463],{"className":10462,"style":962},[931],[15,10464],{},[15,10466,111],{"className":10467},[148],[15,10469,42],{"className":10470},[73],[15,10472],{"className":10473,"style":10474},[77],"margin-right:2em;",[15,10476],{"className":10477,"style":78},[77],[15,10479,10481,10487],{"className":10480},[67],[15,10482,10484],{"className":10483},[67],[15,10485,10383],{"className":10486},[67,10382],[15,10488,10490],{"className":10489},[918],[15,10491,10493,10513],{"className":10492},[922,923],[15,10494,10496,10510],{"className":10495},[927],[15,10497,10499],{"className":10498,"style":1733},[931],[15,10500,10501,10504],{"style":10398},[15,10502],{"className":10503,"style":940},[939],[15,10505,10507],{"className":10506},[944,945,946,947],[15,10508,1682],{"className":10509},[67,68,947],[15,10511,955],{"className":10512},[954],[15,10514,10516],{"className":10515},[927],[15,10517,10519],{"className":10518,"style":962},[931],[15,10520],{},[15,10522],{"className":10523,"style":199},[77],[15,10525,1599],{"className":10526},[203],[15,10528],{"className":10529,"style":199},[77],[15,10531,10533,10536,10539,10542,10545],{"className":10532},[58],[15,10534],{"className":10535,"style":124},[62],[15,10537,1343],{"className":10538,"style":82},[67,68],[15,10540],{"className":10541,"style":82},[77],[15,10543,10252],{"className":10544},[1648],[15,10546],{"className":10547,"style":82},[77],[15,10549,10551,10554,10557,10597],{"className":10550},[58],[15,10552],{"className":10553,"style":124},[62],[15,10555,1419],{"className":10556},[132],[15,10558,10560,10563],{"className":10559},[67],[15,10561,1343],{"className":10562,"style":82},[67,68],[15,10564,10566],{"className":10565},[918],[15,10567,10569,10589],{"className":10568},[922,923],[15,10570,10572,10586],{"className":10571},[927],[15,10573,10575],{"className":10574,"style":1733},[931],[15,10576,10577,10580],{"style":1499},[15,10578],{"className":10579,"style":940},[939],[15,10581,10583],{"className":10582},[944,945,946,947],[15,10584,1682],{"className":10585},[67,68,947],[15,10587,955],{"className":10588},[954],[15,10590,10592],{"className":10591},[927],[15,10593,10595],{"className":10594,"style":962},[931],[15,10596],{},[15,10598,1444],{"className":10599},[148],"\n其中 ",[15,10602,10604,10626],{"className":10603,"translate":19},[18],[15,10605,10607],{"className":10606},[23],[25,10608,10609],{"xmlns":27},[29,10610,10611,10623],{},[32,10612,10613],{},[863,10614,10615,10621],{},[32,10616,10617,10619],{},[35,10618,98],{"mathvariant":878},[35,10620,10218],{"mathvariant":878},[35,10622,1682],{},[47,10624,10625],{"encoding":49},"\\mathrm{Pa}_i",[15,10627,10629],{"className":10628,"ariaHidden":41},[54],[15,10630,10632,10635],{"className":10631},[58],[15,10633],{"className":10634,"style":1865},[62],[15,10636,10638,10644],{"className":10637},[67],[15,10639,10641],{"className":10640},[67],[15,10642,10383],{"className":10643},[67,10382],[15,10645,10647],{"className":10646},[918],[15,10648,10650,10670],{"className":10649},[922,923],[15,10651,10653,10667],{"className":10652},[927],[15,10654,10656],{"className":10655,"style":1733},[931],[15,10657,10658,10661],{"style":10398},[15,10659],{"className":10660,"style":940},[939],[15,10662,10664],{"className":10663},[944,945,946,947],[15,10665,1682],{"className":10666},[67,68,947],[15,10668,955],{"className":10669},[954],[15,10671,10673],{"className":10672},[927],[15,10674,10676],{"className":10675,"style":962},[931],[15,10677],{},"（",[15,10680,10682,10699],{"className":10681,"translate":19},[18],[15,10683,10685],{"className":10684},[23],[25,10686,10687],{"xmlns":27},[29,10688,10689,10697],{},[32,10690,10691],{},[863,10692,10693,10695],{},[35,10694,1343],{},[35,10696,1682],{},[47,10698,1983],{"encoding":49},[15,10700,10702],{"className":10701,"ariaHidden":41},[54],[15,10703,10705,10708],{"className":10704},[58],[15,10706],{"className":10707,"style":1865},[62],[15,10709,10711,10714],{"className":10710},[67],[15,10712,1343],{"className":10713,"style":82},[67,68],[15,10715,10717],{"className":10716},[918],[15,10718,10720,10740],{"className":10719},[922,923],[15,10721,10723,10737],{"className":10722},[927],[15,10724,10726],{"className":10725,"style":1733},[931],[15,10727,10728,10731],{"style":1499},[15,10729],{"className":10730,"style":940},[939],[15,10732,10734],{"className":10733},[944,945,946,947],[15,10735,1682],{"className":10736},[67,68,947],[15,10738,955],{"className":10739},[954],[15,10741,10743],{"className":10742},[927],[15,10744,10746],{"className":10745,"style":962},[931],[15,10747],{}," 的「父集合」）是被假设直接影响 ",[15,10750,10752,10769],{"className":10751,"translate":19},[18],[15,10753,10755],{"className":10754},[23],[25,10756,10757],{"xmlns":27},[29,10758,10759,10767],{},[32,10760,10761],{},[863,10762,10763,10765],{},[35,10764,1343],{},[35,10766,1682],{},[47,10768,1983],{"encoding":49},[15,10770,10772],{"className":10771,"ariaHidden":41},[54],[15,10773,10775,10778],{"className":10774},[58],[15,10776],{"className":10777,"style":1865},[62],[15,10779,10781,10784],{"className":10780},[67],[15,10782,1343],{"className":10783,"style":82},[67,68],[15,10785,10787],{"className":10786},[918],[15,10788,10790,10810],{"className":10789},[922,923],[15,10791,10793,10807],{"className":10792},[927],[15,10794,10796],{"className":10795,"style":1733},[931],[15,10797,10798,10801],{"style":1499},[15,10799],{"className":10800,"style":940},[939],[15,10802,10804],{"className":10803},[944,945,946,947],[15,10805,1682],{"className":10806},[67,68,947],[15,10808,955],{"className":10809},[954],[15,10811,10813],{"className":10812},[927],[15,10814,10816],{"className":10815,"style":962},[931],[15,10817],{}," 的其余内生变量子集，",[15,10820,10822,10844],{"className":10821,"translate":19},[18],[15,10823,10825],{"className":10824},[23],[25,10826,10827],{"xmlns":27},[29,10828,10829,10841],{},[32,10830,10831,10837,10839],{},[863,10832,10833,10835],{},[35,10834,2458],{},[35,10836,1682],{},[39,10838,1599],{},[35,10840,2458],{},[47,10842,10843],{"encoding":49},"U_i \\subseteq U",[15,10845,10847,10902],{"className":10846,"ariaHidden":41},[54],[15,10848,10850,10853,10893,10896,10899],{"className":10849},[58],[15,10851],{"className":10852,"style":1865},[62],[15,10854,10856,10859],{"className":10855},[67],[15,10857,2458],{"className":10858,"style":2570},[67,68],[15,10860,10862],{"className":10861},[918],[15,10863,10865,10885],{"className":10864},[922,923],[15,10866,10868,10882],{"className":10867},[927],[15,10869,10871],{"className":10870,"style":1733},[931],[15,10872,10873,10876],{"style":2585},[15,10874],{"className":10875,"style":940},[939],[15,10877,10879],{"className":10878},[944,945,946,947],[15,10880,1682],{"className":10881},[67,68,947],[15,10883,955],{"className":10884},[954],[15,10886,10888],{"className":10887},[927],[15,10889,10891],{"className":10890,"style":962},[931],[15,10892],{},[15,10894],{"className":10895,"style":199},[77],[15,10897,1599],{"className":10898},[203],[15,10900],{"className":10901,"style":199},[77],[15,10903,10905,10908],{"className":10904},[58],[15,10906],{"className":10907,"style":299},[62],[15,10909,2458],{"className":10910,"style":2570},[67,68]," 是影响 ",[15,10913,10915,10932],{"className":10914,"translate":19},[18],[15,10916,10918],{"className":10917},[23],[25,10919,10920],{"xmlns":27},[29,10921,10922,10930],{},[32,10923,10924],{},[863,10925,10926,10928],{},[35,10927,1343],{},[35,10929,1682],{},[47,10931,1983],{"encoding":49},[15,10933,10935],{"className":10934,"ariaHidden":41},[54],[15,10936,10938,10941],{"className":10937},[58],[15,10939],{"className":10940,"style":1865},[62],[15,10942,10944,10947],{"className":10943},[67],[15,10945,1343],{"className":10946,"style":82},[67,68],[15,10948,10950],{"className":10949},[918],[15,10951,10953,10973],{"className":10952},[922,923],[15,10954,10956,10970],{"className":10955},[927],[15,10957,10959],{"className":10958,"style":1733},[931],[15,10960,10961,10964],{"style":1499},[15,10962],{"className":10963,"style":940},[939],[15,10965,10967],{"className":10966},[944,945,946,947],[15,10968,1682],{"className":10969},[67,68,947],[15,10971,955],{"className":10972},[954],[15,10974,10976],{"className":10975},[927],[15,10977,10979],{"className":10978,"style":962},[931],[15,10980],{}," 的外生噪声；",[510,10983,10984,11028,11029,11057],{},[15,10985,10987,11007],{"className":10986,"translate":19},[18],[15,10988,10990],{"className":10989},[23],[25,10991,10992],{"xmlns":27},[29,10993,10994,11004],{},[32,10995,10996,10998,11000,11002],{},[35,10997,98],{},[39,10999,102],{"stretchy":101},[35,11001,2458],{},[39,11003,111],{"stretchy":101},[47,11005,11006],{"encoding":49},"P(U)",[15,11008,11010],{"className":11009,"ariaHidden":41},[54],[15,11011,11013,11016,11019,11022,11025],{"className":11012},[58],[15,11014],{"className":11015,"style":124},[62],[15,11017,98],{"className":11018,"style":128},[67,68],[15,11020,102],{"className":11021},[132],[15,11023,2458],{"className":11024,"style":2570},[67,68],[15,11026,111],{"className":11027},[148]," 是外生变量集合 ",[15,11030,11032,11045],{"className":11031,"translate":19},[18],[15,11033,11035],{"className":11034},[23],[25,11036,11037],{"xmlns":27},[29,11038,11039,11043],{},[32,11040,11041],{},[35,11042,2458],{},[47,11044,2458],{"encoding":49},[15,11046,11048],{"className":11047,"ariaHidden":41},[54],[15,11049,11051,11054],{"className":11050},[58],[15,11052],{"className":11053,"style":299},[62],[15,11055,2458],{"className":11056,"style":2570},[67,68]," 上的联合概率分布。",[1314,11059,11060],{},[11,11061,11062,11065,11066,11094,11095,11165,11166,11258,11259,11288,11289,11429,11430,2249],{},[305,11063,11064],{},"定义 2.2（诱导因果图）"," 给定 SCM ",[15,11067,11069,11082],{"className":11068,"translate":19},[18],[15,11070,11072],{"className":11071},[23],[25,11073,11074],{"xmlns":27},[29,11075,11076,11080],{},[32,11077,11078],{},[35,11079,9469],{},[47,11081,9469],{"encoding":49},[15,11083,11085],{"className":11084,"ariaHidden":41},[54],[15,11086,11088,11091],{"className":11087},[58],[15,11089],{"className":11090,"style":299},[62],[15,11092,9469],{"className":11093,"style":2570},[67,68],"，其对应的因果图 ",[15,11096,11098,11116],{"className":11097,"translate":19},[18],[15,11099,11101],{"className":11100},[23],[25,11102,11103],{"xmlns":27},[29,11104,11105,11113],{},[32,11106,11107],{},[863,11108,11109,11111],{},[35,11110,1336],{},[35,11112,9469],{},[47,11114,11115],{"encoding":49},"G_M",[15,11117,11119],{"className":11118,"ariaHidden":41},[54],[15,11120,11122,11125],{"className":11121},[58],[15,11123],{"className":11124,"style":1865},[62],[15,11126,11128,11131],{"className":11127},[67],[15,11129,1336],{"className":11130},[67,68],[15,11132,11134],{"className":11133},[918],[15,11135,11137,11157],{"className":11136},[922,923],[15,11138,11140,11154],{"className":11139},[927],[15,11141,11143],{"className":11142,"style":7358},[931],[15,11144,11145,11148],{"style":7289},[15,11146],{"className":11147,"style":940},[939],[15,11149,11151],{"className":11150},[944,945,946,947],[15,11152,9469],{"className":11153,"style":2570},[67,68,947],[15,11155,955],{"className":11156},[954],[15,11158,11160],{"className":11159},[927],[15,11161,11163],{"className":11162,"style":962},[931],[15,11164],{}," 定义为：",[15,11167,11169,11191],{"className":11168,"translate":19},[18],[15,11170,11172],{"className":11171},[23],[25,11173,11174],{"xmlns":27},[29,11175,11176,11188],{},[32,11177,11178,11184,11186],{},[863,11179,11180,11182],{},[35,11181,1343],{},[35,11183,9469],{},[39,11185,602],{},[35,11187,1343],{},[47,11189,11190],{"encoding":49},"V_M = V",[15,11192,11194,11249],{"className":11193,"ariaHidden":41},[54],[15,11195,11197,11200,11240,11243,11246],{"className":11196},[58],[15,11198],{"className":11199,"style":1865},[62],[15,11201,11203,11206],{"className":11202},[67],[15,11204,1343],{"className":11205,"style":82},[67,68],[15,11207,11209],{"className":11208},[918],[15,11210,11212,11232],{"className":11211},[922,923],[15,11213,11215,11229],{"className":11214},[927],[15,11216,11218],{"className":11217,"style":7358},[931],[15,11219,11220,11223],{"style":1499},[15,11221],{"className":11222,"style":940},[939],[15,11224,11226],{"className":11225},[944,945,946,947],[15,11227,9469],{"className":11228,"style":2570},[67,68,947],[15,11230,955],{"className":11231},[954],[15,11233,11235],{"className":11234},[927],[15,11236,11238],{"className":11237,"style":962},[931],[15,11239],{},[15,11241],{"className":11242,"style":199},[77],[15,11244,602],{"className":11245},[203],[15,11247],{"className":11248,"style":199},[77],[15,11250,11252,11255],{"className":11251},[58],[15,11253],{"className":11254,"style":299},[62],[15,11256,1343],{"className":11257,"style":82},[67,68],"，且对每个 ",[15,11260,11262,11275],{"className":11261,"translate":19},[18],[15,11263,11265],{"className":11264},[23],[25,11266,11267],{"xmlns":27},[29,11268,11269,11273],{},[32,11270,11271],{},[35,11272,1682],{},[47,11274,1682],{"encoding":49},[15,11276,11278],{"className":11277,"ariaHidden":41},[54],[15,11279,11281,11285],{"className":11280},[58],[15,11282],{"className":11283,"style":11284},[62],"height:0.6595em;",[15,11286,1682],{"className":11287},[67,68],"、每个 ",[15,11290,11292,11322],{"className":11291,"translate":19},[18],[15,11293,11295],{"className":11294},[23],[25,11296,11297],{"xmlns":27},[29,11298,11299,11319],{},[32,11300,11301,11307,11309],{},[863,11302,11303,11305],{},[35,11304,1343],{},[35,11306,1691],{},[39,11308,1696],{},[863,11310,11311,11317],{},[32,11312,11313,11315],{},[35,11314,98],{"mathvariant":878},[35,11316,10218],{"mathvariant":878},[35,11318,1682],{},[47,11320,11321],{"encoding":49},"V_j \\in \\mathrm{Pa}_i",[15,11323,11325,11380],{"className":11324,"ariaHidden":41},[54],[15,11326,11328,11331,11371,11374,11377],{"className":11327},[58],[15,11329],{"className":11330,"style":1921},[62],[15,11332,11334,11337],{"className":11333},[67],[15,11335,1343],{"className":11336,"style":82},[67,68],[15,11338,11340],{"className":11339},[918],[15,11341,11343,11363],{"className":11342},[922,923],[15,11344,11346,11360],{"className":11345},[927],[15,11347,11349],{"className":11348,"style":1733},[931],[15,11350,11351,11354],{"style":1499},[15,11352],{"className":11353,"style":940},[939],[15,11355,11357],{"className":11356},[944,945,946,947],[15,11358,1691],{"className":11359,"style":1791},[67,68,947],[15,11361,955],{"className":11362},[954],[15,11364,11366],{"className":11365},[927],[15,11367,11369],{"className":11368,"style":1801},[931],[15,11370],{},[15,11372],{"className":11373,"style":199},[77],[15,11375,1696],{"className":11376},[203],[15,11378],{"className":11379,"style":199},[77],[15,11381,11383,11386],{"className":11382},[58],[15,11384],{"className":11385,"style":1865},[62],[15,11387,11389,11395],{"className":11388},[67],[15,11390,11392],{"className":11391},[67],[15,11393,10383],{"className":11394},[67,10382],[15,11396,11398],{"className":11397},[918],[15,11399,11401,11421],{"className":11400},[922,923],[15,11402,11404,11418],{"className":11403},[927],[15,11405,11407],{"className":11406,"style":1733},[931],[15,11408,11409,11412],{"style":10398},[15,11410],{"className":11411,"style":940},[939],[15,11413,11415],{"className":11414},[944,945,946,947],[15,11416,1682],{"className":11417},[67,68,947],[15,11419,955],{"className":11420},[954],[15,11422,11424],{"className":11423},[927],[15,11425,11427],{"className":11426,"style":962},[931],[15,11428],{},"，画一条边 ",[15,11431,11433,11459],{"className":11432,"translate":19},[18],[15,11434,11436],{"className":11435},[23],[25,11437,11438],{"xmlns":27},[29,11439,11440,11456],{},[32,11441,11442,11448,11450],{},[863,11443,11444,11446],{},[35,11445,1343],{},[35,11447,1691],{},[39,11449,1846],{},[863,11451,11452,11454],{},[35,11453,1343],{},[35,11455,1682],{},[47,11457,11458],{"encoding":49},"V_j \\to V_i",[15,11460,11462,11517],{"className":11461,"ariaHidden":41},[54],[15,11463,11465,11468,11508,11511,11514],{"className":11464},[58],[15,11466],{"className":11467,"style":1921},[62],[15,11469,11471,11474],{"className":11470},[67],[15,11472,1343],{"className":11473,"style":82},[67,68],[15,11475,11477],{"className":11476},[918],[15,11478,11480,11500],{"className":11479},[922,923],[15,11481,11483,11497],{"className":11482},[927],[15,11484,11486],{"className":11485,"style":1733},[931],[15,11487,11488,11491],{"style":1499},[15,11489],{"className":11490,"style":940},[939],[15,11492,11494],{"className":11493},[944,945,946,947],[15,11495,1691],{"className":11496,"style":1791},[67,68,947],[15,11498,955],{"className":11499},[954],[15,11501,11503],{"className":11502},[927],[15,11504,11506],{"className":11505,"style":1801},[931],[15,11507],{},[15,11509],{"className":11510,"style":199},[77],[15,11512,1846],{"className":11513},[203],[15,11515],{"className":11516,"style":199},[77],[15,11518,11520,11523],{"className":11519},[58],[15,11521],{"className":11522,"style":1865},[62],[15,11524,11526,11529],{"className":11525},[67],[15,11527,1343],{"className":11528,"style":82},[67,68],[15,11530,11532],{"className":11531},[918],[15,11533,11535,11555],{"className":11534},[922,923],[15,11536,11538,11552],{"className":11537},[927],[15,11539,11541],{"className":11540,"style":1733},[931],[15,11542,11543,11546],{"style":1499},[15,11544],{"className":11545,"style":940},[939],[15,11547,11549],{"className":11548},[944,945,946,947],[15,11550,1682],{"className":11551},[67,68,947],[15,11553,955],{"className":11554},[954],[15,11556,11558],{"className":11557},[927],[15,11559,11561],{"className":11560,"style":962},[931],[15,11562],{},[1314,11564,11565],{},[11,11566,11567,7007,11570,11639,11640,11780,11781,11784,11785,11813,11814,11817,11818,11948],{},[305,11568,11569],{},"定义 2.3（马尔可夫型 SCM，Markovian SCM）",[15,11571,11573,11590],{"className":11572,"translate":19},[18],[15,11574,11576],{"className":11575},[23],[25,11577,11578],{"xmlns":27},[29,11579,11580,11588],{},[32,11581,11582],{},[863,11583,11584,11586],{},[35,11585,1336],{},[35,11587,9469],{},[47,11589,11115],{"encoding":49},[15,11591,11593],{"className":11592,"ariaHidden":41},[54],[15,11594,11596,11599],{"className":11595},[58],[15,11597],{"className":11598,"style":1865},[62],[15,11600,11602,11605],{"className":11601},[67],[15,11603,1336],{"className":11604},[67,68],[15,11606,11608],{"className":11607},[918],[15,11609,11611,11631],{"className":11610},[922,923],[15,11612,11614,11628],{"className":11613},[927],[15,11615,11617],{"className":11616,"style":7358},[931],[15,11618,11619,11622],{"style":7289},[15,11620],{"className":11621,"style":940},[939],[15,11623,11625],{"className":11624},[944,945,946,947],[15,11626,9469],{"className":11627,"style":2570},[67,68,947],[15,11629,955],{"className":11630},[954],[15,11632,11634],{"className":11633},[927],[15,11635,11637],{"className":11636,"style":962},[931],[15,11638],{}," 是无环的，且各外生变量 ",[15,11641,11643,11673],{"className":11642,"translate":19},[18],[15,11644,11646],{"className":11645},[23],[25,11647,11648],{"xmlns":27},[29,11649,11650,11670],{},[32,11651,11652,11658,11660,11662,11664],{},[863,11653,11654,11656],{},[35,11655,2458],{},[1425,11657,1427],{},[39,11659,42],{"separator":41},[39,11661,1432],{},[39,11663,42],{"separator":41},[863,11665,11666,11668],{},[35,11667,2458],{},[35,11669,9611],{},[47,11671,11672],{"encoding":49},"U_1, \\dots, U_m",[15,11674,11676],{"className":11675,"ariaHidden":41},[54],[15,11677,11679,11682,11722,11725,11728,11731,11734,11737,11740],{"className":11678},[58],[15,11680],{"className":11681,"style":63},[62],[15,11683,11685,11688],{"className":11684},[67],[15,11686,2458],{"className":11687,"style":2570},[67,68],[15,11689,11691],{"className":11690},[918],[15,11692,11694,11714],{"className":11693},[922,923],[15,11695,11697,11711],{"className":11696},[927],[15,11698,11700],{"className":11699,"style":1496},[931],[15,11701,11702,11705],{"style":2585},[15,11703],{"className":11704,"style":940},[939],[15,11706,11708],{"className":11707},[944,945,946,947],[15,11709,1427],{"className":11710},[67,947],[15,11712,955],{"className":11713},[954],[15,11715,11717],{"className":11716},[927],[15,11718,11720],{"className":11719,"style":962},[931],[15,11721],{},[15,11723,42],{"className":11724},[73],[15,11726],{"className":11727,"style":78},[77],[15,11729,1432],{"className":11730},[1529],[15,11732],{"className":11733,"style":78},[77],[15,11735,42],{"className":11736},[73],[15,11738],{"className":11739,"style":78},[77],[15,11741,11743,11746],{"className":11742},[67],[15,11744,2458],{"className":11745,"style":2570},[67,68],[15,11747,11749],{"className":11748},[918],[15,11750,11752,11772],{"className":11751},[922,923],[15,11753,11755,11769],{"className":11754},[927],[15,11756,11758],{"className":11757,"style":932},[931],[15,11759,11760,11763],{"style":2585},[15,11761],{"className":11762,"style":940},[939],[15,11764,11766],{"className":11765},[944,945,946,947],[15,11767,9611],{"className":11768},[67,68,947],[15,11770,955],{"className":11771},[954],[15,11773,11775],{"className":11774},[927],[15,11776,11778],{"className":11777,"style":962},[931],[15,11779],{}," 两两",[305,11782,11783],{},"相互独立","（即不存在同时影响两个及以上内生变量的「隐藏共同噪声」），则称 ",[15,11786,11788,11801],{"className":11787,"translate":19},[18],[15,11789,11791],{"className":11790},[23],[25,11792,11793],{"xmlns":27},[29,11794,11795,11799],{},[32,11796,11797],{},[35,11798,9469],{},[47,11800,9469],{"encoding":49},[15,11802,11804],{"className":11803,"ariaHidden":41},[54],[15,11805,11807,11810],{"className":11806},[58],[15,11808],{"className":11809,"style":299},[62],[15,11811,9469],{"className":11812,"style":2570},[67,68]," 为马尔可夫型 SCM。若外生变量之间允许相关（对应存在未显式建模的混杂因子），则称为",[305,11815,11816],{},"半马尔可夫型（semi-Markovian）","，此时因果图通常需要补充双向虚线弧 ",[15,11819,11821,11852],{"className":11820,"translate":19},[18],[15,11822,11824],{"className":11823},[23],[25,11825,11826],{"xmlns":27},[29,11827,11828,11849],{},[32,11829,11830,11836,11843],{},[863,11831,11832,11834],{},[35,11833,1343],{},[35,11835,1682],{},[11837,11838,11840],"mstyle",{"mathcolor":11839},"#cc0000",[238,11841,11842],{},"\\dashleftrightarrow",[863,11844,11845,11847],{},[35,11846,1343],{},[35,11848,1691],{},[47,11850,11851],{"encoding":49},"V_i \\dashleftrightarrow V_j",[15,11853,11855],{"className":11854,"ariaHidden":41},[54],[15,11856,11858,11861,11901,11908],{"className":11857},[58],[15,11859],{"className":11860,"style":1711},[62],[15,11862,11864,11867],{"className":11863},[67],[15,11865,1343],{"className":11866,"style":82},[67,68],[15,11868,11870],{"className":11869},[918],[15,11871,11873,11893],{"className":11872},[922,923],[15,11874,11876,11890],{"className":11875},[927],[15,11877,11879],{"className":11878,"style":1733},[931],[15,11880,11881,11884],{"style":1499},[15,11882],{"className":11883,"style":940},[939],[15,11885,11887],{"className":11886},[944,945,946,947],[15,11888,1682],{"className":11889},[67,68,947],[15,11891,955],{"className":11892},[954],[15,11894,11896],{"className":11895},[927],[15,11897,11899],{"className":11898,"style":962},[931],[15,11900],{},[15,11902,11905],{"className":11903,"style":11904},[67,4123],"color:#cc0000;",[15,11906,11842],{"className":11907,"style":11904},[67],[15,11909,11911,11914],{"className":11910},[67],[15,11912,1343],{"className":11913,"style":82},[67,68],[15,11915,11917],{"className":11916},[918],[15,11918,11920,11940],{"className":11919},[922,923],[15,11921,11923,11937],{"className":11922},[927],[15,11924,11926],{"className":11925,"style":1733},[931],[15,11927,11928,11931],{"style":1499},[15,11929],{"className":11930,"style":940},[939],[15,11932,11934],{"className":11933},[944,945,946,947],[15,11935,1691],{"className":11936,"style":1791},[67,68,947],[15,11938,955],{"className":11939},[954],[15,11941,11943],{"className":11942},[927],[15,11944,11946],{"className":11945,"style":1801},[931],[15,11947],{}," 以标示这种隐藏依赖。本文后续讨论若无特别说明，均限于马尔可夫型 SCM。",[1309,11950,11952],{"id":11951},"_22-诱导分布与马尔可夫性","2.2 诱导分布与马尔可夫性",[1314,11954,11955],{},[11,11956,11957,11960,11961,11989,11990,12018,12019,12168,12169,12197,12198,12241,12242,12270,12271,12357,12358,2104,12386,2249],{},[305,11958,11959],{},"定义 2.4（诱导概率分布）"," 给定马尔可夫型 SCM ",[15,11962,11964,11977],{"className":11963,"translate":19},[18],[15,11965,11967],{"className":11966},[23],[25,11968,11969],{"xmlns":27},[29,11970,11971,11975],{},[32,11972,11973],{},[35,11974,9469],{},[47,11976,9469],{"encoding":49},[15,11978,11980],{"className":11979,"ariaHidden":41},[54],[15,11981,11983,11986],{"className":11982},[58],[15,11984],{"className":11985,"style":299},[62],[15,11987,9469],{"className":11988,"style":2570},[67,68],"，由于每个内生变量都是外生变量的确定性函数（递归代入 ",[15,11991,11993,12006],{"className":11992,"translate":19},[18],[15,11994,11996],{"className":11995},[23],[25,11997,11998],{"xmlns":27},[29,11999,12000,12004],{},[32,12001,12002],{},[35,12003,9484],{},[47,12005,9484],{"encoding":49},[15,12007,12009],{"className":12008,"ariaHidden":41},[54],[15,12010,12012,12015],{"className":12011},[58],[15,12013],{"className":12014,"style":299},[62],[15,12016,9484],{"className":12017,"style":128},[67,68]," 中所有方程后可得 ",[15,12020,12022,12055],{"className":12021,"translate":19},[18],[15,12023,12025],{"className":12024},[23],[25,12026,12027],{"xmlns":27},[29,12028,12029,12052],{},[32,12030,12031,12037,12039,12046,12048,12050],{},[863,12032,12033,12035],{},[35,12034,1343],{},[35,12036,1682],{},[39,12038,602],{},[863,12040,12041,12044],{},[35,12042,12043],{},"g",[35,12045,1682],{},[39,12047,102],{"stretchy":101},[35,12049,2458],{},[39,12051,111],{"stretchy":101},[47,12053,12054],{"encoding":49},"V_i = g_i(U)",[15,12056,12058,12113],{"className":12057,"ariaHidden":41},[54],[15,12059,12061,12064,12104,12107,12110],{"className":12060},[58],[15,12062],{"className":12063,"style":1865},[62],[15,12065,12067,12070],{"className":12066},[67],[15,12068,1343],{"className":12069,"style":82},[67,68],[15,12071,12073],{"className":12072},[918],[15,12074,12076,12096],{"className":12075},[922,923],[15,12077,12079,12093],{"className":12078},[927],[15,12080,12082],{"className":12081,"style":1733},[931],[15,12083,12084,12087],{"style":1499},[15,12085],{"className":12086,"style":940},[939],[15,12088,12090],{"className":12089},[944,945,946,947],[15,12091,1682],{"className":12092},[67,68,947],[15,12094,955],{"className":12095},[954],[15,12097,12099],{"className":12098},[927],[15,12100,12102],{"className":12101,"style":962},[931],[15,12103],{},[15,12105],{"className":12106,"style":199},[77],[15,12108,602],{"className":12109},[203],[15,12111],{"className":12112,"style":199},[77],[15,12114,12116,12119,12159,12162,12165],{"className":12115},[58],[15,12117],{"className":12118,"style":124},[62],[15,12120,12122,12125],{"className":12121},[67],[15,12123,12043],{"className":12124,"style":563},[67,68],[15,12126,12128],{"className":12127},[918],[15,12129,12131,12151],{"className":12130},[922,923],[15,12132,12134,12148],{"className":12133},[927],[15,12135,12137],{"className":12136,"style":1733},[931],[15,12138,12139,12142],{"style":935},[15,12140],{"className":12141,"style":940},[939],[15,12143,12145],{"className":12144},[944,945,946,947],[15,12146,1682],{"className":12147},[67,68,947],[15,12149,955],{"className":12150},[954],[15,12152,12154],{"className":12153},[927],[15,12155,12157],{"className":12156,"style":962},[931],[15,12158],{},[15,12160,102],{"className":12161},[132],[15,12163,2458],{"className":12164,"style":2570},[67,68],[15,12166,111],{"className":12167},[148],"），",[15,12170,12172,12185],{"className":12171,"translate":19},[18],[15,12173,12175],{"className":12174},[23],[25,12176,12177],{"xmlns":27},[29,12178,12179,12183],{},[32,12180,12181],{},[35,12182,2458],{},[47,12184,2458],{"encoding":49},[15,12186,12188],{"className":12187,"ariaHidden":41},[54],[15,12189,12191,12194],{"className":12190},[58],[15,12192],{"className":12193,"style":299},[62],[15,12195,2458],{"className":12196,"style":2570},[67,68]," 上的分布 ",[15,12199,12201,12220],{"className":12200,"translate":19},[18],[15,12202,12204],{"className":12203},[23],[25,12205,12206],{"xmlns":27},[29,12207,12208,12218],{},[32,12209,12210,12212,12214,12216],{},[35,12211,98],{},[39,12213,102],{"stretchy":101},[35,12215,2458],{},[39,12217,111],{"stretchy":101},[47,12219,11006],{"encoding":49},[15,12221,12223],{"className":12222,"ariaHidden":41},[54],[15,12224,12226,12229,12232,12235,12238],{"className":12225},[58],[15,12227],{"className":12228,"style":124},[62],[15,12230,98],{"className":12231,"style":128},[67,68],[15,12233,102],{"className":12234},[132],[15,12236,2458],{"className":12237,"style":2570},[67,68],[15,12239,111],{"className":12240},[148]," 唯一诱导出 ",[15,12243,12245,12258],{"className":12244,"translate":19},[18],[15,12246,12248],{"className":12247},[23],[25,12249,12250],{"xmlns":27},[29,12251,12252,12256],{},[32,12253,12254],{},[35,12255,1343],{},[47,12257,1343],{"encoding":49},[15,12259,12261],{"className":12260,"ariaHidden":41},[54],[15,12262,12264,12267],{"className":12263},[58],[15,12265],{"className":12266,"style":299},[62],[15,12268,1343],{"className":12269,"style":82},[67,68]," 上的一个联合分布 ",[15,12272,12274,12298],{"className":12273,"translate":19},[18],[15,12275,12277],{"className":12276},[23],[25,12278,12279],{"xmlns":27},[29,12280,12281,12295],{},[32,12282,12283,12289,12291,12293],{},[863,12284,12285,12287],{},[35,12286,98],{},[35,12288,9469],{},[39,12290,102],{"stretchy":101},[35,12292,1343],{},[39,12294,111],{"stretchy":101},[47,12296,12297],{"encoding":49},"P_M(V)",[15,12299,12301],{"className":12300,"ariaHidden":41},[54],[15,12302,12304,12307,12348,12351,12354],{"className":12303},[58],[15,12305],{"className":12306,"style":124},[62],[15,12308,12310,12313],{"className":12309},[67],[15,12311,98],{"className":12312,"style":128},[67,68],[15,12314,12316],{"className":12315},[918],[15,12317,12319,12340],{"className":12318},[922,923],[15,12320,12322,12337],{"className":12321},[927],[15,12323,12325],{"className":12324,"style":7358},[931],[15,12326,12328,12331],{"style":12327},"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;",[15,12329],{"className":12330,"style":940},[939],[15,12332,12334],{"className":12333},[944,945,946,947],[15,12335,9469],{"className":12336,"style":2570},[67,68,947],[15,12338,955],{"className":12339},[954],[15,12341,12343],{"className":12342},[927],[15,12344,12346],{"className":12345,"style":962},[931],[15,12347],{},[15,12349,102],{"className":12350},[132],[15,12352,1343],{"className":12353,"style":82},[67,68],[15,12355,111],{"className":12356},[148],"，称为 ",[15,12359,12361,12374],{"className":12360,"translate":19},[18],[15,12362,12364],{"className":12363},[23],[25,12365,12366],{"xmlns":27},[29,12367,12368,12372],{},[32,12369,12370],{},[35,12371,9469],{},[47,12373,9469],{"encoding":49},[15,12375,12377],{"className":12376,"ariaHidden":41},[54],[15,12378,12380,12383],{"className":12379},[58],[15,12381],{"className":12382,"style":299},[62],[15,12384,9469],{"className":12385,"style":2570},[67,68],[305,12387,12388,12389,12392],{},"诱导分布（induced distribution）",[305,12390,12391],{},"或","观测分布",[1314,12394,12395],{},[11,12396,12397,7007,12400,12428,12429,12513,12514,12951],{},[305,12398,12399],{},"定理 2.1（马尔可夫分解，Markov Factorization）",[15,12401,12403,12416],{"className":12402,"translate":19},[18],[15,12404,12406],{"className":12405},[23],[25,12407,12408],{"xmlns":27},[29,12409,12410,12414],{},[32,12411,12412],{},[35,12413,9469],{},[47,12415,9469],{"encoding":49},[15,12417,12419],{"className":12418,"ariaHidden":41},[54],[15,12420,12422,12425],{"className":12421},[58],[15,12423],{"className":12424,"style":299},[62],[15,12426,9469],{"className":12427,"style":2570},[67,68]," 为马尔可夫型 SCM，其诱导分布 ",[15,12430,12432,12455],{"className":12431,"translate":19},[18],[15,12433,12435],{"className":12434},[23],[25,12436,12437],{"xmlns":27},[29,12438,12439,12453],{},[32,12440,12441,12447,12449,12451],{},[863,12442,12443,12445],{},[35,12444,98],{},[35,12446,9469],{},[39,12448,102],{"stretchy":101},[35,12450,1343],{},[39,12452,111],{"stretchy":101},[47,12454,12297],{"encoding":49},[15,12456,12458],{"className":12457,"ariaHidden":41},[54],[15,12459,12461,12464,12504,12507,12510],{"className":12460},[58],[15,12462],{"className":12463,"style":124},[62],[15,12465,12467,12470],{"className":12466},[67],[15,12468,98],{"className":12469,"style":128},[67,68],[15,12471,12473],{"className":12472},[918],[15,12474,12476,12496],{"className":12475},[922,923],[15,12477,12479,12493],{"className":12478},[927],[15,12480,12482],{"className":12481,"style":7358},[931],[15,12483,12484,12487],{"style":12327},[15,12485],{"className":12486,"style":940},[939],[15,12488,12490],{"className":12489},[944,945,946,947],[15,12491,9469],{"className":12492,"style":2570},[67,68,947],[15,12494,955],{"className":12495},[954],[15,12497,12499],{"className":12498},[927],[15,12500,12502],{"className":12501,"style":962},[931],[15,12503],{},[15,12505,102],{"className":12506},[132],[15,12508,1343],{"className":12509,"style":82},[67,68],[15,12511,111],{"className":12512},[148]," 可分解为：\n",[15,12515,12517,12600],{"className":12516,"translate":19},[18],[15,12518,12520],{"className":12519},[23],[25,12521,12522],{"xmlns":27},[29,12523,12524,12597],{},[32,12525,12526,12532,12534,12541,12543,12545,12547,12553,12555,12557,12573,12575,12577,12583,12585,12595],{},[863,12527,12528,12530],{},[35,12529,98],{},[35,12531,9469],{},[39,12533,102],{"stretchy":101},[863,12535,12536,12539],{},[35,12537,12538],{},"v",[1425,12540,1427],{},[39,12542,42],{"separator":41},[39,12544,1432],{},[39,12546,42],{"separator":41},[863,12548,12549,12551],{},[35,12550,12538],{},[35,12552,1441],{},[39,12554,111],{"stretchy":101},[39,12556,602],{},[12558,12559,12560,12563,12571],"msubsup",{},[39,12561,12562],{},"∏",[32,12564,12565,12567,12569],{},[35,12566,1682],{},[39,12568,602],{},[1425,12570,1427],{},[35,12572,1441],{},[35,12574,98],{},[39,12576,102],{"stretchy":101},[863,12578,12579,12581],{},[35,12580,12538],{},[35,12582,1682],{},[39,12584,170],{},[863,12586,12587,12593],{},[32,12588,12589,12591],{},[35,12590,11],{"mathvariant":878},[35,12592,10218],{"mathvariant":878},[35,12594,1682],{},[39,12596,111],{"stretchy":101},[47,12598,12599],{"encoding":49},"P_M(v_1, \\dots, v_n) = \\prod_{i=1}^n P(v_i \\mid \\mathrm{pa}_i)",[15,12601,12603,12762,12895],{"className":12602,"ariaHidden":41},[54],[15,12604,12606,12609,12649,12652,12692,12695,12698,12701,12704,12707,12710,12750,12753,12756,12759],{"className":12605},[58],[15,12607],{"className":12608,"style":124},[62],[15,12610,12612,12615],{"className":12611},[67],[15,12613,98],{"className":12614,"style":128},[67,68],[15,12616,12618],{"className":12617},[918],[15,12619,12621,12641],{"className":12620},[922,923],[15,12622,12624,12638],{"className":12623},[927],[15,12625,12627],{"className":12626,"style":7358},[931],[15,12628,12629,12632],{"style":12327},[15,12630],{"className":12631,"style":940},[939],[15,12633,12635],{"className":12634},[944,945,946,947],[15,12636,9469],{"className":12637,"style":2570},[67,68,947],[15,12639,955],{"className":12640},[954],[15,12642,12644],{"className":12643},[927],[15,12645,12647],{"className":12646,"style":962},[931],[15,12648],{},[15,12650,102],{"className":12651},[132],[15,12653,12655,12658],{"className":12654},[67],[15,12656,12538],{"className":12657,"style":563},[67,68],[15,12659,12661],{"className":12660},[918],[15,12662,12664,12684],{"className":12663},[922,923],[15,12665,12667,12681],{"className":12666},[927],[15,12668,12670],{"className":12669,"style":1496},[931],[15,12671,12672,12675],{"style":935},[15,12673],{"className":12674,"style":940},[939],[15,12676,12678],{"className":12677},[944,945,946,947],[15,12679,1427],{"className":12680},[67,947],[15,12682,955],{"className":12683},[954],[15,12685,12687],{"className":12686},[927],[15,12688,12690],{"className":12689,"style":962},[931],[15,12691],{},[15,12693,42],{"className":12694},[73],[15,12696],{"className":12697,"style":78},[77],[15,12699,1432],{"className":12700},[1529],[15,12702],{"className":12703,"style":78},[77],[15,12705,42],{"className":12706},[73],[15,12708],{"className":12709,"style":78},[77],[15,12711,12713,12716],{"className":12712},[67],[15,12714,12538],{"className":12715,"style":563},[67,68],[15,12717,12719],{"className":12718},[918],[15,12720,12722,12742],{"className":12721},[922,923],[15,12723,12725,12739],{"className":12724},[927],[15,12726,12728],{"className":12727,"style":932},[931],[15,12729,12730,12733],{"style":935},[15,12731],{"className":12732,"style":940},[939],[15,12734,12736],{"className":12735},[944,945,946,947],[15,12737,1441],{"className":12738},[67,68,947],[15,12740,955],{"className":12741},[954],[15,12743,12745],{"className":12744},[927],[15,12746,12748],{"className":12747,"style":962},[931],[15,12749],{},[15,12751,111],{"className":12752},[148],[15,12754],{"className":12755,"style":199},[77],[15,12757,602],{"className":12758},[203],[15,12760],{"className":12761,"style":199},[77],[15,12763,12765,12769,12837,12840,12843,12846,12886,12889,12892],{"className":12764},[58],[15,12766],{"className":12767,"style":12768},[62],"height:1.104em;vertical-align:-0.2997em;",[15,12770,12773,12779],{"className":12771},[12772],"mop",[15,12774,12562],{"className":12775,"style":12778},[12772,12776,12777],"op-symbol","small-op","position:relative;top:0em;",[15,12780,12782],{"className":12781},[918],[15,12783,12785,12828],{"className":12784},[922,923],[15,12786,12788,12825],{"className":12787},[927],[15,12789,12792,12813],{"className":12790,"style":12791},[931],"height:0.8043em;",[15,12793,12795,12798],{"style":12794},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[15,12796],{"className":12797,"style":940},[939],[15,12799,12801],{"className":12800},[944,945,946,947],[15,12802,12804,12807,12810],{"className":12803},[67,947],[15,12805,1682],{"className":12806},[67,68,947],[15,12808,602],{"className":12809},[203,947],[15,12811,1427],{"className":12812},[67,947],[15,12814,12816,12819],{"style":12815},"top:-3.2029em;margin-right:0.05em;",[15,12817],{"className":12818,"style":940},[939],[15,12820,12822],{"className":12821},[944,945,946,947],[15,12823,1441],{"className":12824},[67,68,947],[15,12826,955],{"className":12827},[954],[15,12829,12831],{"className":12830},[927],[15,12832,12835],{"className":12833,"style":12834},[931],"height:0.2997em;",[15,12836],{},[15,12838],{"className":12839,"style":78},[77],[15,12841,98],{"className":12842,"style":128},[67,68],[15,12844,102],{"className":12845},[132],[15,12847,12849,12852],{"className":12848},[67],[15,12850,12538],{"className":12851,"style":563},[67,68],[15,12853,12855],{"className":12854},[918],[15,12856,12858,12878],{"className":12857},[922,923],[15,12859,12861,12875],{"className":12860},[927],[15,12862,12864],{"className":12863,"style":1733},[931],[15,12865,12866,12869],{"style":935},[15,12867],{"className":12868,"style":940},[939],[15,12870,12872],{"className":12871},[944,945,946,947],[15,12873,1682],{"className":12874},[67,68,947],[15,12876,955],{"className":12877},[954],[15,12879,12881],{"className":12880},[927],[15,12882,12884],{"className":12883,"style":962},[931],[15,12885],{},[15,12887],{"className":12888,"style":199},[77],[15,12890,170],{"className":12891},[203],[15,12893],{"className":12894,"style":199},[77],[15,12896,12898,12901,12948],{"className":12897},[58],[15,12899],{"className":12900,"style":124},[62],[15,12902,12904,12911],{"className":12903},[67],[15,12905,12907],{"className":12906},[67],[15,12908,12910],{"className":12909},[67,10382],"pa",[15,12912,12914],{"className":12913},[918],[15,12915,12917,12939],{"className":12916},[922,923],[15,12918,12920,12936],{"className":12919},[927],[15,12921,12924],{"className":12922,"style":12923},[931],"height:0.2175em;",[15,12925,12927,12930],{"style":12926},"top:-2.4559em;margin-right:0.05em;",[15,12928],{"className":12929,"style":940},[939],[15,12931,12933],{"className":12932},[944,945,946,947],[15,12934,1682],{"className":12935},[67,68,947],[15,12937,955],{"className":12938},[954],[15,12940,12942],{"className":12941},[927],[15,12943,12946],{"className":12944,"style":12945},[931],"height:0.2441em;",[15,12947],{},[15,12949,111],{"className":12950},[148],"\n即联合分布可写成每个变量在给定其父节点条件下的条件分布之乘积。",[11,12953,12954,12957,12958,13028,13029,13098,13099,431,13175,13244,13245,13622],{},[4666,12955,12956],{},"证明梗概","：由于 ",[15,12959,12961,12979],{"className":12960,"translate":19},[18],[15,12962,12964],{"className":12963},[23],[25,12965,12966],{"xmlns":27},[29,12967,12968,12976],{},[32,12969,12970],{},[863,12971,12972,12974],{},[35,12973,2458],{},[35,12975,1682],{},[47,12977,12978],{"encoding":49},"U_i",[15,12980,12982],{"className":12981,"ariaHidden":41},[54],[15,12983,12985,12988],{"className":12984},[58],[15,12986],{"className":12987,"style":1865},[62],[15,12989,12991,12994],{"className":12990},[67],[15,12992,2458],{"className":12993,"style":2570},[67,68],[15,12995,12997],{"className":12996},[918],[15,12998,13000,13020],{"className":12999},[922,923],[15,13001,13003,13017],{"className":13002},[927],[15,13004,13006],{"className":13005,"style":1733},[931],[15,13007,13008,13011],{"style":2585},[15,13009],{"className":13010,"style":940},[939],[15,13012,13014],{"className":13013},[944,945,946,947],[15,13015,1682],{"className":13016},[67,68,947],[15,13018,955],{"className":13019},[954],[15,13021,13023],{"className":13022},[927],[15,13024,13026],{"className":13025,"style":962},[931],[15,13027],{}," 相互独立，且 ",[15,13030,13032,13049],{"className":13031,"translate":19},[18],[15,13033,13035],{"className":13034},[23],[25,13036,13037],{"xmlns":27},[29,13038,13039,13047],{},[32,13040,13041],{},[863,13042,13043,13045],{},[35,13044,1343],{},[35,13046,1682],{},[47,13048,1983],{"encoding":49},[15,13050,13052],{"className":13051,"ariaHidden":41},[54],[15,13053,13055,13058],{"className":13054},[58],[15,13056],{"className":13057,"style":1865},[62],[15,13059,13061,13064],{"className":13060},[67],[15,13062,1343],{"className":13063,"style":82},[67,68],[15,13065,13067],{"className":13066},[918],[15,13068,13070,13090],{"className":13069},[922,923],[15,13071,13073,13087],{"className":13072},[927],[15,13074,13076],{"className":13075,"style":1733},[931],[15,13077,13078,13081],{"style":1499},[15,13079],{"className":13080,"style":940},[939],[15,13082,13084],{"className":13083},[944,945,946,947],[15,13085,1682],{"className":13086},[67,68,947],[15,13088,955],{"className":13089},[954],[15,13091,13093],{"className":13092},[927],[15,13094,13096],{"className":13095,"style":962},[931],[15,13097],{}," 仅是 ",[15,13100,13102,13123],{"className":13101,"translate":19},[18],[15,13103,13105],{"className":13104},[23],[25,13106,13107],{"xmlns":27},[29,13108,13109,13121],{},[32,13110,13111],{},[863,13112,13113,13119],{},[32,13114,13115,13117],{},[35,13116,98],{"mathvariant":878},[35,13118,10218],{"mathvariant":878},[35,13120,1682],{},[47,13122,10625],{"encoding":49},[15,13124,13126],{"className":13125,"ariaHidden":41},[54],[15,13127,13129,13132],{"className":13128},[58],[15,13130],{"className":13131,"style":1865},[62],[15,13133,13135,13141],{"className":13134},[67],[15,13136,13138],{"className":13137},[67],[15,13139,10383],{"className":13140},[67,10382],[15,13142,13144],{"className":13143},[918],[15,13145,13147,13167],{"className":13146},[922,923],[15,13148,13150,13164],{"className":13149},[927],[15,13151,13153],{"className":13152,"style":1733},[931],[15,13154,13155,13158],{"style":10398},[15,13156],{"className":13157,"style":940},[939],[15,13159,13161],{"className":13160},[944,945,946,947],[15,13162,1682],{"className":13163},[67,68,947],[15,13165,955],{"className":13166},[954],[15,13168,13170],{"className":13169},[927],[15,13171,13173],{"className":13172,"style":962},[931],[15,13174],{},[15,13176,13178,13195],{"className":13177,"translate":19},[18],[15,13179,13181],{"className":13180},[23],[25,13182,13183],{"xmlns":27},[29,13184,13185,13193],{},[32,13186,13187],{},[863,13188,13189,13191],{},[35,13190,2458],{},[35,13192,1682],{},[47,13194,12978],{"encoding":49},[15,13196,13198],{"className":13197,"ariaHidden":41},[54],[15,13199,13201,13204],{"className":13200},[58],[15,13202],{"className":13203,"style":1865},[62],[15,13205,13207,13210],{"className":13206},[67],[15,13208,2458],{"className":13209,"style":2570},[67,68],[15,13211,13213],{"className":13212},[918],[15,13214,13216,13236],{"className":13215},[922,923],[15,13217,13219,13233],{"className":13218},[927],[15,13220,13222],{"className":13221,"style":1733},[931],[15,13223,13224,13227],{"style":2585},[15,13225],{"className":13226,"style":940},[939],[15,13228,13230],{"className":13229},[944,945,946,947],[15,13231,1682],{"className":13232},[67,68,947],[15,13234,955],{"className":13235},[954],[15,13237,13239],{"className":13238},[927],[15,13240,13242],{"className":13241,"style":962},[931],[15,13243],{}," 的函数，按图的拓扑序（即父节点排在子节点之前的节点序列）逐一代入，可归纳证明 ",[15,13246,13248,13318],{"className":13247,"translate":19},[18],[15,13249,13251],{"className":13250},[23],[25,13252,13253],{"xmlns":27},[29,13254,13255,13315],{},[32,13256,13257,13263,13265,13267,13269,13271,13273,13275,13281,13283,13289,13292,13298,13301,13303,13305],{},[863,13258,13259,13261],{},[35,13260,1343],{},[35,13262,1682],{},[39,13264,236],{},[238,13266,240],{},[238,13268,240],{},[238,13270,240],{},[39,13272,236],{},[39,13274,1419],{"stretchy":101},[863,13276,13277,13279],{},[35,13278,1343],{},[35,13280,1691],{},[39,13282,8863],{},[863,13284,13285,13287],{},[35,13286,1343],{},[35,13288,1691],{},[238,13290,13291],{}," 非 ",[863,13293,13294,13296],{},[35,13295,1343],{},[35,13297,1682],{},[238,13299,13300],{}," 的后代",[39,13302,1444],{"stretchy":101},[39,13304,170],{},[863,13306,13307,13313],{},[32,13308,13309,13311],{},[35,13310,98],{"mathvariant":878},[35,13312,10218],{"mathvariant":878},[35,13314,1682],{},[47,13316,13317],{"encoding":49},"V_i \\perp\\!\\!\\!\\perp \\{V_j : V_j \\text{ 非 } V_i\\text{ 的后代}\\} \\mid \\mathrm{Pa}_i",[15,13319,13321,13382,13394,13452,13573],{"className":13320,"ariaHidden":41},[54],[15,13322,13324,13327,13367,13370,13373,13376,13379],{"className":13323},[58],[15,13325],{"className":13326,"style":7268},[62],[15,13328,13330,13333],{"className":13329},[67],[15,13331,1343],{"className":13332,"style":82},[67,68],[15,13334,13336],{"className":13335},[918],[15,13337,13339,13359],{"className":13338},[922,923],[15,13340,13342,13356],{"className":13341},[927],[15,13343,13345],{"className":13344,"style":1733},[931],[15,13346,13347,13350],{"style":1499},[15,13348],{"className":13349,"style":940},[939],[15,13351,13353],{"className":13352},[944,945,946,947],[15,13354,1682],{"className":13355},[67,68,947],[15,13357,955],{"className":13358},[954],[15,13360,13362],{"className":13361},[927],[15,13363,13365],{"className":13364,"style":962},[931],[15,13366],{},[15,13368],{"className":13369,"style":199},[77],[15,13371,236],{"className":13372},[203],[15,13374],{"className":13375,"style":274},[77],[15,13377],{"className":13378,"style":274},[77],[15,13380],{"className":13381,"style":274},[77],[15,13383,13385,13388,13391],{"className":13384},[58],[15,13386],{"className":13387,"style":261},[62],[15,13389,236],{"className":13390},[203],[15,13392],{"className":13393,"style":199},[77],[15,13395,13397,13400,13403,13443,13446,13449],{"className":13396},[58],[15,13398],{"className":13399,"style":1711},[62],[15,13401,1419],{"className":13402},[132],[15,13404,13406,13409],{"className":13405},[67],[15,13407,1343],{"className":13408,"style":82},[67,68],[15,13410,13412],{"className":13411},[918],[15,13413,13415,13435],{"className":13414},[922,923],[15,13416,13418,13432],{"className":13417},[927],[15,13419,13421],{"className":13420,"style":1733},[931],[15,13422,13423,13426],{"style":1499},[15,13424],{"className":13425,"style":940},[939],[15,13427,13429],{"className":13428},[944,945,946,947],[15,13430,1691],{"className":13431,"style":1791},[67,68,947],[15,13433,955],{"className":13434},[954],[15,13436,13438],{"className":13437},[927],[15,13439,13441],{"className":13440,"style":1801},[931],[15,13442],{},[15,13444],{"className":13445,"style":199},[77],[15,13447,8863],{"className":13448},[203],[15,13450],{"className":13451,"style":199},[77],[15,13453,13455,13458,13498,13511,13551,13561,13564,13567,13570],{"className":13454},[58],[15,13456],{"className":13457,"style":1711},[62],[15,13459,13461,13464],{"className":13460},[67],[15,13462,1343],{"className":13463,"style":82},[67,68],[15,13465,13467],{"className":13466},[918],[15,13468,13470,13490],{"className":13469},[922,923],[15,13471,13473,13487],{"className":13472},[927],[15,13474,13476],{"className":13475,"style":1733},[931],[15,13477,13478,13481],{"style":1499},[15,13479],{"className":13480,"style":940},[939],[15,13482,13484],{"className":13483},[944,945,946,947],[15,13485,1691],{"className":13486,"style":1791},[67,68,947],[15,13488,955],{"className":13489},[954],[15,13491,13493],{"className":13492},[927],[15,13494,13496],{"className":13495,"style":1801},[931],[15,13497],{},[15,13499,13501,13504,13508],{"className":13500},[67,4123],[15,13502,3926],{"className":13503},[67],[15,13505,13507],{"className":13506},[67,7759],"非",[15,13509,3926],{"className":13510},[67],[15,13512,13514,13517],{"className":13513},[67],[15,13515,1343],{"className":13516,"style":82},[67,68],[15,13518,13520],{"className":13519},[918],[15,13521,13523,13543],{"className":13522},[922,923],[15,13524,13526,13540],{"className":13525},[927],[15,13527,13529],{"className":13528,"style":1733},[931],[15,13530,13531,13534],{"style":1499},[15,13532],{"className":13533,"style":940},[939],[15,13535,13537],{"className":13536},[944,945,946,947],[15,13538,1682],{"className":13539},[67,68,947],[15,13541,955],{"className":13542},[954],[15,13544,13546],{"className":13545},[927],[15,13547,13549],{"className":13548,"style":962},[931],[15,13550],{},[15,13552,13554,13557],{"className":13553},[67,4123],[15,13555,3926],{"className":13556},[67],[15,13558,13560],{"className":13559},[67,7759],"的后代",[15,13562,1444],{"className":13563},[148],[15,13565],{"className":13566,"style":199},[77],[15,13568,170],{"className":13569},[203],[15,13571],{"className":13572,"style":199},[77],[15,13574,13576,13579],{"className":13575},[58],[15,13577],{"className":13578,"style":1865},[62],[15,13580,13582,13588],{"className":13581},[67],[15,13583,13585],{"className":13584},[67],[15,13586,10383],{"className":13587},[67,10382],[15,13589,13591],{"className":13590},[918],[15,13592,13594,13614],{"className":13593},[922,923],[15,13595,13597,13611],{"className":13596},[927],[15,13598,13600],{"className":13599,"style":1733},[931],[15,13601,13602,13605],{"style":10398},[15,13603],{"className":13604,"style":940},[939],[15,13606,13608],{"className":13607},[944,945,946,947],[15,13609,1682],{"className":13610},[67,68,947],[15,13612,955],{"className":13613},[954],[15,13615,13617],{"className":13616},[927],[15,13618,13620],{"className":13619,"style":962},[931],[15,13621],{},"，这正是定理 1.1 中马尔可夫性假设的来源，也是贝叶斯网络理论中「局部马尔可夫性」与「因子分解」等价性定理的因果版本。",[11,13624,13625,13626,13629],{},"这一定理揭示了 SCM 与传统贝叶斯网络的联系与区别：",[305,13627,13628],{},"二者在纯观测层面（第一层关联）诱导出相同的概率分解公式","，唯一的区别在于 SCM 额外赋予了每条边「直接原因」的因果语义，从而支持贝叶斯网络本身不具备的干预与反事实计算——这一区别将在第三部分具体展开。",[1309,13631,13633],{"id":13632},"_23-洒水器模型的-scm-表示","2.3 洒水器模型的 SCM 表示",[11,13635,13636,13637,505],{},"沿用例 1.1 的因果图，一个具体的马尔可夫型 SCM 实例可定义如下。设内生变量均为二元 ",[15,13638,13640,13662],{"className":13639,"translate":19},[18],[15,13641,13643],{"className":13642},[23],[25,13644,13645],{"xmlns":27},[29,13646,13647,13659],{},[32,13648,13649,13651,13653,13655,13657],{},[39,13650,1419],{"stretchy":101},[1425,13652,2461],{},[39,13654,42],{"separator":41},[1425,13656,1427],{},[39,13658,1444],{"stretchy":101},[47,13660,13661],{"encoding":49},"\\{0,1\\}",[15,13663,13665],{"className":13664,"ariaHidden":41},[54],[15,13666,13668,13671,13674,13677,13680,13683,13686],{"className":13667},[58],[15,13669],{"className":13670,"style":124},[62],[15,13672,1419],{"className":13673},[132],[15,13675,2461],{"className":13676},[67],[15,13678,42],{"className":13679},[73],[15,13681],{"className":13682,"style":78},[77],[15,13684,1427],{"className":13685},[67],[15,13687,1444],{"className":13688},[148],[15,13690,13693],{"className":13691,"translate":19},[13692],"katex-display",[15,13694,13696,14357],{"className":13695,"translate":19},[18],[15,13697,13699],{"className":13698},[23],[25,13700,13702],{"xmlns":27,"display":13701},"block",[29,13703,13704,14354],{},[13705,13706,13710,13793,13979,14180],"mtable",{"rowspacing":13707,"columnalign":13708,"columnspacing":13709},"0.25em","right left right left","0em 1em 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&:= U_S, &U_S &\\sim \\mathrm{Bernoulli}(0.3) \\\\\nR &:= \\mathbb{1}[S = 1] \\cdot U_R^{(1)} + \\mathbb{1}[S=0]\\cdot U_R^{(0)}, &U_R^{(1)} &\\sim \\mathrm{Bernoulli}(0.8),\\ U_R^{(0)} \\sim \\mathrm{Bernoulli}(0.1)\\\\\nSp &:= \\mathbb{1}[S=1]\\cdot U_{Sp}^{(1)} + \\mathbb{1}[S=0]\\cdot U_{Sp}^{(0)}, &U_{Sp}^{(1)} &\\sim \\mathrm{Bernoulli}(0.1),\\ U_{Sp}^{(0)} \\sim \\mathrm{Bernoulli}(0.6)\\\\\nW &:= \\max(R, Sp) \\cdot U_W + \\big(1-\\max(R,Sp)\\big)\\cdot U_W', &U_W &\\sim \\mathrm{Bernoulli}(0.95),\\ U_W' \\sim 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",[15,15926,15928,15941],{"className":15927,"translate":19},[18],[15,15929,15931],{"className":15930},[23],[25,15932,15933],{"xmlns":27},[29,15934,15935,15939],{},[32,15936,15937],{},[35,15938,2458],{},[47,15940,2458],{"encoding":49},[15,15942,15944],{"className":15943,"ariaHidden":41},[54],[15,15945,15947,15950],{"className":15946},[58],[15,15948],{"className":15949,"style":299},[62],[15,15951,2458],{"className":15952,"style":2570},[67,68]," 变量相互独立。这一具体赋值把因果图 ",[15,15955,15957,15970],{"className":15956,"translate":19},[18],[15,15958,15960],{"className":15959},[23],[25,15961,15962],{"xmlns":27},[29,15963,15964,15968],{},[32,15965,15966],{},[35,15967,1336],{},[47,15969,1336],{"encoding":49},[15,15971,15973],{"className":15972,"ariaHidden":41},[54],[15,15974,15976,15979],{"className":15975},[58],[15,15977],{"className":15978,"style":299},[62],[15,15980,1336],{"className":15981},[67,68]," 「填满」为一个可计算的生成过程：给定外生变量的一次采样（一次「自然实现」），内生变量的取值随之",[305,15984,15985],{},"唯一确定","。这正是结构方程「确定性」这一特征的体现——随机性完全由外生变量 ",[15,15988,15990,16003],{"className":15989,"translate":19},[18],[15,15991,15993],{"className":15992},[23],[25,15994,15995],{"xmlns":27},[29,15996,15997,16001],{},[32,15998,15999],{},[35,16000,2458],{},[47,16002,2458],{"encoding":49},[15,16004,16006],{"className":16005,"ariaHidden":41},[54],[15,16007,16009,16012],{"className":16008},[58],[15,16010],{"className":16011,"style":299},[62],[15,16013,2458],{"className":16014,"style":2570},[67,68]," 承担，内生变量之间的关系在给定 ",[15,16017,16019,16032],{"className":16018,"translate":19},[18],[15,16020,16022],{"className":16021},[23],[25,16023,16024],{"xmlns":27},[29,16025,16026,16030],{},[32,16027,16028],{},[35,16029,2458],{},[47,16031,2458],{"encoding":49},[15,16033,16035],{"className":16034,"ariaHidden":41},[54],[15,16036,16038,16041],{"className":16037},[58],[15,16039],{"className":16040,"style":299},[62],[15,16042,2458],{"className":16043,"style":2570},[67,68]," 后不再含有任何随机成分。这一设计并非技术上的简化，而是使后文反事实推理（第三部分 3.3 节）得以定义的必要前提：唯有把所有随机性封装进 ",[15,16046,16048,16061],{"className":16047,"translate":19},[18],[15,16049,16051],{"className":16050},[23],[25,16052,16053],{"xmlns":27},[29,16054,16055,16059],{},[32,16056,16057],{},[35,16058,2458],{},[47,16060,2458],{"encoding":49},[15,16062,16064],{"className":16063,"ariaHidden":41},[54],[15,16065,16067,16070],{"className":16066},[58],[15,16068],{"className":16069,"style":299},[62],[15,16071,2458],{"className":16072,"style":2570},[67,68],"，「同一个体在不同假设情景下会如何」这一问题才有明确的数学对象可以对应。",[1305,16075,16076],{"id":16076},"结构方程与因果计算",[11,16078,16079,16080,16124],{},"第二部分给出的 SCM 已经具备了计算观测分布 ",[15,16081,16083,16103],{"className":16082,"translate":19},[18],[15,16084,16086],{"className":16085},[23],[25,16087,16088],{"xmlns":27},[29,16089,16090,16100],{},[32,16091,16092,16094,16096,16098],{},[35,16093,98],{},[39,16095,102],{"stretchy":101},[35,16097,1343],{},[39,16099,111],{"stretchy":101},[47,16101,16102],{"encoding":49},"P(V)",[15,16104,16106],{"className":16105,"ariaHidden":41},[54],[15,16107,16109,16112,16115,16118,16121],{"className":16108},[58],[15,16110],{"className":16111,"style":124},[62],[15,16113,98],{"className":16114,"style":128},[67,68],[15,16116,102],{"className":16117},[132],[15,16119,1343],{"className":16120,"style":82},[67,68],[15,16122,111],{"className":16123},[148]," 的全部要素。本部分讨论结构方程如何进一步支持第二、三层的因果计算。",[1309,16126,16128],{"id":16127},"_31-结构方程的非对称性","3.1 结构方程的非对称性",[1314,16130,16131],{},[11,16132,16133,16136,16137,16205,16206,16272,16273,16276,16277,16280,16281,16309,16310,16338,16339,16447,16448,811,16499,16527,16528,16531,16532,16560,16561,16589,16590,16593],{},[305,16134,16135],{},"定义 3.1（结构方程 vs. 代数方程）"," 形如 ",[15,16138,16140,16166],{"className":16139,"translate":19},[18],[15,16141,16143],{"className":16142},[23],[25,16144,16145],{"xmlns":27},[29,16146,16147,16163],{},[32,16148,16149,16151,16153,16155,16157,16159,16161],{},[35,16150,45],{},[39,16152,8863],{},[39,16154,602],{},[35,16156,5724],{},[39,16158,102],{"stretchy":101},[35,16160,37],{},[39,16162,111],{"stretchy":101},[47,16164,16165],{"encoding":49},"Y := f(X)",[15,16167,16169,16187],{"className":16168,"ariaHidden":41},[54],[15,16170,16172,16175,16178,16181,16184],{"className":16171},[58],[15,16173],{"className":16174,"style":299},[62],[15,16176,45],{"className":16177,"style":82},[67,68],[15,16179],{"className":16180,"style":199},[77],[15,16182,8899],{"className":16183},[203],[15,16185],{"className":16186,"style":199},[77],[15,16188,16190,16193,16196,16199,16202],{"className":16189},[58],[15,16191],{"className":16192,"style":124},[62],[15,16194,5724],{"className":16195,"style":5772},[67,68],[15,16197,102],{"className":16198},[132],[15,16200,37],{"className":16201,"style":69},[67,68],[15,16203,111],{"className":16204},[148]," 的结构方程与代数方程 ",[15,16207,16209,16233],{"className":16208,"translate":19},[18],[15,16210,16212],{"className":16211},[23],[25,16213,16214],{"xmlns":27},[29,16215,16216,16230],{},[32,16217,16218,16220,16222,16224,16226,16228],{},[35,16219,45],{},[39,16221,602],{},[35,16223,5724],{},[39,16225,102],{"stretchy":101},[35,16227,37],{},[39,16229,111],{"stretchy":101},[47,16231,16232],{"encoding":49},"Y = f(X)",[15,16234,16236,16254],{"className":16235,"ariaHidden":41},[54],[15,16237,16239,16242,16245,16248,16251],{"className":16238},[58],[15,16240],{"className":16241,"style":299},[62],[15,16243,45],{"className":16244,"style":82},[67,68],[15,16246],{"className":16247,"style":199},[77],[15,16249,602],{"className":16250},[203],[15,16252],{"className":16253,"style":199},[77],[15,16255,16257,16260,16263,16266,16269],{"className":16256},[58],[15,16258],{"className":16259,"style":124},[62],[15,16261,5724],{"className":16262,"style":5772},[67,68],[15,16264,102],{"className":16265},[132],[15,16267,37],{"className":16268,"style":69},[67,68],[15,16270,111],{"className":16271},[148]," 在数值上等价，但语义不同：结构方程蕴含一种非对称的",[305,16274,16275],{},"生成关系","，规定右边变量的取值决定左边变量的取值，而这一决定关系",[305,16278,16279],{},"不可逆","——即便 ",[15,16282,16284,16297],{"className":16283,"translate":19},[18],[15,16285,16287],{"className":16286},[23],[25,16288,16289],{"xmlns":27},[29,16290,16291,16295],{},[32,16292,16293],{},[35,16294,5724],{},[47,16296,5724],{"encoding":49},[15,16298,16300],{"className":16299,"ariaHidden":41},[54],[15,16301,16303,16306],{"className":16302},[58],[15,16304],{"className":16305,"style":4456},[62],[15,16307,5724],{"className":16308,"style":5772},[67,68]," 可逆，从 ",[15,16311,16313,16326],{"className":16312,"translate":19},[18],[15,16314,16316],{"className":16315},[23],[25,16317,16318],{"xmlns":27},[29,16319,16320,16324],{},[32,16321,16322],{},[35,16323,534],{},[47,16325,534],{"encoding":49},[15,16327,16329],{"className":16328,"ariaHidden":41},[54],[15,16330,16332,16335],{"className":16331},[58],[15,16333],{"className":16334,"style":6432},[62],[15,16336,534],{"className":16337,"style":563},[67,68]," 反解出 ",[15,16340,16342,16374],{"className":16341,"translate":19},[18],[15,16343,16345],{"className":16344},[23],[25,16346,16347],{"xmlns":27},[29,16348,16349,16371],{},[32,16350,16351,16353,16355,16365,16367,16369],{},[35,16352,539],{},[39,16354,602],{},[872,16356,16357,16359],{},[35,16358,5724],{},[32,16360,16361,16363],{},[39,16362,14235],{},[1425,16364,1427],{},[39,16366,102],{"stretchy":101},[35,16368,534],{},[39,16370,111],{"stretchy":101},[47,16372,16373],{"encoding":49},"x = f^{-1}(y)",[15,16375,16377,16395],{"className":16376,"ariaHidden":41},[54],[15,16378,16380,16383,16386,16389,16392],{"className":16379},[58],[15,16381],{"className":16382,"style":635},[62],[15,16384,539],{"className":16385},[67,68],[15,16387],{"className":16388,"style":199},[77],[15,16390,602],{"className":16391},[203],[15,16393],{"className":16394,"style":199},[77],[15,16396,16398,16402,16438,16441,16444],{"className":16397},[58],[15,16399],{"className":16400,"style":16401},[62],"height:1.0641em;vertical-align:-0.25em;",[15,16403,16405,16408],{"className":16404},[67],[15,16406,5724],{"className":16407,"style":5772},[67,68],[15,16409,16411],{"className":16410},[918],[15,16412,16414],{"className":16413},[922],[15,16415,16417],{"className":16416},[927],[15,16418,16421],{"className":16419,"style":16420},[931],"height:0.8141em;",[15,16422,16423,16426],{"style":1002},[15,16424],{"className":16425,"style":940},[939],[15,16427,16429],{"className":16428},[944,945,946,947],[15,16430,16432,16435],{"className":16431},[67,947],[15,16433,14235],{"className":16434},[67,947],[15,16436,1427],{"className":16437},[67,947],[15,16439,102],{"className":16440},[132],[15,16442,534],{"className":16443,"style":563},[67,68],[15,16445,111],{"className":16446},[148]," 得到的也只是「给定 ",[15,16449,16451,16469],{"className":16450,"translate":19},[18],[15,16452,16454],{"className":16453},[23],[25,16455,16456],{"xmlns":27},[29,16457,16458,16466],{},[32,16459,16460,16462,16464],{},[35,16461,45],{},[39,16463,602],{},[35,16465,534],{},[47,16467,16468],{"encoding":49},"Y=y",[15,16470,16472,16490],{"className":16471,"ariaHidden":41},[54],[15,16473,16475,16478,16481,16484,16487],{"className":16474},[58],[15,16476],{"className":16477,"style":299},[62],[15,16479,45],{"className":16480,"style":82},[67,68],[15,16482],{"className":16483,"style":199},[77],[15,16485,602],{"className":16486},[203],[15,16488],{"className":16489,"style":199},[77],[15,16491,16493,16496],{"className":16492},[58],[15,16494],{"className":16495,"style":6432},[62],[15,16497,534],{"className":16498,"style":563},[67,68],[15,16500,16502,16515],{"className":16501,"translate":19},[18],[15,16503,16505],{"className":16504},[23],[25,16506,16507],{"xmlns":27},[29,16508,16509,16513],{},[32,16510,16511],{},[35,16512,37],{},[47,16514,37],{"encoding":49},[15,16516,16518],{"className":16517,"ariaHidden":41},[54],[15,16519,16521,16524],{"className":16520},[58],[15,16522],{"className":16523,"style":299},[62],[15,16525,37],{"className":16526,"style":69},[67,68]," 的取值应为多少」这一",[305,16529,16530],{},"代数","关系，而非「改变 ",[15,16533,16535,16548],{"className":16534,"translate":19},[18],[15,16536,16538],{"className":16537},[23],[25,16539,16540],{"xmlns":27},[29,16541,16542,16546],{},[32,16543,16544],{},[35,16545,37],{},[47,16547,37],{"encoding":49},[15,16549,16551],{"className":16550,"ariaHidden":41},[54],[15,16552,16554,16557],{"className":16553},[58],[15,16555],{"className":16556,"style":299},[62],[15,16558,37],{"className":16559,"style":69},[67,68]," 会如何改变 ",[15,16562,16564,16577],{"className":16563,"translate":19},[18],[15,16565,16567],{"className":16566},[23],[25,16568,16569],{"xmlns":27},[29,16570,16571,16575],{},[32,16572,16573],{},[35,16574,45],{},[47,16576,45],{"encoding":49},[15,16578,16580],{"className":16579,"ariaHidden":41},[54],[15,16581,16583,16586],{"className":16582},[58],[15,16584],{"className":16585,"style":299},[62],[15,16587,45],{"className":16588,"style":82},[67,68],"」这一",[305,16591,16592],{},"因果","关系的镜像。",[1314,16595,16596],{},[11,16597,16598,16601,16602,16630,16631,16659,16660,16725,16726,16784,16785,16848,16849,16852,16853,16946,16947,4335,16950,16978,16979,17076,17077,17105,17106,17168,17169,2249],{},[305,16599,16600],{},"例 3.1（欧姆定律的因果解读）"," 设某电路中电压源固定输出 ",[15,16603,16605,16618],{"className":16604,"translate":19},[18],[15,16606,16608],{"className":16607},[23],[25,16609,16610],{"xmlns":27},[29,16611,16612,16616],{},[32,16613,16614],{},[35,16615,1343],{},[47,16617,1343],{"encoding":49},[15,16619,16621],{"className":16620,"ariaHidden":41},[54],[15,16622,16624,16627],{"className":16623},[58],[15,16625],{"className":16626,"style":299},[62],[15,16628,1343],{"className":16629,"style":82},[67,68],"，电阻为 ",[15,16632,16634,16647],{"className":16633,"translate":19},[18],[15,16635,16637],{"className":16636},[23],[25,16638,16639],{"xmlns":27},[29,16640,16641,16645],{},[32,16642,16643],{},[35,16644,3784],{},[47,16646,3784],{"encoding":49},[15,16648,16650],{"className":16649,"ariaHidden":41},[54],[15,16651,16653,16656],{"className":16652},[58],[15,16654],{"className":16655,"style":299},[62],[15,16657,3784],{"className":16658,"style":3843},[67,68],"，依据电路物理机制，电流由前两者共同决定：结构方程应写作\n",[15,16661,16663,16689],{"className":16662,"translate":19},[18],[15,16664,16666],{"className":16665},[23],[25,16667,16668],{"xmlns":27},[29,16669,16670,16686],{},[32,16671,16672,16675,16677,16679,16681,16684],{},[35,16673,16674],{},"I",[39,16676,8863],{},[39,16678,602],{},[35,16680,1343],{},[35,16682,16683],{"mathvariant":878},"\u002F",[35,16685,3784],{},[47,16687,16688],{"encoding":49},"I := V\u002FR",[15,16690,16692,16710],{"className":16691,"ariaHidden":41},[54],[15,16693,16695,16698,16701,16704,16707],{"className":16694},[58],[15,16696],{"className":16697,"style":299},[62],[15,16699,16674],{"className":16700,"style":69},[67,68],[15,16702],{"className":16703,"style":199},[77],[15,16705,8899],{"className":16706},[203],[15,16708],{"className":16709,"style":199},[77],[15,16711,16713,16716,16719,16722],{"className":16712},[58],[15,16714],{"className":16715,"style":124},[62],[15,16717,1343],{"className":16718,"style":82},[67,68],[15,16720,16683],{"className":16721},[67],[15,16723,3784],{"className":16724,"style":3843},[67,68],"\n而非 ",[15,16727,16729,16751],{"className":16728,"translate":19},[18],[15,16730,16732],{"className":16731},[23],[25,16733,16734],{"xmlns":27},[29,16735,16736,16748],{},[32,16737,16738,16740,16742,16744,16746],{},[35,16739,1343],{},[39,16741,8863],{},[39,16743,602],{},[35,16745,16674],{},[35,16747,3784],{},[47,16749,16750],{"encoding":49},"V := IR",[15,16752,16754,16772],{"className":16753,"ariaHidden":41},[54],[15,16755,16757,16760,16763,16766,16769],{"className":16756},[58],[15,16758],{"className":16759,"style":299},[62],[15,16761,1343],{"className":16762,"style":82},[67,68],[15,16764],{"className":16765,"style":199},[77],[15,16767,8899],{"className":16768},[203],[15,16770],{"className":16771,"style":199},[77],[15,16773,16775,16778,16781],{"className":16774},[58],[15,16776],{"className":16777,"style":299},[62],[15,16779,16674],{"className":16780,"style":69},[67,68],[15,16782,3784],{"className":16783,"style":3843},[67,68]," 或 ",[15,16786,16788,16812],{"className":16787,"translate":19},[18],[15,16789,16791],{"className":16790},[23],[25,16792,16793],{"xmlns":27},[29,16794,16795,16809],{},[32,16796,16797,16799,16801,16803,16805,16807],{},[35,16798,3784],{},[39,16800,8863],{},[39,16802,602],{},[35,16804,1343],{},[35,16806,16683],{"mathvariant":878},[35,16808,16674],{},[47,16810,16811],{"encoding":49},"R := V\u002FI",[15,16813,16815,16833],{"className":16814,"ariaHidden":41},[54],[15,16816,16818,16821,16824,16827,16830],{"className":16817},[58],[15,16819],{"className":16820,"style":299},[62],[15,16822,3784],{"className":16823,"style":3843},[67,68],[15,16825],{"className":16826,"style":199},[77],[15,16828,8899],{"className":16829},[203],[15,16831],{"className":16832,"style":199},[77],[15,16834,16836,16839,16842,16845],{"className":16835},[58],[15,16837],{"className":16838,"style":124},[62],[15,16840,1343],{"className":16841,"style":82},[67,68],[15,16843,16683],{"className":16844},[67],[15,16846,16674],{"className":16847,"style":69},[67,68],"。三个代数式在数值上完全等价，但只有前者正确刻画了该电路的",[305,16850,16851],{},"生成机制","。这一区分的实践意义在于：若外部操作者通过某种装置强行将电流设定为 ",[15,16854,16856,16878],{"className":16855,"translate":19},[18],[15,16857,16859],{"className":16858},[23],[25,16860,16861],{"xmlns":27},[29,16862,16863,16875],{},[32,16864,16865,16867,16869],{},[35,16866,16674],{},[39,16868,602],{},[863,16870,16871,16873],{},[35,16872,1682],{},[1425,16874,2461],{},[47,16876,16877],{"encoding":49},"I = i_0",[15,16879,16881,16899],{"className":16880,"ariaHidden":41},[54],[15,16882,16884,16887,16890,16893,16896],{"className":16883},[58],[15,16885],{"className":16886,"style":299},[62],[15,16888,16674],{"className":16889,"style":69},[67,68],[15,16891],{"className":16892,"style":199},[77],[15,16894,602],{"className":16895},[203],[15,16897],{"className":16898,"style":199},[77],[15,16900,16902,16906],{"className":16901},[58],[15,16903],{"className":16904,"style":16905},[62],"height:0.8095em;vertical-align:-0.15em;",[15,16907,16909,16912],{"className":16908},[67],[15,16910,1682],{"className":16911},[67,68],[15,16913,16915],{"className":16914},[918],[15,16916,16918,16938],{"className":16917},[922,923],[15,16919,16921,16935],{"className":16920},[927],[15,16922,16924],{"className":16923,"style":1496},[931],[15,16925,16926,16929],{"style":7289},[15,16927],{"className":16928,"style":940},[939],[15,16930,16932],{"className":16931},[944,945,946,947],[15,16933,2461],{"className":16934},[67,947],[15,16936,955],{"className":16937},[954],[15,16939,16941],{"className":16940},[927],[15,16942,16944],{"className":16943,"style":962},[931],[15,16945],{},"（例如接入恒流源），依据正确的结构方程，会导致",[305,16948,16949],{},"电压",[15,16951,16953,16966],{"className":16952,"translate":19},[18],[15,16954,16956],{"className":16955},[23],[25,16957,16958],{"xmlns":27},[29,16959,16960,16964],{},[32,16961,16962],{},[35,16963,1343],{},[47,16965,1343],{"encoding":49},[15,16967,16969],{"className":16968,"ariaHidden":41},[54],[15,16970,16972,16975],{"className":16971},[58],[15,16973],{"className":16974,"style":299},[62],[15,16976,1343],{"className":16977,"style":82},[67,68]," 相应改变以满足 ",[15,16980,16982,17006],{"className":16981,"translate":19},[18],[15,16983,16985],{"className":16984},[23],[25,16986,16987],{"xmlns":27},[29,16988,16989,17003],{},[32,16990,16991,16993,16995,17001],{},[35,16992,1343],{},[39,16994,602],{},[863,16996,16997,16999],{},[35,16998,1682],{},[1425,17000,2461],{},[35,17002,3784],{},[47,17004,17005],{"encoding":49},"V = i_0 R",[15,17007,17009,17027],{"className":17008,"ariaHidden":41},[54],[15,17010,17012,17015,17018,17021,17024],{"className":17011},[58],[15,17013],{"className":17014,"style":299},[62],[15,17016,1343],{"className":17017,"style":82},[67,68],[15,17019],{"className":17020,"style":199},[77],[15,17022,602],{"className":17023},[203],[15,17025],{"className":17026,"style":199},[77],[15,17028,17030,17033,17073],{"className":17029},[58],[15,17031],{"className":17032,"style":1865},[62],[15,17034,17036,17039],{"className":17035},[67],[15,17037,1682],{"className":17038},[67,68],[15,17040,17042],{"className":17041},[918],[15,17043,17045,17065],{"className":17044},[922,923],[15,17046,17048,17062],{"className":17047},[927],[15,17049,17051],{"className":17050,"style":1496},[931],[15,17052,17053,17056],{"style":7289},[15,17054],{"className":17055,"style":940},[939],[15,17057,17059],{"className":17058},[944,945,946,947],[15,17060,2461],{"className":17061},[67,947],[15,17063,955],{"className":17064},[954],[15,17066,17068],{"className":17067},[927],[15,17069,17071],{"className":17070,"style":962},[931],[15,17072],{},[15,17074,3784],{"className":17075,"style":3843},[67,68],"，而电阻 ",[15,17078,17080,17093],{"className":17079,"translate":19},[18],[15,17081,17083],{"className":17082},[23],[25,17084,17085],{"xmlns":27},[29,17086,17087,17091],{},[32,17088,17089],{},[35,17090,3784],{},[47,17092,3784],{"encoding":49},[15,17094,17096],{"className":17095,"ariaHidden":41},[54],[15,17097,17099,17102],{"className":17098},[58],[15,17100],{"className":17101,"style":299},[62],[15,17103,3784],{"className":17104,"style":3843},[67,68]," 不受影响；若错误地采用 ",[15,17107,17109,17132],{"className":17108,"translate":19},[18],[15,17110,17112],{"className":17111},[23],[25,17113,17114],{"xmlns":27},[29,17115,17116,17130],{},[32,17117,17118,17120,17122,17124,17126,17128],{},[35,17119,3784],{},[39,17121,8863],{},[39,17123,602],{},[35,17125,1343],{},[35,17127,16683],{"mathvariant":878},[35,17129,16674],{},[47,17131,16811],{"encoding":49},[15,17133,17135,17153],{"className":17134,"ariaHidden":41},[54],[15,17136,17138,17141,17144,17147,17150],{"className":17137},[58],[15,17139],{"className":17140,"style":299},[62],[15,17142,3784],{"className":17143,"style":3843},[67,68],[15,17145],{"className":17146,"style":199},[77],[15,17148,8899],{"className":17149},[203],[15,17151],{"className":17152,"style":199},[77],[15,17154,17156,17159,17162,17165],{"className":17155},[58],[15,17157],{"className":17158,"style":124},[62],[15,17160,1343],{"className":17161,"style":82},[67,68],[15,17163,16683],{"className":17164},[67],[15,17166,16674],{"className":17167,"style":69},[67,68]," 作为该情境下的结构方程，则会得出「电阻会因电流改变而改变」这一荒谬结论。",[305,17170,17171],{},"选对结构方程的方向，等价于选对了系统中「谁是自变量、谁是因变量」这一物理事实，这一信息无法从代数关系本身获得，必须来自对系统机制的外部知识",[1309,17173,17175],{"id":17174},"_32-干预与-do-算子","3.2 干预与 do-算子",[1314,17177,17178],{},[11,17179,17180,11065,17183,17295,17296,17347,17348,17418,17419,4335,17422,17616,17617,17847,17848,17876,17877,18064],{},[305,17181,17182],{},"定义 3.2（干预，do-operator）",[15,17184,17186,17226],{"className":17185,"translate":19},[18],[15,17187,17189],{"className":17188},[23],[25,17190,17191],{"xmlns":27},[29,17192,17193,17223],{},[32,17194,17195,17197,17199,17201,17203,17205,17207,17209,17211,17213,17215,17217,17219,17221],{},[35,17196,9469],{},[39,17198,602],{},[39,17200,2445],{"stretchy":101},[35,17202,2458],{},[39,17204,42],{"separator":41},[35,17206,1343],{},[39,17208,42],{"separator":41},[35,17210,9484],{},[39,17212,42],{"separator":41},[35,17214,98],{},[39,17216,102],{"stretchy":101},[35,17218,2458],{},[39,17220,111],{"stretchy":101},[39,17222,2493],{"stretchy":101},[47,17224,17225],{"encoding":49},"M = \\langle U,V,F,P(U)\\rangle",[15,17227,17229,17247],{"className":17228,"ariaHidden":41},[54],[15,17230,17232,17235,17238,17241,17244],{"className":17231},[58],[15,17233],{"className":17234,"style":299},[62],[15,17236,9469],{"className":17237,"style":2570},[67,68],[15,17239],{"className":17240,"style":199},[77],[15,17242,602],{"className":17243},[203],[15,17245],{"className":17246,"style":199},[77],[15,17248,17250,17253,17256,17259,17262,17265,17268,17271,17274,17277,17280,17283,17286,17289,17292],{"className":17249},[58],[15,17251],{"className":17252,"style":124},[62],[15,17254,2445],{"className":17255},[132],[15,17257,2458],{"className":17258,"style":2570},[67,68],[15,17260,42],{"className":17261},[73],[15,17263],{"className":17264,"style":78},[77],[15,17266,1343],{"className":17267,"style":82},[67,68],[15,17269,42],{"className":17270},[73],[15,17272],{"className":17273,"style":78},[77],[15,17275,9484],{"className":17276,"style":128},[67,68],[15,17278,42],{"className":17279},[73],[15,17281],{"className":17282,"style":78},[77],[15,17284,98],{"className":17285,"style":128},[67,68],[15,17287,102],{"className":17288},[132],[15,17290,2458],{"className":17291,"style":2570},[67,68],[15,17293,9569],{"className":17294},[148],"，对变量 ",[15,17297,17299,17317],{"className":17298,"translate":19},[18],[15,17300,17302],{"className":17301},[23],[25,17303,17304],{"xmlns":27},[29,17305,17306,17314],{},[32,17307,17308,17310,17312],{},[35,17309,37],{},[39,17311,1696],{},[35,17313,1343],{},[47,17315,17316],{"encoding":49},"X \\in V",[15,17318,17320,17338],{"className":17319,"ariaHidden":41},[54],[15,17321,17323,17326,17329,17332,17335],{"className":17322},[58],[15,17324],{"className":17325,"style":6645},[62],[15,17327,37],{"className":17328,"style":69},[67,68],[15,17330],{"className":17331,"style":199},[77],[15,17333,1696],{"className":17334},[203],[15,17336],{"className":17337,"style":199},[77],[15,17339,17341,17344],{"className":17340},[58],[15,17342],{"className":17343,"style":299},[62],[15,17345,1343],{"className":17346,"style":82},[67,68]," 施加干预 ",[15,17349,17351,17376],{"className":17350,"translate":19},[18],[15,17352,17354],{"className":17353},[23],[25,17355,17356],{"xmlns":27},[29,17357,17358,17374],{},[32,17359,17360,17362,17364,17366,17368,17370,17372],{},[35,17361,696],{},[35,17363,699],{},[39,17365,102],{"stretchy":101},[35,17367,37],{},[39,17369,602],{},[35,17371,539],{},[39,17373,111],{"stretchy":101},[47,17375,8079],{"encoding":49},[15,17377,17379,17406],{"className":17378,"ariaHidden":41},[54],[15,17380,17382,17385,17388,17391,17394,17397,17400,17403],{"className":17381},[58],[15,17383],{"className":17384,"style":124},[62],[15,17386,696],{"className":17387},[67,68],[15,17389,699],{"className":17390},[67,68],[15,17392,102],{"className":17393},[132],[15,17395,37],{"className":17396,"style":69},[67,68],[15,17398],{"className":17399,"style":199},[77],[15,17401,602],{"className":17402},[203],[15,17404],{"className":17405,"style":199},[77],[15,17407,17409,17412,17415],{"className":17408},[58],[15,17410],{"className":17411,"style":124},[62],[15,17413,539],{"className":17414},[67,68],[15,17416,111],{"className":17417},[148],"，得到一个新的",[305,17420,17421],{},"子模型（submodel）",[15,17423,17425,17473],{"className":17424,"translate":19},[18],[15,17426,17428],{"className":17427},[23],[25,17429,17430],{"xmlns":27},[29,17431,17432,17470],{},[32,17433,17434,17440,17442,17444,17446,17448,17450,17452,17458,17460,17462,17464,17466,17468],{},[863,17435,17436,17438],{},[35,17437,9469],{},[35,17439,539],{},[39,17441,602],{},[39,17443,2445],{"stretchy":101},[35,17445,2458],{},[39,17447,42],{"separator":41},[35,17449,1343],{},[39,17451,42],{"separator":41},[863,17453,17454,17456],{},[35,17455,9484],{},[35,17457,539],{},[39,17459,42],{"separator":41},[35,17461,98],{},[39,17463,102],{"stretchy":101},[35,17465,2458],{},[39,17467,111],{"stretchy":101},[39,17469,2493],{"stretchy":101},[47,17471,17472],{"encoding":49},"M_x = \\langle U, V, F_x, P(U)\\rangle",[15,17474,17476,17531],{"className":17475,"ariaHidden":41},[54],[15,17477,17479,17482,17522,17525,17528],{"className":17478},[58],[15,17480],{"className":17481,"style":1865},[62],[15,17483,17485,17488],{"className":17484},[67],[15,17486,9469],{"className":17487,"style":2570},[67,68],[15,17489,17491],{"className":17490},[918],[15,17492,17494,17514],{"className":17493},[922,923],[15,17495,17497,17511],{"className":17496},[927],[15,17498,17500],{"className":17499,"style":932},[931],[15,17501,17502,17505],{"style":2585},[15,17503],{"className":17504,"style":940},[939],[15,17506,17508],{"className":17507},[944,945,946,947],[15,17509,539],{"className":17510},[67,68,947],[15,17512,955],{"className":17513},[954],[15,17515,17517],{"className":17516},[927],[15,17518,17520],{"className":17519,"style":962},[931],[15,17521],{},[15,17523],{"className":17524,"style":199},[77],[15,17526,602],{"className":17527},[203],[15,17529],{"className":17530,"style":199},[77],[15,17532,17534,17537,17540,17543,17546,17549,17552,17555,17558,17598,17601,17604,17607,17610,17613],{"className":17533},[58],[15,17535],{"className":17536,"style":124},[62],[15,17538,2445],{"className":17539},[132],[15,17541,2458],{"className":17542,"style":2570},[67,68],[15,17544,42],{"className":17545},[73],[15,17547],{"className":17548,"style":78},[77],[15,17550,1343],{"className":17551,"style":82},[67,68],[15,17553,42],{"className":17554},[73],[15,17556],{"className":17557,"style":78},[77],[15,17559,17561,17564],{"className":17560},[67],[15,17562,9484],{"className":17563,"style":128},[67,68],[15,17565,17567],{"className":17566},[918],[15,17568,17570,17590],{"className":17569},[922,923],[15,17571,17573,17587],{"className":17572},[927],[15,17574,17576],{"className":17575,"style":932},[931],[15,17577,17578,17581],{"style":12327},[15,17579],{"className":17580,"style":940},[939],[15,17582,17584],{"className":17583},[944,945,946,947],[15,17585,539],{"className":17586},[67,68,947],[15,17588,955],{"className":17589},[954],[15,17591,17593],{"className":17592},[927],[15,17594,17596],{"className":17595,"style":962},[931],[15,17597],{},[15,17599,42],{"className":17600},[73],[15,17602],{"className":17603,"style":78},[77],[15,17605,98],{"className":17606,"style":128},[67,68],[15,17608,102],{"className":17609},[132],[15,17611,2458],{"className":17612,"style":2570},[67,68],[15,17614,9569],{"className":17615},[148],"，其中\n",[15,17618,17620,17673],{"className":17619,"translate":19},[18],[15,17621,17623],{"className":17622},[23],[25,17624,17625],{"xmlns":27},[29,17626,17627,17670],{},[32,17628,17629,17635,17637,17639,17641,17643,17645,17651,17653,17655,17658,17660,17662,17664,17666,17668],{},[863,17630,17631,17633],{},[35,17632,9484],{},[35,17634,539],{},[39,17636,602],{},[39,17638,102],{"stretchy":101},[35,17640,9484],{},[39,17642,10252],{},[39,17644,1419],{"stretchy":101},[863,17646,17647,17649],{},[35,17648,5724],{},[35,17650,37],{},[39,17652,1444],{"stretchy":101},[39,17654,111],{"stretchy":101},[39,17656,17657],{},"∪",[39,17659,1419],{"stretchy":101},[35,17661,37],{},[39,17663,8863],{},[39,17665,602],{},[35,17667,539],{},[39,17669,1444],{"stretchy":101},[47,17671,17672],{"encoding":49},"F_x = (F \\setminus \\{f_X\\}) \\cup \\{X := x\\}",[15,17674,17676,17731,17752,17814,17835],{"className":17675,"ariaHidden":41},[54],[15,17677,17679,17682,17722,17725,17728],{"className":17678},[58],[15,17680],{"className":17681,"style":1865},[62],[15,17683,17685,17688],{"className":17684},[67],[15,17686,9484],{"className":17687,"style":128},[67,68],[15,17689,17691],{"className":17690},[918],[15,17692,17694,17714],{"className":17693},[922,923],[15,17695,17697,17711],{"className":17696},[927],[15,17698,17700],{"className":17699,"style":932},[931],[15,17701,17702,17705],{"style":12327},[15,17703],{"className":17704,"style":940},[939],[15,17706,17708],{"className":17707},[944,945,946,947],[15,17709,539],{"className":17710},[67,68,947],[15,17712,955],{"className":17713},[954],[15,17715,17717],{"className":17716},[927],[15,17718,17720],{"className":17719,"style":962},[931],[15,17721],{},[15,17723],{"className":17724,"style":199},[77],[15,17726,602],{"className":17727},[203],[15,17729],{"className":17730,"style":199},[77],[15,17732,17734,17737,17740,17743,17746,17749],{"className":17733},[58],[15,17735],{"className":17736,"style":124},[62],[15,17738,102],{"className":17739},[132],[15,17741,9484],{"className":17742,"style":128},[67,68],[15,17744],{"className":17745,"style":82},[77],[15,17747,10252],{"className":17748},[1648],[15,17750],{"className":17751,"style":82},[77],[15,17753,17755,17758,17761,17801,17805,17808,17811],{"className":17754},[58],[15,17756],{"className":17757,"style":124},[62],[15,17759,1419],{"className":17760},[132],[15,17762,17764,17767],{"className":17763},[67],[15,17765,5724],{"className":17766,"style":5772},[67,68],[15,17768,17770],{"className":17769},[918],[15,17771,17773,17793],{"className":17772},[922,923],[15,17774,17776,17790],{"className":17775},[927],[15,17777,17779],{"className":17778,"style":7358},[931],[15,17780,17781,17784],{"style":10023},[15,17782],{"className":17783,"style":940},[939],[15,17785,17787],{"className":17786},[944,945,946,947],[15,17788,37],{"className":17789,"style":69},[67,68,947],[15,17791,955],{"className":17792},[954],[15,17794,17796],{"className":17795},[927],[15,17797,17799],{"className":17798,"style":962},[931],[15,17800],{},[15,17802,17804],{"className":17803},[148],"})",[15,17806],{"className":17807,"style":82},[77],[15,17809,17657],{"className":17810},[1648],[15,17812],{"className":17813,"style":82},[77],[15,17815,17817,17820,17823,17826,17829,17832],{"className":17816},[58],[15,17818],{"className":17819,"style":124},[62],[15,17821,1419],{"className":17822},[132],[15,17824,37],{"className":17825,"style":69},[67,68],[15,17827],{"className":17828,"style":199},[77],[15,17830,8899],{"className":17831},[203],[15,17833],{"className":17834,"style":199},[77],[15,17836,17838,17841,17844],{"className":17837},[58],[15,17839],{"className":17840,"style":124},[62],[15,17842,539],{"className":17843},[67,68],[15,17845,1444],{"className":17846},[148],"\n即把 ",[15,17849,17851,17864],{"className":17850,"translate":19},[18],[15,17852,17854],{"className":17853},[23],[25,17855,17856],{"xmlns":27},[29,17857,17858,17862],{},[32,17859,17860],{},[35,17861,37],{},[47,17863,37],{"encoding":49},[15,17865,17867],{"className":17866,"ariaHidden":41},[54],[15,17868,17870,17873],{"className":17869},[58],[15,17871],{"className":17872,"style":299},[62],[15,17874,37],{"className":17875,"style":69},[67,68]," 原有的结构方程 ",[15,17878,17880,17920],{"className":17879,"translate":19},[18],[15,17881,17883],{"className":17882},[23],[25,17884,17885],{"xmlns":27},[29,17886,17887,17917],{},[32,17888,17889,17895,17897,17907,17909,17915],{},[863,17890,17891,17893],{},[35,17892,5724],{},[35,17894,37],{},[39,17896,102],{"stretchy":101},[863,17898,17899,17905],{},[32,17900,17901,17903],{},[35,17902,98],{"mathvariant":878},[35,17904,10218],{"mathvariant":878},[35,17906,37],{},[39,17908,42],{"separator":41},[863,17910,17911,17913],{},[35,17912,2458],{},[35,17914,37],{},[39,17916,111],{"stretchy":101},[47,17918,17919],{"encoding":49},"f_X(\\mathrm{Pa}_X, U_X)",[15,17921,17923],{"className":17922,"ariaHidden":41},[54],[15,17924,17926,17929,17969,17972,18015,18018,18021,18061],{"className":17925},[58],[15,17927],{"className":17928,"style":124},[62],[15,17930,17932,17935],{"className":17931},[67],[15,17933,5724],{"className":17934,"style":5772},[67,68],[15,17936,17938],{"className":17937},[918],[15,17939,17941,17961],{"className":17940},[922,923],[15,17942,17944,17958],{"className":17943},[927],[15,17945,17947],{"className":17946,"style":7358},[931],[15,17948,17949,17952],{"style":10023},[15,17950],{"className":17951,"style":940},[939],[15,17953,17955],{"className":17954},[944,945,946,947],[15,17956,37],{"className":17957,"style":69},[67,68,947],[15,17959,955],{"className":17960},[954],[15,17962,17964],{"className":17963},[927],[15,17965,17967],{"className":17966,"style":962},[931],[15,17968],{},[15,17970,102],{"className":17971},[132],[15,17973,17975,17981],{"className":17974},[67],[15,17976,17978],{"className":17977},[67],[15,17979,10383],{"className":17980},[67,10382],[15,17982,17984],{"className":17983},[918],[15,17985,17987,18007],{"className":17986},[922,923],[15,17988,17990,18004],{"className":17989},[927],[15,17991,17993],{"className":17992,"style":7358},[931],[15,17994,17995,17998],{"style":10398},[15,17996],{"className":17997,"style":940},[939],[15,17999,18001],{"className":18000},[944,945,946,947],[15,18002,37],{"className":18003,"style":69},[67,68,947],[15,18005,955],{"className":18006},[954],[15,18008,18010],{"className":18009},[927],[15,18011,18013],{"className":18012,"style":962},[931],[15,18014],{},[15,18016,42],{"className":18017},[73],[15,18019],{"className":18020,"style":78},[77],[15,18022,18024,18027],{"className":18023},[67],[15,18025,2458],{"className":18026,"style":2570},[67,68],[15,18028,18030],{"className":18029},[918],[15,18031,18033,18053],{"className":18032},[922,923],[15,18034,18036,18050],{"className":18035},[927],[15,18037,18039],{"className":18038,"style":7358},[931],[15,18040,18041,18044],{"style":2585},[15,18042],{"className":18043,"style":940},[939],[15,18045,18047],{"className":18046},[944,945,946,947],[15,18048,37],{"className":18049,"style":69},[67,68,947],[15,18051,955],{"className":18052},[954],[15,18054,18056],{"className":18055},[927],[15,18057,18059],{"className":18058,"style":962},[931],[15,18060],{},[15,18062,111],{"className":18063},[148]," 整体替换为常量赋值，其余所有方程保持不变。",[1314,18066,18067],{},[11,18068,18069,18072,18073,18101,18102,18172,18173,18243,18244],{},[305,18070,18071],{},"定义 3.3（干预分布）"," 变量 ",[15,18074,18076,18089],{"className":18075,"translate":19},[18],[15,18077,18079],{"className":18078},[23],[25,18080,18081],{"xmlns":27},[29,18082,18083,18087],{},[32,18084,18085],{},[35,18086,45],{},[47,18088,45],{"encoding":49},[15,18090,18092],{"className":18091,"ariaHidden":41},[54],[15,18093,18095,18098],{"className":18094},[58],[15,18096],{"className":18097,"style":299},[62],[15,18099,45],{"className":18100,"style":82},[67,68]," 在干预 ",[15,18103,18105,18130],{"className":18104,"translate":19},[18],[15,18106,18108],{"className":18107},[23],[25,18109,18110],{"xmlns":27},[29,18111,18112,18128],{},[32,18113,18114,18116,18118,18120,18122,18124,18126],{},[35,18115,696],{},[35,18117,699],{},[39,18119,102],{"stretchy":101},[35,18121,37],{},[39,18123,602],{},[35,18125,539],{},[39,18127,111],{"stretchy":101},[47,18129,8079],{"encoding":49},[15,18131,18133,18160],{"className":18132,"ariaHidden":41},[54],[15,18134,18136,18139,18142,18145,18148,18151,18154,18157],{"className":18135},[58],[15,18137],{"className":18138,"style":124},[62],[15,18140,696],{"className":18141},[67,68],[15,18143,699],{"className":18144},[67,68],[15,18146,102],{"className":18147},[132],[15,18149,37],{"className":18150,"style":69},[67,68],[15,18152],{"className":18153,"style":199},[77],[15,18155,602],{"className":18156},[203],[15,18158],{"className":18159,"style":199},[77],[15,18161,18163,18166,18169],{"className":18162},[58],[15,18164],{"className":18165,"style":124},[62],[15,18167,539],{"className":18168},[67,68],[15,18170,111],{"className":18171},[148]," 下的分布，定义为子模型 ",[15,18174,18176,18194],{"className":18175,"translate":19},[18],[15,18177,18179],{"className":18178},[23],[25,18180,18181],{"xmlns":27},[29,18182,18183,18191],{},[32,18184,18185],{},[863,18186,18187,18189],{},[35,18188,9469],{},[35,18190,539],{},[47,18192,18193],{"encoding":49},"M_x",[15,18195,18197],{"className":18196,"ariaHidden":41},[54],[15,18198,18200,18203],{"className":18199},[58],[15,18201],{"className":18202,"style":1865},[62],[15,18204,18206,18209],{"className":18205},[67],[15,18207,9469],{"className":18208,"style":2570},[67,68],[15,18210,18212],{"className":18211},[918],[15,18213,18215,18235],{"className":18214},[922,923],[15,18216,18218,18232],{"className":18217},[927],[15,18219,18221],{"className":18220,"style":932},[931],[15,18222,18223,18226],{"style":2585},[15,18224],{"className":18225,"style":940},[939],[15,18227,18229],{"className":18228},[944,945,946,947],[15,18230,539],{"className":18231},[67,68,947],[15,18233,955],{"className":18234},[954],[15,18236,18238],{"className":18237},[927],[15,18239,18241],{"className":18240,"style":962},[931],[15,18242],{}," 的诱导分布：\n",[15,18245,18247,18299],{"className":18246,"translate":19},[18],[15,18248,18250],{"className":18249},[23],[25,18251,18252],{"xmlns":27},[29,18253,18254,18296],{},[32,18255,18256,18258,18260,18262,18264,18266,18268,18270,18272,18274,18276,18278,18280,18290,18292,18294],{},[35,18257,98],{},[39,18259,102],{"stretchy":101},[35,18261,534],{},[39,18263,170],{},[35,18265,696],{},[35,18267,699],{},[39,18269,102],{"stretchy":101},[35,18271,539],{},[39,18273,111],{"stretchy":101},[39,18275,111],{"stretchy":101},[39,18277,8863],{},[39,18279,602],{},[863,18281,18282,18284],{},[35,18283,98],{},[863,18285,18286,18288],{},[35,18287,9469],{},[35,18289,539],{},[39,18291,102],{"stretchy":101},[35,18293,534],{},[39,18295,111],{"stretchy":101},[47,18297,18298],{"encoding":49},"P(y \\mid do(x)) := P_{M_x}(y)",[15,18300,18302,18326,18356],{"className":18301,"ariaHidden":41},[54],[15,18303,18305,18308,18311,18314,18317,18320,18323],{"className":18304},[58],[15,18306],{"className":18307,"style":124},[62],[15,18309,98],{"className":18310,"style":128},[67,68],[15,18312,102],{"className":18313},[132],[15,18315,534],{"className":18316,"style":563},[67,68],[15,18318],{"className":18319,"style":199},[77],[15,18321,170],{"className":18322},[203],[15,18324],{"className":18325,"style":199},[77],[15,18327,18329,18332,18335,18338,18341,18344,18347,18350,18353],{"className":18328},[58],[15,18330],{"className":18331,"style":124},[62],[15,18333,696],{"className":18334},[67,68],[15,18336,699],{"className":18337},[67,68],[15,18339,102],{"className":18340},[132],[15,18342,539],{"className":18343},[67,68],[15,18345,759],{"className":18346},[148],[15,18348],{"className":18349,"style":199},[77],[15,18351,8899],{"className":18352},[203],[15,18354],{"className":18355,"style":199},[77],[15,18357,18359,18363,18449,18452,18455],{"className":18358},[58],[15,18360],{"className":18361,"style":18362},[62],"height:1.0001em;vertical-align:-0.2501em;",[15,18364,18366,18369],{"className":18365},[67],[15,18367,98],{"className":18368,"style":128},[67,68],[15,18370,18372],{"className":18371},[918],[15,18373,18375,18440],{"className":18374},[922,923],[15,18376,18378,18437],{"className":18377},[927],[15,18379,18381],{"className":18380,"style":7358},[931],[15,18382,18383,18386],{"style":12327},[15,18384],{"className":18385,"style":940},[939],[15,18387,18389],{"className":18388},[944,945,946,947],[15,18390,18392],{"className":18391},[67,947],[15,18393,18395,18398],{"className":18394},[67,947],[15,18396,9469],{"className":18397,"style":2570},[67,68,947],[15,18399,18401],{"className":18400},[918],[15,18402,18404,18428],{"className":18403},[922,923],[15,18405,18407,18425],{"className":18406},[927],[15,18408,18411],{"className":18409,"style":18410},[931],"height:0.1645em;",[15,18412,18414,18418],{"style":18413},"top:-2.357em;margin-left:-0.109em;margin-right:0.0714em;",[15,18415],{"className":18416,"style":18417},[939],"height:2.5em;",[15,18419,18422],{"className":18420},[944,18421,15089,947],"reset-size3",[15,18423,539],{"className":18424},[67,68,947],[15,18426,955],{"className":18427},[954],[15,18429,18431],{"className":18430},[927],[15,18432,18435],{"className":18433,"style":18434},[931],"height:0.143em;",[15,18436],{},[15,18438,955],{"className":18439},[954],[15,18441,18443],{"className":18442},[927],[15,18444,18447],{"className":18445,"style":18446},[931],"height:0.2501em;",[15,18448],{},[15,18450,102],{"className":18451},[132],[15,18453,534],{"className":18454,"style":563},[67,68],[15,18456,111],{"className":18457},[148],[11,18459,18460,18463,18464,18534,18535,18563,18564,18592,18593,18621,18622,18740,18741,18769,18770,18798],{},[305,18461,18462],{},"在图上的对应操作","：干预 ",[15,18465,18467,18492],{"className":18466,"translate":19},[18],[15,18468,18470],{"className":18469},[23],[25,18471,18472],{"xmlns":27},[29,18473,18474,18490],{},[32,18475,18476,18478,18480,18482,18484,18486,18488],{},[35,18477,696],{},[35,18479,699],{},[39,18481,102],{"stretchy":101},[35,18483,37],{},[39,18485,602],{},[35,18487,539],{},[39,18489,111],{"stretchy":101},[47,18491,8079],{"encoding":49},[15,18493,18495,18522],{"className":18494,"ariaHidden":41},[54],[15,18496,18498,18501,18504,18507,18510,18513,18516,18519],{"className":18497},[58],[15,18499],{"className":18500,"style":124},[62],[15,18502,696],{"className":18503},[67,68],[15,18505,699],{"className":18506},[67,68],[15,18508,102],{"className":18509},[132],[15,18511,37],{"className":18512,"style":69},[67,68],[15,18514],{"className":18515,"style":199},[77],[15,18517,602],{"className":18518},[203],[15,18520],{"className":18521,"style":199},[77],[15,18523,18525,18528,18531],{"className":18524},[58],[15,18526],{"className":18527,"style":124},[62],[15,18529,539],{"className":18530},[67,68],[15,18532,111],{"className":18533},[148]," 对应从因果图 ",[15,18536,18538,18551],{"className":18537,"translate":19},[18],[15,18539,18541],{"className":18540},[23],[25,18542,18543],{"xmlns":27},[29,18544,18545,18549],{},[32,18546,18547],{},[35,18548,1336],{},[47,18550,1336],{"encoding":49},[15,18552,18554],{"className":18553,"ariaHidden":41},[54],[15,18555,18557,18560],{"className":18556},[58],[15,18558],{"className":18559,"style":299},[62],[15,18561,1336],{"className":18562},[67,68]," 中删去 ",[15,18565,18567,18580],{"className":18566,"translate":19},[18],[15,18568,18570],{"className":18569},[23],[25,18571,18572],{"xmlns":27},[29,18573,18574,18578],{},[32,18575,18576],{},[35,18577,37],{},[47,18579,37],{"encoding":49},[15,18581,18583],{"className":18582,"ariaHidden":41},[54],[15,18584,18586,18589],{"className":18585},[58],[15,18587],{"className":18588,"style":299},[62],[15,18590,37],{"className":18591,"style":69},[67,68]," 的所有入边（即切断 ",[15,18594,18596,18609],{"className":18595,"translate":19},[18],[15,18597,18599],{"className":18598},[23],[25,18600,18601],{"xmlns":27},[29,18602,18603,18607],{},[32,18604,18605],{},[35,18606,37],{},[47,18608,37],{"encoding":49},[15,18610,18612],{"className":18611,"ariaHidden":41},[54],[15,18613,18615,18618],{"className":18614},[58],[15,18616],{"className":18617,"style":299},[62],[15,18619,37],{"className":18620,"style":69},[67,68]," 与其父节点的连接），得到修改后的图 ",[15,18623,18625,18649],{"className":18624,"translate":19},[18],[15,18626,18628],{"className":18627},[23],[25,18629,18630],{"xmlns":27},[29,18631,18632,18646],{},[32,18633,18634],{},[863,18635,18636,18638],{},[35,18637,1336],{},[18639,18640,18641,18643],"mover",{"accent":41},[35,18642,37],{},[39,18644,18645],{"stretchy":41},"‾",[47,18647,18648],{"encoding":49},"G_{\\overline{X}}",[15,18650,18652],{"className":18651,"ariaHidden":41},[54],[15,18653,18655,18659],{"className":18654},[58],[15,18656],{"className":18657,"style":18658},[62],"height:0.9884em;vertical-align:-0.305em;",[15,18660,18662,18665],{"className":18661},[67],[15,18663,1336],{"className":18664},[67,68],[15,18666,18668],{"className":18667},[918],[15,18669,18671,18731],{"className":18670},[922,923],[15,18672,18674,18728],{"className":18673},[927],[15,18675,18678],{"className":18676,"style":18677},[931],"height:0.3448em;",[15,18679,18681,18685],{"style":18680},"top:-2.695em;margin-left:0em;margin-right:0.05em;",[15,18682],{"className":18683,"style":18684},[939],"height:3em;",[15,18686,18688],{"className":18687},[944,945,946,947],[15,18689,18691],{"className":18690},[67,947],[15,18692,18695],{"className":18693},[67,18694,947],"overline",[15,18696,18698],{"className":18697},[922],[15,18699,18701],{"className":18700},[927],[15,18702,18705,18717],{"className":18703,"style":18704},[931],"height:0.9283em;",[15,18706,18708,18711],{"style":18707},"top:-3em;",[15,18709],{"className":18710,"style":18684},[939],[15,18712,18714],{"className":18713},[67,947],[15,18715,37],{"className":18716,"style":69},[67,68,947],[15,18718,18720,18723],{"style":18719},"top:-3.8303em;",[15,18721],{"className":18722,"style":18684},[939],[15,18724],{"className":18725,"style":18727},[18726,947],"overline-line","border-bottom-width:0.049em;",[15,18729,955],{"className":18730},[954],[15,18732,18734],{"className":18733},[927],[15,18735,18738],{"className":18736,"style":18737},[931],"height:0.305em;",[15,18739],{},"，同时保留 ",[15,18742,18744,18757],{"className":18743,"translate":19},[18],[15,18745,18747],{"className":18746},[23],[25,18748,18749],{"xmlns":27},[29,18750,18751,18755],{},[32,18752,18753],{},[35,18754,37],{},[47,18756,37],{"encoding":49},[15,18758,18760],{"className":18759,"ariaHidden":41},[54],[15,18761,18763,18766],{"className":18762},[58],[15,18764],{"className":18765,"style":299},[62],[15,18767,37],{"className":18768,"style":69},[67,68]," 的所有出边不变。这一操作直观地表达了「外部干预使得 ",[15,18771,18773,18786],{"className":18772,"translate":19},[18],[15,18774,18776],{"className":18775},[23],[25,18777,18778],{"xmlns":27},[29,18779,18780,18784],{},[32,18781,18782],{},[35,18783,37],{},[47,18785,37],{"encoding":49},[15,18787,18789],{"className":18788,"ariaHidden":41},[54],[15,18790,18792,18795],{"className":18791},[58],[15,18793],{"className":18794,"style":299},[62],[15,18796,37],{"className":18797,"style":69},[67,68]," 不再由其自然原因决定，而是由外部力量强制设定」这一语义。",[1314,18800,18801],{},[11,18802,18803,18806,18807,19510,19511,19543],{},[305,18804,18805],{},"定理 3.1（截断因子分解公式，Truncated Factorization）"," 对马尔可夫型 SCM，\n",[15,18808,18810,18956],{"className":18809,"translate":19},[18],[15,18811,18813],{"className":18812},[23],[25,18814,18815],{"xmlns":27},[29,18816,18817,18953],{},[32,18818,18819,18821,18823,18829,18831,18833,18835,18841,18843,18845,18847,18849,18851,18853,18855,18857],{},[35,18820,98],{},[39,18822,102],{"stretchy":101},[863,18824,18825,18827],{},[35,18826,12538],{},[1425,18828,1427],{},[39,18830,42],{"separator":41},[39,18832,1432],{},[39,18834,42],{"separator":41},[863,18836,18837,18839],{},[35,18838,12538],{},[35,18840,1441],{},[39,18842,170],{},[35,18844,696],{},[35,18846,699],{},[39,18848,102],{"stretchy":101},[35,18850,539],{},[39,18852,111],{"stretchy":101},[39,18854,111],{"stretchy":101},[39,18856,602],{},[32,18858,18859,18861],{},[39,18860,1419],{"fence":41},[13705,18862,18866,18938],{"rowspacing":18863,"columnalign":18864,"columnspacing":18865},"0.36em","left left","1em",[13711,18867,18868,18915],{},[13714,18869,18870],{},[11837,18871,18872],{"scriptlevel":2461,"displaystyle":101},[32,18873,18874,18891,18893,18895,18901,18903,18913],{},[863,18875,18876,18878],{},[39,18877,12562],{},[32,18879,18880,18886,18889],{},[863,18881,18882,18884],{},[35,18883,1343],{},[35,18885,1682],{},[39,18887,18888],{"mathvariant":878},"≠",[35,18890,37],{},[35,18892,98],{},[39,18894,102],{"stretchy":101},[863,18896,18897,18899],{},[35,18898,12538],{},[35,18900,1682],{},[39,18902,170],{},[863,18904,18905,18911],{},[32,18906,18907,18909],{},[35,18908,11],{"mathvariant":878},[35,18910,10218],{"mathvariant":878},[35,18912,1682],{},[39,18914,111],{"stretchy":101},[13714,18916,18917],{},[11837,18918,18919],{"scriptlevel":2461,"displaystyle":101},[32,18920,18921,18924,18926,18929,18931,18933,18935],{},[238,18922,18923],{},"若 ",[35,18925,12538],{},[238,18927,18928],{}," 的取值与 ",[35,18930,37],{},[39,18932,602],{},[35,18934,539],{},[238,18936,18937],{}," 相容",[13711,18939,18940,18946],{},[13714,18941,18942],{},[11837,18943,18944],{"scriptlevel":2461,"displaystyle":101},[1425,18945,2461],{},[13714,18947,18948],{},[11837,18949,18950],{"scriptlevel":2461,"displaystyle":101},[238,18951,18952],{},"否则",[47,18954,18955],{"encoding":49},"P(v_1,\\dots,v_n \\mid do(x)) = \\begin{cases} \\prod_{V_i \\neq X} P(v_i \\mid \\mathrm{pa}_i) & \\text{若 } v \\text{ 的取值与 } X=x \\text{ 相容} \\\\ 0 & \\text{否则}\\end{cases}",[15,18957,18959,19078,19108],{"className":18958,"ariaHidden":41},[54],[15,18960,18962,18965,18968,18971,19011,19014,19017,19020,19023,19026,19029,19069,19072,19075],{"className":18961},[58],[15,18963],{"className":18964,"style":124},[62],[15,18966,98],{"className":18967,"style":128},[67,68],[15,18969,102],{"className":18970},[132],[15,18972,18974,18977],{"className":18973},[67],[15,18975,12538],{"className":18976,"style":563},[67,68],[15,18978,18980],{"className":18979},[918],[15,18981,18983,19003],{"className":18982},[922,923],[15,18984,18986,19000],{"className":18985},[927],[15,18987,18989],{"className":18988,"style":1496},[931],[15,18990,18991,18994],{"style":935},[15,18992],{"className":18993,"style":940},[939],[15,18995,18997],{"className":18996},[944,945,946,947],[15,18998,1427],{"className":18999},[67,947],[15,19001,955],{"className":19002},[954],[15,19004,19006],{"className":19005},[927],[15,19007,19009],{"className":19008,"style":962},[931],[15,19010],{},[15,19012,42],{"className":19013},[73],[15,19015],{"className":19016,"style":78},[77],[15,19018,1432],{"className":19019},[1529],[15,19021],{"className":19022,"style":78},[77],[15,19024,42],{"className":19025},[73],[15,19027],{"className":19028,"style":78},[77],[15,19030,19032,19035],{"className":19031},[67],[15,19033,12538],{"className":19034,"style":563},[67,68],[15,19036,19038],{"className":19037},[918],[15,19039,19041,19061],{"className":19040},[922,923],[15,19042,19044,19058],{"className":19043},[927],[15,19045,19047],{"className":19046,"style":932},[931],[15,19048,19049,19052],{"style":935},[15,19050],{"className":19051,"style":940},[939],[15,19053,19055],{"className":19054},[944,945,946,947],[15,19056,1441],{"className":19057},[67,68,947],[15,19059,955],{"className":19060},[954],[15,19062,19064],{"className":19063},[927],[15,19065,19067],{"className":19066,"style":962},[931],[15,19068],{},[15,19070],{"className":19071,"style":199},[77],[15,19073,170],{"className":19074},[203],[15,19076],{"className":19077,"style":199},[77],[15,19079,19081,19084,19087,19090,19093,19096,19099,19102,19105],{"className":19080},[58],[15,19082],{"className":19083,"style":124},[62],[15,19085,696],{"className":19086},[67,68],[15,19088,699],{"className":19089},[67,68],[15,19091,102],{"className":19092},[132],[15,19094,539],{"className":19095},[67,68],[15,19097,759],{"className":19098},[148],[15,19100],{"className":19101,"style":199},[77],[15,19103,602],{"className":19104},[203],[15,19106],{"className":19107,"style":199},[77],[15,19109,19111,19115],{"className":19110},[58],[15,19112],{"className":19113,"style":19114},[62],"height:3em;vertical-align:-1.25em;",[15,19116,19118,19127,19506],{"className":19117},[1529],[15,19119,19123],{"className":19120,"style":19122},[132,19121],"delimcenter","top:0em;",[15,19124,1419],{"className":19125},[15088,19126],"size4",[15,19128,19130],{"className":19129},[67],[15,19131,19133,19407,19410],{"className":19132},[13705],[15,19134,19136],{"className":19135},[14454],[15,19137,19139,19398],{"className":19138},[922,923],[15,19140,19142,19395],{"className":19141},[927],[15,19143,19146,19383],{"className":19144,"style":19145},[931],"height:1.6919em;",[15,19147,19149,19153],{"style":19148},"top:-3.6919em;",[15,19150],{"className":19151,"style":19152},[939],"height:3.008em;",[15,19154,19156,19279,19282,19285,19288,19328,19331,19334,19337,19380],{"className":19155},[67],[15,19157,19159,19162],{"className":19158},[12772],[15,19160,12562],{"className":19161,"style":12778},[12772,12776,12777],[15,19163,19165],{"className":19164},[918],[15,19166,19168,19270],{"className":19167},[922,923],[15,19169,19171,19267],{"className":19170},[927],[15,19172,19175],{"className":19173,"style":19174},[931],"height:0.1864em;",[15,19176,19177,19180],{"style":12794},[15,19178],{"className":19179,"style":940},[939],[15,19181,19183],{"className":19182},[944,945,946,947],[15,19184,19186,19228,19264],{"className":19185},[67,947],[15,19187,19189,19192],{"className":19188},[67,947],[15,19190,1343],{"className":19191,"style":82},[67,68,947],[15,19193,19195],{"className":19194},[918],[15,19196,19198,19220],{"className":19197},[922,923],[15,19199,19201,19217],{"className":19200},[927],[15,19202,19205],{"className":19203,"style":19204},[931],"height:0.3281em;",[15,19206,19208,19211],{"style":19207},"top:-2.357em;margin-left:-0.2222em;margin-right:0.0714em;",[15,19209],{"className":19210,"style":18417},[939],[15,19212,19214],{"className":19213},[944,18421,15089,947],[15,19215,1682],{"className":19216},[67,68,947],[15,19218,955],{"className":19219},[954],[15,19221,19223],{"className":19222},[927],[15,19224,19226],{"className":19225,"style":18434},[931],[15,19227],{},[15,19229,19231,19258,19261],{"className":19230},[203,947],[15,19232,19234],{"className":19233},[203,947],[15,19235,19237],{"className":19236},[67,4469,947],[15,19238,19240],{"className":19239},[4473,947],[15,19241,19243,19246,19255],{"className":19242},[4477,947],[15,19244],{"className":19245,"style":4456},[62],[15,19247,19249],{"className":19248},[4484],[15,19250,19252],{"className":19251},[67,947],[15,19253,4491],{"className":19254},[203,947],[15,19256],{"className":19257},[4495],[15,19259],{"className":19260},[77,4499,947],[15,19262,602],{"className":19263},[203,947],[15,19265,37],{"className":19266,"style":69},[67,68,947],[15,19268,955],{"className":19269},[954],[15,19271,19273],{"className":19272},[927],[15,19274,19277],{"className":19275,"style":19276},[931],"height:0.4358em;",[15,19278],{},[15,19280],{"className":19281,"style":78},[77],[15,19283,98],{"className":19284,"style":128},[67,68],[15,19286,102],{"className":19287},[132],[15,19289,19291,19294],{"className":19290},[67],[15,19292,12538],{"className":19293,"style":563},[67,68],[15,19295,19297],{"className":19296},[918],[15,19298,19300,19320],{"className":19299},[922,923],[15,19301,19303,19317],{"className":19302},[927],[15,19304,19306],{"className":19305,"style":1733},[931],[15,19307,19308,19311],{"style":935},[15,19309],{"className":19310,"style":940},[939],[15,19312,19314],{"className":19313},[944,945,946,947],[15,19315,1682],{"className":19316},[67,68,947],[15,19318,955],{"className":19319},[954],[15,19321,19323],{"className":19322},[927],[15,19324,19326],{"className":19325,"style":962},[931],[15,19327],{},[15,19329],{"className":19330,"style":199},[77],[15,19332,170],{"className":19333},[203],[15,19335],{"className":19336,"style":199},[77],[15,19338,19340,19346],{"className":19339},[67],[15,19341,19343],{"className":19342},[67],[15,19344,12910],{"className":19345},[67,10382],[15,19347,19349],{"className":19348},[918],[15,19350,19352,19372],{"className":19351},[922,923],[15,19353,19355,19369],{"className":19354},[927],[15,19356,19358],{"className":19357,"style":12923},[931],[15,19359,19360,19363],{"style":12926},[15,19361],{"className":19362,"style":940},[939],[15,19364,19366],{"className":19365},[944,945,946,947],[15,19367,1682],{"className":19368},[67,68,947],[15,19370,955],{"className":19371},[954],[15,19373,19375],{"className":19374},[927],[15,19376,19378],{"className":19377,"style":12945},[931],[15,19379],{},[15,19381,111],{"className":19382},[148],[15,19384,19386,19389],{"style":19385},"top:-2.2481em;",[15,19387],{"className":19388,"style":19152},[939],[15,19390,19392],{"className":19391},[67],[15,19393,2461],{"className":19394},[67],[15,19396,955],{"className":19397},[954],[15,19399,19401],{"className":19400},[927],[15,19402,19405],{"className":19403,"style":19404},[931],"height:1.1919em;",[15,19406],{},[15,19408],{"className":19409,"style":15217},[15216],[15,19411,19413],{"className":19412},[14454],[15,19414,19416,19498],{"className":19415},[922,923],[15,19417,19419,19495],{"className":19418},[927],[15,19420,19422,19481],{"className":19421,"style":19145},[931],[15,19423,19424,19427],{"style":19148},[15,19425],{"className":19426,"style":19152},[939],[15,19428,19430,19440,19443,19456,19459,19462,19465,19468,19471],{"className":19429},[67],[15,19431,19433,19437],{"className":19432},[67,4123],[15,19434,19436],{"className":19435},[67,7759],"若",[15,19438,3926],{"className":19439},[67],[15,19441,12538],{"className":19442,"style":563},[67,68],[15,19444,19446,19449,19453],{"className":19445},[67,4123],[15,19447,3926],{"className":19448},[67],[15,19450,19452],{"className":19451},[67,7759],"的取值与",[15,19454,3926],{"className":19455},[67],[15,19457,37],{"className":19458,"style":69},[67,68],[15,19460],{"className":19461,"style":199},[77],[15,19463,602],{"className":19464},[203],[15,19466],{"className":19467,"style":199},[77],[15,19469,539],{"className":19470},[67,68],[15,19472,19474,19477],{"className":19473},[67,4123],[15,19475,3926],{"className":19476},[67],[15,19478,19480],{"className":19479},[67,7759],"相容",[15,19482,19483,19486],{"style":19385},[15,19484],{"className":19485,"style":19152},[939],[15,19487,19489],{"className":19488},[67],[15,19490,19492],{"className":19491},[67,4123],[15,19493,18952],{"className":19494},[67,7759],[15,19496,955],{"className":19497},[954],[15,19499,19501],{"className":19500},[927],[15,19502,19504],{"className":19503,"style":19404},[931],[15,19505],{},[15,19507],{"className":19508},[148,19509],"nulldelimiter","\n即干预分布等于观测分布的马尔可夫分解式中",[305,19512,19513,19514,19542],{},"删去 ",[15,19515,19517,19530],{"className":19516,"translate":19},[18],[15,19518,19520],{"className":19519},[23],[25,19521,19522],{"xmlns":27},[29,19523,19524,19528],{},[32,19525,19526],{},[35,19527,37],{},[47,19529,37],{"encoding":49},[15,19531,19533],{"className":19532,"ariaHidden":41},[54],[15,19534,19536,19539],{"className":19535},[58],[15,19537],{"className":19538,"style":299},[62],[15,19540,37],{"className":19541,"style":69},[67,68]," 对应因子后","的乘积。这一公式是连接观测数据（第一层）与干预效果（第二层）的桥梁，也是后续「后门准则」「前门准则」等可识别性理论的直接推论。",[1314,19545,19546,19609,20707],{},[11,19547,19548,19551,19552,19608],{},[305,19549,19550],{},"例 3.2（观察与干预的数值区分）"," 沿用洒水器例子。设已知 ",[15,19553,19555,19575],{"className":19554,"translate":19},[18],[15,19556,19558],{"className":19557},[23],[25,19559,19560],{"xmlns":27},[29,19561,19562,19572],{},[32,19563,19564,19566,19568,19570],{},[35,19565,3779],{},[35,19567,11],{},[39,19569,602],{},[1425,19571,1427],{},[47,19573,19574],{"encoding":49},"Sp=1",[15,19576,19578,19599],{"className":19577,"ariaHidden":41},[54],[15,19579,19581,19584,19587,19590,19593,19596],{"className":19580},[58],[15,19582],{"className":19583,"style":63},[62],[15,19585,3779],{"className":19586,"style":1396},[67,68],[15,19588,11],{"className":19589},[67,68],[15,19591],{"className":19592,"style":199},[77],[15,19594,602],{"className":19595},[203],[15,19597],{"className":19598,"style":199},[77],[15,19600,19602,19605],{"className":19601},[58],[15,19603],{"className":19604,"style":3149},[62],[15,19606,1427],{"className":19607},[67],"（洒水器开着）。",[507,19610,19611,20004],{},[510,19612,19613,4335,19616,12957,19731,19787,19788,19816,19817,19872,19873,19924,19925,20003],{},[305,19614,19615],{},"观察情形",[15,19617,19619,19653],{"className":19618,"translate":19},[18],[15,19620,19622],{"className":19621},[23],[25,19623,19624],{"xmlns":27},[29,19625,19626,19650],{},[32,19627,19628,19630,19632,19634,19636,19638,19640,19642,19644,19646,19648],{},[35,19629,98],{},[39,19631,102],{"stretchy":101},[35,19633,3784],{},[39,19635,602],{},[1425,19637,1427],{},[39,19639,170],{},[35,19641,3779],{},[35,19643,11],{},[39,19645,602],{},[1425,19647,1427],{},[39,19649,111],{"stretchy":101},[47,19651,19652],{"encoding":49},"P(R=1 \\mid Sp=1)",[15,19654,19656,19680,19698,19719],{"className":19655,"ariaHidden":41},[54],[15,19657,19659,19662,19665,19668,19671,19674,19677],{"className":19658},[58],[15,19660],{"className":19661,"style":124},[62],[15,19663,98],{"className":19664,"style":128},[67,68],[15,19666,102],{"className":19667},[132],[15,19669,3784],{"className":19670,"style":3843},[67,68],[15,19672],{"className":19673,"style":199},[77],[15,19675,602],{"className":19676},[203],[15,19678],{"className":19679,"style":199},[77],[15,19681,19683,19686,19689,19692,19695],{"className":19682},[58],[15,19684],{"className":19685,"style":124},[62],[15,19687,1427],{"className":19688},[67],[15,19690],{"className":19691,"style":199},[77],[15,19693,170],{"className":19694},[203],[15,19696],{"className":19697,"style":199},[77],[15,19699,19701,19704,19707,19710,19713,19716],{"className":19700},[58],[15,19702],{"className":19703,"style":63},[62],[15,19705,3779],{"className":19706,"style":1396},[67,68],[15,19708,11],{"className":19709},[67,68],[15,19711],{"className":19712,"style":199},[77],[15,19714,602],{"className":19715},[203],[15,19717],{"className":19718,"style":199},[77],[15,19720,19722,19725,19728],{"className":19721},[58],[15,19723],{"className":19724,"style":124},[62],[15,19726,1427],{"className":19727},[67],[15,19729,111],{"className":19730},[148],[15,19732,19734,19754],{"className":19733,"translate":19},[18],[15,19735,19737],{"className":19736},[23],[25,19738,19739],{"xmlns":27},[29,19740,19741,19751],{},[32,19742,19743,19745,19747,19749],{},[35,19744,3779],{},[39,19746,1846],{},[35,19748,3779],{},[35,19750,11],{},[47,19752,19753],{"encoding":49},"S \\to Sp",[15,19755,19757,19775],{"className":19756,"ariaHidden":41},[54],[15,19758,19760,19763,19766,19769,19772],{"className":19759},[58],[15,19761],{"className":19762,"style":299},[62],[15,19764,3779],{"className":19765,"style":1396},[67,68],[15,19767],{"className":19768,"style":199},[77],[15,19770,1846],{"className":19771},[203],[15,19773],{"className":19774,"style":199},[77],[15,19776,19778,19781,19784],{"className":19777},[58],[15,19779],{"className":19780,"style":63},[62],[15,19782,3779],{"className":19783,"style":1396},[67,68],[15,19785,11],{"className":19786},[67,68],"，观察到洒水器开启会更新我们对季节 ",[15,19789,19791,19804],{"className":19790,"translate":19},[18],[15,19792,19794],{"className":19793},[23],[25,19795,19796],{"xmlns":27},[29,19797,19798,19802],{},[32,19799,19800],{},[35,19801,3779],{},[47,19803,3779],{"encoding":49},[15,19805,19807],{"className":19806,"ariaHidden":41},[54],[15,19808,19810,19813],{"className":19809},[58],[15,19811],{"className":19812,"style":299},[62],[15,19814,3779],{"className":19815,"style":1396},[67,68]," 的信念（贝叶斯反推），例如若干燥季节更常开洒水器，则观察到 ",[15,19818,19820,19839],{"className":19819,"translate":19},[18],[15,19821,19823],{"className":19822},[23],[25,19824,19825],{"xmlns":27},[29,19826,19827,19837],{},[32,19828,19829,19831,19833,19835],{},[35,19830,3779],{},[35,19832,11],{},[39,19834,602],{},[1425,19836,1427],{},[47,19838,19574],{"encoding":49},[15,19840,19842,19863],{"className":19841,"ariaHidden":41},[54],[15,19843,19845,19848,19851,19854,19857,19860],{"className":19844},[58],[15,19846],{"className":19847,"style":63},[62],[15,19849,3779],{"className":19850,"style":1396},[67,68],[15,19852,11],{"className":19853},[67,68],[15,19855],{"className":19856,"style":199},[77],[15,19858,602],{"className":19859},[203],[15,19861],{"className":19862,"style":199},[77],[15,19864,19866,19869],{"className":19865},[58],[15,19867],{"className":19868,"style":3149},[62],[15,19870,1427],{"className":19871},[67]," 会提高「当前是干燥季节」的后验概率，进而压低 ",[15,19874,19876,19894],{"className":19875,"translate":19},[18],[15,19877,19879],{"className":19878},[23],[25,19880,19881],{"xmlns":27},[29,19882,19883,19891],{},[32,19884,19885,19887,19889],{},[35,19886,3784],{},[39,19888,602],{},[1425,19890,1427],{},[47,19892,19893],{"encoding":49},"R=1",[15,19895,19897,19915],{"className":19896,"ariaHidden":41},[54],[15,19898,19900,19903,19906,19909,19912],{"className":19899},[58],[15,19901],{"className":19902,"style":299},[62],[15,19904,3784],{"className":19905,"style":3843},[67,68],[15,19907],{"className":19908,"style":199},[77],[15,19910,602],{"className":19911},[203],[15,19913],{"className":19914,"style":199},[77],[15,19916,19918,19921],{"className":19917},[58],[15,19919],{"className":19920,"style":3149},[62],[15,19922,1427],{"className":19923},[67]," 的概率。此计算通过叉结构 ",[15,19926,19928,19952],{"className":19927,"translate":19},[18],[15,19929,19931],{"className":19930},[23],[25,19932,19933],{"xmlns":27},[29,19934,19935,19949],{},[32,19936,19937,19939,19941,19943,19945,19947],{},[35,19938,3784],{},[39,19940,4882],{},[35,19942,3779],{},[39,19944,1846],{},[35,19946,3779],{},[35,19948,11],{},[47,19950,19951],{"encoding":49},"R \\leftarrow S \\to Sp",[15,19953,19955,19973,19991],{"className":19954,"ariaHidden":41},[54],[15,19956,19958,19961,19964,19967,19970],{"className":19957},[58],[15,19959],{"className":19960,"style":299},[62],[15,19962,3784],{"className":19963,"style":3843},[67,68],[15,19965],{"className":19966,"style":199},[77],[15,19968,4882],{"className":19969},[203],[15,19971],{"className":19972,"style":199},[77],[15,19974,19976,19979,19982,19985,19988],{"className":19975},[58],[15,19977],{"className":19978,"style":299},[62],[15,19980,3779],{"className":19981,"style":1396},[67,68],[15,19983],{"className":19984,"style":199},[77],[15,19986,1846],{"className":19987},[203],[15,19989],{"className":19990,"style":199},[77],[15,19992,19994,19997,20000],{"className":19993},[58],[15,19995],{"className":19996,"style":63},[62],[15,19998,3779],{"className":19999,"style":1396},[67,68],[15,20001,11],{"className":20002},[67,68]," 这条未被阻断的路径进行。",[510,20005,20006,4335,20009,20141,20142,20197,20198,20226,20227,20304,20305,20360,20361,20706],{},[305,20007,20008],{},"干预情形",[15,20010,20012,20054],{"className":20011,"translate":19},[18],[15,20013,20015],{"className":20014},[23],[25,20016,20017],{"xmlns":27},[29,20018,20019,20051],{},[32,20020,20021,20023,20025,20027,20029,20031,20033,20035,20037,20039,20041,20043,20045,20047,20049],{},[35,20022,98],{},[39,20024,102],{"stretchy":101},[35,20026,3784],{},[39,20028,602],{},[1425,20030,1427],{},[39,20032,170],{},[35,20034,696],{},[35,20036,699],{},[39,20038,102],{"stretchy":101},[35,20040,3779],{},[35,20042,11],{},[39,20044,602],{},[1425,20046,1427],{},[39,20048,111],{"stretchy":101},[39,20050,111],{"stretchy":101},[47,20052,20053],{"encoding":49},"P(R=1 \\mid do(Sp=1))",[15,20055,20057,20081,20099,20129],{"className":20056,"ariaHidden":41},[54],[15,20058,20060,20063,20066,20069,20072,20075,20078],{"className":20059},[58],[15,20061],{"className":20062,"style":124},[62],[15,20064,98],{"className":20065,"style":128},[67,68],[15,20067,102],{"className":20068},[132],[15,20070,3784],{"className":20071,"style":3843},[67,68],[15,20073],{"className":20074,"style":199},[77],[15,20076,602],{"className":20077},[203],[15,20079],{"className":20080,"style":199},[77],[15,20082,20084,20087,20090,20093,20096],{"className":20083},[58],[15,20085],{"className":20086,"style":124},[62],[15,20088,1427],{"className":20089},[67],[15,20091],{"className":20092,"style":199},[77],[15,20094,170],{"className":20095},[203],[15,20097],{"className":20098,"style":199},[77],[15,20100,20102,20105,20108,20111,20114,20117,20120,20123,20126],{"className":20101},[58],[15,20103],{"className":20104,"style":124},[62],[15,20106,696],{"className":20107},[67,68],[15,20109,699],{"className":20110},[67,68],[15,20112,102],{"className":20113},[132],[15,20115,3779],{"className":20116,"style":1396},[67,68],[15,20118,11],{"className":20119},[67,68],[15,20121],{"className":20122,"style":199},[77],[15,20124,602],{"className":20125},[203],[15,20127],{"className":20128,"style":199},[77],[15,20130,20132,20135,20138],{"className":20131},[58],[15,20133],{"className":20134,"style":124},[62],[15,20136,1427],{"className":20137},[67],[15,20139,759],{"className":20140},[148],"：依据定义 3.2，干预会切断 ",[15,20143,20145,20164],{"className":20144,"translate":19},[18],[15,20146,20148],{"className":20147},[23],[25,20149,20150],{"xmlns":27},[29,20151,20152,20162],{},[32,20153,20154,20156,20158,20160],{},[35,20155,3779],{},[39,20157,1846],{},[35,20159,3779],{},[35,20161,11],{},[47,20163,19753],{"encoding":49},[15,20165,20167,20185],{"className":20166,"ariaHidden":41},[54],[15,20168,20170,20173,20176,20179,20182],{"className":20169},[58],[15,20171],{"className":20172,"style":299},[62],[15,20174,3779],{"className":20175,"style":1396},[67,68],[15,20177],{"className":20178,"style":199},[77],[15,20180,1846],{"className":20181},[203],[15,20183],{"className":20184,"style":199},[77],[15,20186,20188,20191,20194],{"className":20187},[58],[15,20189],{"className":20190,"style":63},[62],[15,20192,3779],{"className":20193,"style":1396},[67,68],[15,20195,11],{"className":20196},[67,68]," 这条边，于是 ",[15,20199,20201,20214],{"className":20200,"translate":19},[18],[15,20202,20204],{"className":20203},[23],[25,20205,20206],{"xmlns":27},[29,20207,20208,20212],{},[32,20209,20210],{},[35,20211,3779],{},[47,20213,3779],{"encoding":49},[15,20215,20217],{"className":20216,"ariaHidden":41},[54],[15,20218,20220,20223],{"className":20219},[58],[15,20221],{"className":20222,"style":299},[62],[15,20224,3779],{"className":20225,"style":1396},[67,68]," 的分布完全不受「我们把洒水器打开」这一操作的影响；而 ",[15,20228,20230,20253],{"className":20229,"translate":19},[18],[15,20231,20233],{"className":20232},[23],[25,20234,20235],{"xmlns":27},[29,20236,20237,20251],{},[32,20238,20239,20241,20243,20245,20247,20249],{},[35,20240,3784],{},[39,20242,4882],{},[35,20244,3779],{},[39,20246,1846],{},[35,20248,3779],{},[35,20250,11],{},[47,20252,19951],{"encoding":49},[15,20254,20256,20274,20292],{"className":20255,"ariaHidden":41},[54],[15,20257,20259,20262,20265,20268,20271],{"className":20258},[58],[15,20260],{"className":20261,"style":299},[62],[15,20263,3784],{"className":20264,"style":3843},[67,68],[15,20266],{"className":20267,"style":199},[77],[15,20269,4882],{"className":20270},[203],[15,20272],{"className":20273,"style":199},[77],[15,20275,20277,20280,20283,20286,20289],{"className":20276},[58],[15,20278],{"className":20279,"style":299},[62],[15,20281,3779],{"className":20282,"style":1396},[67,68],[15,20284],{"className":20285,"style":199},[77],[15,20287,1846],{"className":20288},[203],[15,20290],{"className":20291,"style":199},[77],[15,20293,20295,20298,20301],{"className":20294},[58],[15,20296],{"className":20297,"style":63},[62],[15,20299,3779],{"className":20300,"style":1396},[67,68],[15,20302,11],{"className":20303},[67,68]," 这条路径由于 ",[15,20306,20308,20327],{"className":20307,"translate":19},[18],[15,20309,20311],{"className":20310},[23],[25,20312,20313],{"xmlns":27},[29,20314,20315,20325],{},[32,20316,20317,20319,20321,20323],{},[35,20318,3779],{},[39,20320,1846],{},[35,20322,3779],{},[35,20324,11],{},[47,20326,19753],{"encoding":49},[15,20328,20330,20348],{"className":20329,"ariaHidden":41},[54],[15,20331,20333,20336,20339,20342,20345],{"className":20332},[58],[15,20334],{"className":20335,"style":299},[62],[15,20337,3779],{"className":20338,"style":1396},[67,68],[15,20340],{"className":20341,"style":199},[77],[15,20343,1846],{"className":20344},[203],[15,20346],{"className":20347,"style":199},[77],[15,20349,20351,20354,20357],{"className":20350},[58],[15,20352],{"className":20353,"style":63},[62],[15,20355,3779],{"className":20356,"style":1396},[67,68],[15,20358,11],{"className":20359},[67,68]," 边已被切断，不再传递任何信息。因此\n",[15,20362,20364,20454],{"className":20363,"translate":19},[18],[15,20365,20367],{"className":20366},[23],[25,20368,20369],{"xmlns":27},[29,20370,20371,20451],{},[32,20372,20373,20375,20377,20379,20381,20383,20385,20387,20389,20391,20393,20395,20397,20399,20401,20403,20405,20407,20409,20411,20413,20415,20417,20419,20427,20429,20431,20433,20435,20437,20439,20441,20443,20445,20447,20449],{},[35,20374,98],{},[39,20376,102],{"stretchy":101},[35,20378,3784],{},[39,20380,602],{},[1425,20382,1427],{},[39,20384,170],{},[35,20386,696],{},[35,20388,699],{},[39,20390,102],{"stretchy":101},[35,20392,3779],{},[35,20394,11],{},[39,20396,602],{},[1425,20398,1427],{},[39,20400,111],{"stretchy":101},[39,20402,111],{"stretchy":101},[39,20404,602],{},[35,20406,98],{},[39,20408,102],{"stretchy":101},[35,20410,3784],{},[39,20412,602],{},[1425,20414,1427],{},[39,20416,111],{"stretchy":101},[39,20418,602],{},[863,20420,20421,20424],{},[39,20422,20423],{},"∑",[35,20425,20426],{},"s",[35,20428,98],{},[39,20430,102],{"stretchy":101},[35,20432,3784],{},[39,20434,602],{},[1425,20436,1427],{},[39,20438,170],{},[35,20440,20426],{},[39,20442,111],{"stretchy":101},[35,20444,98],{},[39,20446,102],{"stretchy":101},[35,20448,20426],{},[39,20450,111],{"stretchy":101},[47,20452,20453],{"encoding":49},"P(R=1 \\mid do(Sp=1)) = P(R=1) = \\sum_s P(R=1\\mid s)P(s)",[15,20455,20457,20481,20499,20529,20550,20574,20595,20664,20682],{"className":20456,"ariaHidden":41},[54],[15,20458,20460,20463,20466,20469,20472,20475,20478],{"className":20459},[58],[15,20461],{"className":20462,"style":124},[62],[15,20464,98],{"className":20465,"style":128},[67,68],[15,20467,102],{"className":20468},[132],[15,20470,3784],{"className":20471,"style":3843},[67,68],[15,20473],{"className":20474,"style":199},[77],[15,20476,602],{"className":20477},[203],[15,20479],{"className":20480,"style":199},[77],[15,20482,20484,20487,20490,20493,20496],{"className":20483},[58],[15,20485],{"className":20486,"style":124},[62],[15,20488,1427],{"className":20489},[67],[15,20491],{"className":20492,"style":199},[77],[15,20494,170],{"className":20495},[203],[15,20497],{"className":20498,"style":199},[77],[15,20500,20502,20505,20508,20511,20514,20517,20520,20523,20526],{"className":20501},[58],[15,20503],{"className":20504,"style":124},[62],[15,20506,696],{"className":20507},[67,68],[15,20509,699],{"className":20510},[67,68],[15,20512,102],{"className":20513},[132],[15,20515,3779],{"className":20516,"style":1396},[67,68],[15,20518,11],{"className":20519},[67,68],[15,20521],{"className":20522,"style":199},[77],[15,20524,602],{"className":20525},[203],[15,20527],{"className":20528,"style":199},[77],[15,20530,20532,20535,20538,20541,20544,20547],{"className":20531},[58],[15,20533],{"className":20534,"style":124},[62],[15,20536,1427],{"className":20537},[67],[15,20539,759],{"className":20540},[148],[15,20542],{"className":20543,"style":199},[77],[15,20545,602],{"className":20546},[203],[15,20548],{"className":20549,"style":199},[77],[15,20551,20553,20556,20559,20562,20565,20568,20571],{"className":20552},[58],[15,20554],{"className":20555,"style":124},[62],[15,20557,98],{"className":20558,"style":128},[67,68],[15,20560,102],{"className":20561},[132],[15,20563,3784],{"className":20564,"style":3843},[67,68],[15,20566],{"className":20567,"style":199},[77],[15,20569,602],{"className":20570},[203],[15,20572],{"className":20573,"style":199},[77],[15,20575,20577,20580,20583,20586,20589,20592],{"className":20576},[58],[15,20578],{"className":20579,"style":124},[62],[15,20581,1427],{"className":20582},[67],[15,20584,111],{"className":20585},[148],[15,20587],{"className":20588,"style":199},[77],[15,20590,602],{"className":20591},[203],[15,20593],{"className":20594,"style":199},[77],[15,20596,20598,20602,20643,20646,20649,20652,20655,20658,20661],{"className":20597},[58],[15,20599],{"className":20600,"style":20601},[62],"height:1.0497em;vertical-align:-0.2997em;",[15,20603,20605,20608],{"className":20604},[12772],[15,20606,20423],{"className":20607,"style":12778},[12772,12776,12777],[15,20609,20611],{"className":20610},[918],[15,20612,20614,20635],{"className":20613},[922,923],[15,20615,20617,20632],{"className":20616},[927],[15,20618,20621],{"className":20619,"style":20620},[931],"height:0.0017em;",[15,20622,20623,20626],{"style":12794},[15,20624],{"className":20625,"style":940},[939],[15,20627,20629],{"className":20628},[944,945,946,947],[15,20630,20426],{"className":20631},[67,68,947],[15,20633,955],{"className":20634},[954],[15,20636,20638],{"className":20637},[927],[15,20639,20641],{"className":20640,"style":12834},[931],[15,20642],{},[15,20644],{"className":20645,"style":78},[77],[15,20647,98],{"className":20648,"style":128},[67,68],[15,20650,102],{"className":20651},[132],[15,20653,3784],{"className":20654,"style":3843},[67,68],[15,20656],{"className":20657,"style":199},[77],[15,20659,602],{"className":20660},[203],[15,20662],{"className":20663,"style":199},[77],[15,20665,20667,20670,20673,20676,20679],{"className":20666},[58],[15,20668],{"className":20669,"style":124},[62],[15,20671,1427],{"className":20672},[67],[15,20674],{"className":20675,"style":199},[77],[15,20677,170],{"className":20678},[203],[15,20680],{"className":20681,"style":199},[77],[15,20683,20685,20688,20691,20694,20697,20700,20703],{"className":20684},[58],[15,20686],{"className":20687,"style":124},[62],[15,20689,20426],{"className":20690},[67,68],[15,20692,111],{"className":20693},[148],[15,20695,98],{"className":20696,"style":128},[67,68],[15,20698,102],{"className":20699},[132],[15,20701,20426],{"className":20702},[67,68],[15,20704,111],{"className":20705},[148],"\n与是否干预洒水器完全无关。",[11,20708,20709,20712,20713,20741,20742,20770,20771,21075,21076,21258,21259,21520,21521,21760,21761,10678,21764,21817],{},[305,20710,20711],{},"数值验证","：把 2.3 节给出的具体参数代入，可以直接把这一差别算出来。由于 ",[15,20714,20716,20729],{"className":20715,"translate":19},[18],[15,20717,20719],{"className":20718},[23],[25,20720,20721],{"xmlns":27},[29,20722,20723,20727],{},[32,20724,20725],{},[35,20726,3779],{},[47,20728,3779],{"encoding":49},[15,20730,20732],{"className":20731,"ariaHidden":41},[54],[15,20733,20735,20738],{"className":20734},[58],[15,20736],{"className":20737,"style":299},[62],[15,20739,3779],{"className":20740,"style":1396},[67,68]," 是唯一影响 ",[15,20743,20745,20758],{"className":20744,"translate":19},[18],[15,20746,20748],{"className":20747},[23],[25,20749,20750],{"xmlns":27},[29,20751,20752,20756],{},[32,20753,20754],{},[35,20755,3784],{},[47,20757,3784],{"encoding":49},[15,20759,20761],{"className":20760,"ariaHidden":41},[54],[15,20762,20764,20767],{"className":20763},[58],[15,20765],{"className":20766,"style":299},[62],[15,20768,3784],{"className":20769,"style":3843},[67,68]," 的变量，\n",[15,20772,20774,20852],{"className":20773,"translate":19},[18],[15,20775,20777],{"className":20776},[23],[25,20778,20779],{"xmlns":27},[29,20780,20781,20849],{},[32,20782,20783,20785,20787,20789,20791,20793,20795,20797,20799,20801,20803,20805,20807,20809,20811,20813,20815,20817,20819,20821,20823,20825,20827,20829,20831,20833,20835,20837,20840,20842,20844,20846],{},[35,20784,98],{},[39,20786,102],{"stretchy":101},[35,20788,3784],{},[39,20790,602],{},[1425,20792,1427],{},[39,20794,170],{},[35,20796,696],{},[35,20798,699],{},[39,20800,102],{"stretchy":101},[35,20802,3779],{},[35,20804,11],{},[39,20806,602],{},[1425,20808,1427],{},[39,20810,111],{"stretchy":101},[39,20812,111],{"stretchy":101},[39,20814,602],{},[35,20816,98],{},[39,20818,102],{"stretchy":101},[35,20820,3784],{},[39,20822,602],{},[1425,20824,1427],{},[39,20826,111],{"stretchy":101},[39,20828,602],{},[1425,20830,13790],{},[39,20832,1604],{},[1425,20834,13929],{},[39,20836,2894],{},[1425,20838,20839],{},"0.7",[39,20841,1604],{},[1425,20843,13976],{},[39,20845,602],{},[1425,20847,20848],{},"0.31",[47,20850,20851],{"encoding":49},"P(R=1\\mid do(Sp=1)) = P(R=1) = 0.3 \\times 0.8 + 0.7 \\times 0.1 = 0.31",[15,20853,20855,20879,20897,20927,20948,20972,20993,21012,21030,21048,21066],{"className":20854,"ariaHidden":41},[54],[15,20856,20858,20861,20864,20867,20870,20873,20876],{"className":20857},[58],[15,20859],{"className":20860,"style":124},[62],[15,20862,98],{"className":20863,"style":128},[67,68],[15,20865,102],{"className":20866},[132],[15,20868,3784],{"className":20869,"style":3843},[67,68],[15,20871],{"className":20872,"style":199},[77],[15,20874,602],{"className":20875},[203],[15,20877],{"className":20878,"style":199},[77],[15,20880,20882,20885,20888,20891,20894],{"className":20881},[58],[15,20883],{"className":20884,"style":124},[62],[15,20886,1427],{"className":20887},[67],[15,20889],{"className":20890,"style":199},[77],[15,20892,170],{"className":20893},[203],[15,20895],{"className":20896,"style":199},[77],[15,20898,20900,20903,20906,20909,20912,20915,20918,20921,20924],{"className":20899},[58],[15,20901],{"className":20902,"style":124},[62],[15,20904,696],{"className":20905},[67,68],[15,20907,699],{"className":20908},[67,68],[15,20910,102],{"className":20911},[132],[15,20913,3779],{"className":20914,"style":1396},[67,68],[15,20916,11],{"className":20917},[67,68],[15,20919],{"className":20920,"style":199},[77],[15,20922,602],{"className":20923},[203],[15,20925],{"className":20926,"style":199},[77],[15,20928,20930,20933,20936,20939,20942,20945],{"className":20929},[58],[15,20931],{"className":20932,"style":124},[62],[15,20934,1427],{"className":20935},[67],[15,20937,759],{"className":20938},[148],[15,20940],{"className":20941,"style":199},[77],[15,20943,602],{"className":20944},[203],[15,20946],{"className":20947,"style":199},[77],[15,20949,20951,20954,20957,20960,20963,20966,20969],{"className":20950},[58],[15,20952],{"className":20953,"style":124},[62],[15,20955,98],{"className":20956,"style":128},[67,68],[15,20958,102],{"className":20959},[132],[15,20961,3784],{"className":20962,"style":3843},[67,68],[15,20964],{"className":20965,"style":199},[77],[15,20967,602],{"className":20968},[203],[15,20970],{"className":20971,"style":199},[77],[15,20973,20975,20978,20981,20984,20987,20990],{"className":20974},[58],[15,20976],{"className":20977,"style":124},[62],[15,20979,1427],{"className":20980},[67],[15,20982,111],{"className":20983},[148],[15,20985],{"className":20986,"style":199},[77],[15,20988,602],{"className":20989},[203],[15,20991],{"className":20992,"style":199},[77],[15,20994,20996,21000,21003,21006,21009],{"className":20995},[58],[15,20997],{"className":20998,"style":20999},[62],"height:0.7278em;vertical-align:-0.0833em;",[15,21001,13790],{"className":21002},[67],[15,21004],{"className":21005,"style":82},[77],[15,21007,1604],{"className":21008},[1648],[15,21010],{"className":21011,"style":82},[77],[15,21013,21015,21018,21021,21024,21027],{"className":21014},[58],[15,21016],{"className":21017,"style":20999},[62],[15,21019,13929],{"className":21020},[67],[15,21022],{"className":21023,"style":82},[77],[15,21025,2894],{"className":21026},[1648],[15,21028],{"className":21029,"style":82},[77],[15,21031,21033,21036,21039,21042,21045],{"className":21032},[58],[15,21034],{"className":21035,"style":20999},[62],[15,21037,20839],{"className":21038},[67],[15,21040],{"className":21041,"style":82},[77],[15,21043,1604],{"className":21044},[1648],[15,21046],{"className":21047,"style":82},[77],[15,21049,21051,21054,21057,21060,21063],{"className":21050},[58],[15,21052],{"className":21053,"style":3149},[62],[15,21055,13976],{"className":21056},[67],[15,21058],{"className":21059,"style":199},[77],[15,21061,602],{"className":21062},[203],[15,21064],{"className":21065,"style":199},[77],[15,21067,21069,21072],{"className":21068},[58],[15,21070],{"className":21071,"style":3149},[62],[15,21073,20848],{"className":21074},[67],"\n而由 ",[15,21077,21079,21126],{"className":21078,"translate":19},[18],[15,21080,21082],{"className":21081},[23],[25,21083,21084],{"xmlns":27},[29,21085,21086,21123],{},[32,21087,21088,21090,21092,21094,21096,21098,21100,21102,21104,21106,21108,21110,21112,21114,21116,21118,21120],{},[35,21089,98],{},[39,21091,102],{"stretchy":101},[35,21093,3779],{},[35,21095,11],{},[39,21097,602],{},[1425,21099,1427],{},[39,21101,111],{"stretchy":101},[39,21103,602],{},[1425,21105,13790],{},[39,21107,1604],{},[1425,21109,13976],{},[39,21111,2894],{},[1425,21113,20839],{},[39,21115,1604],{},[1425,21117,14177],{},[39,21119,602],{},[1425,21121,21122],{},"0.45",[47,21124,21125],{"encoding":49},"P(Sp=1) = 0.3\\times 0.1 + 0.7\\times 0.6 = 0.45",[15,21127,21129,21156,21177,21195,21213,21231,21249],{"className":21128,"ariaHidden":41},[54],[15,21130,21132,21135,21138,21141,21144,21147,21150,21153],{"className":21131},[58],[15,21133],{"className":21134,"style":124},[62],[15,21136,98],{"className":21137,"style":128},[67,68],[15,21139,102],{"className":21140},[132],[15,21142,3779],{"className":21143,"style":1396},[67,68],[15,21145,11],{"className":21146},[67,68],[15,21148],{"className":21149,"style":199},[77],[15,21151,602],{"className":21152},[203],[15,21154],{"className":21155,"style":199},[77],[15,21157,21159,21162,21165,21168,21171,21174],{"className":21158},[58],[15,21160],{"className":21161,"style":124},[62],[15,21163,1427],{"className":21164},[67],[15,21166,111],{"className":21167},[148],[15,21169],{"className":21170,"style":199},[77],[15,21172,602],{"className":21173},[203],[15,21175],{"className":21176,"style":199},[77],[15,21178,21180,21183,21186,21189,21192],{"className":21179},[58],[15,21181],{"className":21182,"style":20999},[62],[15,21184,13790],{"className":21185},[67],[15,21187],{"className":21188,"style":82},[77],[15,21190,1604],{"className":21191},[1648],[15,21193],{"className":21194,"style":82},[77],[15,21196,21198,21201,21204,21207,21210],{"className":21197},[58],[15,21199],{"className":21200,"style":20999},[62],[15,21202,13976],{"className":21203},[67],[15,21205],{"className":21206,"style":82},[77],[15,21208,2894],{"className":21209},[1648],[15,21211],{"className":21212,"style":82},[77],[15,21214,21216,21219,21222,21225,21228],{"className":21215},[58],[15,21217],{"className":21218,"style":20999},[62],[15,21220,20839],{"className":21221},[67],[15,21223],{"className":21224,"style":82},[77],[15,21226,1604],{"className":21227},[1648],[15,21229],{"className":21230,"style":82},[77],[15,21232,21234,21237,21240,21243,21246],{"className":21233},[58],[15,21235],{"className":21236,"style":3149},[62],[15,21238,14177],{"className":21239},[67],[15,21241],{"className":21242,"style":199},[77],[15,21244,602],{"className":21245},[203],[15,21247],{"className":21248,"style":199},[77],[15,21250,21252,21255],{"className":21251},[58],[15,21253],{"className":21254,"style":3149},[62],[15,21256,21122],{"className":21257},[67]," 及 ",[15,21260,21262,21325],{"className":21261,"translate":19},[18],[15,21263,21265],{"className":21264},[23],[25,21266,21267],{"xmlns":27},[29,21268,21269,21322],{},[32,21270,21271,21273,21275,21277,21279,21281,21283,21285,21287,21289,21291,21293,21295,21297,21299,21301,21303,21305,21307,21309,21311,21313,21315,21317,21319],{},[35,21272,98],{},[39,21274,102],{"stretchy":101},[35,21276,3784],{},[39,21278,602],{},[1425,21280,1427],{},[39,21282,42],{"separator":41},[35,21284,3779],{},[35,21286,11],{},[39,21288,602],{},[1425,21290,1427],{},[39,21292,111],{"stretchy":101},[39,21294,602],{},[1425,21296,13790],{},[39,21298,1604],{},[1425,21300,13929],{},[39,21302,1604],{},[1425,21304,13976],{},[39,21306,2894],{},[1425,21308,20839],{},[39,21310,1604],{},[1425,21312,13976],{},[39,21314,1604],{},[1425,21316,14177],{},[39,21318,602],{},[1425,21320,21321],{},"0.066",[47,21323,21324],{"encoding":49},"P(R=1, Sp=1) = 0.3\\times 0.8\\times 0.1 + 0.7\\times 0.1\\times 0.6 = 0.066",[15,21326,21328,21352,21382,21403,21421,21439,21457,21475,21493,21511],{"className":21327,"ariaHidden":41},[54],[15,21329,21331,21334,21337,21340,21343,21346,21349],{"className":21330},[58],[15,21332],{"className":21333,"style":124},[62],[15,21335,98],{"className":21336,"style":128},[67,68],[15,21338,102],{"className":21339},[132],[15,21341,3784],{"className":21342,"style":3843},[67,68],[15,21344],{"className":21345,"style":199},[77],[15,21347,602],{"className":21348},[203],[15,21350],{"className":21351,"style":199},[77],[15,21353,21355,21358,21361,21364,21367,21370,21373,21376,21379],{"className":21354},[58],[15,21356],{"className":21357,"style":63},[62],[15,21359,1427],{"className":21360},[67],[15,21362,42],{"className":21363},[73],[15,21365],{"className":21366,"style":78},[77],[15,21368,3779],{"className":21369,"style":1396},[67,68],[15,21371,11],{"className":21372},[67,68],[15,21374],{"className":21375,"style":199},[77],[15,21377,602],{"className":21378},[203],[15,21380],{"className":21381,"style":199},[77],[15,21383,21385,21388,21391,21394,21397,21400],{"className":21384},[58],[15,21386],{"className":21387,"style":124},[62],[15,21389,1427],{"className":21390},[67],[15,21392,111],{"className":21393},[148],[15,21395],{"className":21396,"style":199},[77],[15,21398,602],{"className":21399},[203],[15,21401],{"className":21402,"style":199},[77],[15,21404,21406,21409,21412,21415,21418],{"className":21405},[58],[15,21407],{"className":21408,"style":20999},[62],[15,21410,13790],{"className":21411},[67],[15,21413],{"className":21414,"style":82},[77],[15,21416,1604],{"className":21417},[1648],[15,21419],{"className":21420,"style":82},[77],[15,21422,21424,21427,21430,21433,21436],{"className":21423},[58],[15,21425],{"className":21426,"style":20999},[62],[15,21428,13929],{"className":21429},[67],[15,21431],{"className":21432,"style":82},[77],[15,21434,1604],{"className":21435},[1648],[15,21437],{"className":21438,"style":82},[77],[15,21440,21442,21445,21448,21451,21454],{"className":21441},[58],[15,21443],{"className":21444,"style":20999},[62],[15,21446,13976],{"className":21447},[67],[15,21449],{"className":21450,"style":82},[77],[15,21452,2894],{"className":21453},[1648],[15,21455],{"className":21456,"style":82},[77],[15,21458,21460,21463,21466,21469,21472],{"className":21459},[58],[15,21461],{"className":21462,"style":20999},[62],[15,21464,20839],{"className":21465},[67],[15,21467],{"className":21468,"style":82},[77],[15,21470,1604],{"className":21471},[1648],[15,21473],{"className":21474,"style":82},[77],[15,21476,21478,21481,21484,21487,21490],{"className":21477},[58],[15,21479],{"className":21480,"style":20999},[62],[15,21482,13976],{"className":21483},[67],[15,21485],{"className":21486,"style":82},[77],[15,21488,1604],{"className":21489},[1648],[15,21491],{"className":21492,"style":82},[77],[15,21494,21496,21499,21502,21505,21508],{"className":21495},[58],[15,21497],{"className":21498,"style":3149},[62],[15,21500,14177],{"className":21501},[67],[15,21503],{"className":21504,"style":199},[77],[15,21506,602],{"className":21507},[203],[15,21509],{"className":21510,"style":199},[77],[15,21512,21514,21517],{"className":21513},[58],[15,21515],{"className":21516,"style":3149},[62],[15,21518,21321],{"className":21519},[67],"，得\n",[15,21522,21524,21573],{"className":21523,"translate":19},[18],[15,21525,21527],{"className":21526},[23],[25,21528,21529],{"xmlns":27},[29,21530,21531,21570],{},[32,21532,21533,21535,21537,21539,21541,21543,21545,21547,21549,21551,21553,21555,21557,21564,21567],{},[35,21534,98],{},[39,21536,102],{"stretchy":101},[35,21538,3784],{},[39,21540,602],{},[1425,21542,1427],{},[39,21544,170],{},[35,21546,3779],{},[35,21548,11],{},[39,21550,602],{},[1425,21552,1427],{},[39,21554,111],{"stretchy":101},[39,21556,602],{},[21558,21559,21560,21562],"mfrac",{},[1425,21561,21321],{},[1425,21563,21122],{},[39,21565,21566],{},"≈",[1425,21568,21569],{},"0.147",[47,21571,21572],{"encoding":49},"P(R=1 \\mid Sp=1) = \\frac{0.066}{0.45} \\approx 0.147",[15,21574,21576,21600,21618,21639,21660,21751],{"className":21575,"ariaHidden":41},[54],[15,21577,21579,21582,21585,21588,21591,21594,21597],{"className":21578},[58],[15,21580],{"className":21581,"style":124},[62],[15,21583,98],{"className":21584,"style":128},[67,68],[15,21586,102],{"className":21587},[132],[15,21589,3784],{"className":21590,"style":3843},[67,68],[15,21592],{"className":21593,"style":199},[77],[15,21595,602],{"className":21596},[203],[15,21598],{"className":21599,"style":199},[77],[15,21601,21603,21606,21609,21612,21615],{"className":21602},[58],[15,21604],{"className":21605,"style":124},[62],[15,21607,1427],{"className":21608},[67],[15,21610],{"className":21611,"style":199},[77],[15,21613,170],{"className":21614},[203],[15,21616],{"className":21617,"style":199},[77],[15,21619,21621,21624,21627,21630,21633,21636],{"className":21620},[58],[15,21622],{"className":21623,"style":63},[62],[15,21625,3779],{"className":21626,"style":1396},[67,68],[15,21628,11],{"className":21629},[67,68],[15,21631],{"className":21632,"style":199},[77],[15,21634,602],{"className":21635},[203],[15,21637],{"className":21638,"style":199},[77],[15,21640,21642,21645,21648,21651,21654,21657],{"className":21641},[58],[15,21643],{"className":21644,"style":124},[62],[15,21646,1427],{"className":21647},[67],[15,21649,111],{"className":21650},[148],[15,21652],{"className":21653,"style":199},[77],[15,21655,602],{"className":21656},[203],[15,21658],{"className":21659,"style":199},[77],[15,21661,21663,21667,21742,21745,21748],{"className":21662},[58],[15,21664],{"className":21665,"style":21666},[62],"height:1.1901em;vertical-align:-0.345em;",[15,21668,21670,21673,21739],{"className":21669},[67],[15,21671],{"className":21672},[132,19509],[15,21674,21676],{"className":21675},[21558],[15,21677,21679,21730],{"className":21678},[922,923],[15,21680,21682,21727],{"className":21681},[927],[15,21683,21686,21701,21712],{"className":21684,"style":21685},[931],"height:0.8451em;",[15,21687,21689,21692],{"style":21688},"top:-2.655em;",[15,21690],{"className":21691,"style":18684},[939],[15,21693,21695],{"className":21694},[944,945,946,947],[15,21696,21698],{"className":21697},[67,947],[15,21699,21122],{"className":21700},[67,947],[15,21702,21704,21707],{"style":21703},"top:-3.23em;",[15,21705],{"className":21706,"style":18684},[939],[15,21708],{"className":21709,"style":21711},[21710],"frac-line","border-bottom-width:0.04em;",[15,21713,21715,21718],{"style":21714},"top:-3.394em;",[15,21716],{"className":21717,"style":18684},[939],[15,21719,21721],{"className":21720},[944,945,946,947],[15,21722,21724],{"className":21723},[67,947],[15,21725,21321],{"className":21726},[67,947],[15,21728,955],{"className":21729},[954],[15,21731,21733],{"className":21732},[927],[15,21734,21737],{"className":21735,"style":21736},[931],"height:0.345em;",[15,21738],{},[15,21740],{"className":21741},[148,19509],[15,21743],{"className":21744,"style":199},[77],[15,21746,21566],{"className":21747},[203],[15,21749],{"className":21750,"style":199},[77],[15,21752,21754,21757],{"className":21753},[58],[15,21755],{"className":21756,"style":3149},[62],[15,21758,21569],{"className":21759},[67],"\n二者相差一倍以上，且方向与正文的分析完全一致：",[305,21762,21763],{},"观察到洒水器开着，反而使我们对「正在下雨」的信念大幅下降",[15,21765,21767,21786],{"className":21766,"translate":19},[18],[15,21768,21770],{"className":21769},[23],[25,21771,21772],{"xmlns":27},[29,21773,21774,21783],{},[32,21775,21776,21778,21781],{},[1425,21777,21569],{},[39,21779,21780],{},"\u003C",[1425,21782,20848],{},[47,21784,21785],{"encoding":49},"0.147 \u003C 0.31",[15,21787,21789,21808],{"className":21788,"ariaHidden":41},[54],[15,21790,21792,21796,21799,21802,21805],{"className":21791},[58],[15,21793],{"className":21794,"style":21795},[62],"height:0.6835em;vertical-align:-0.0391em;",[15,21797,21569],{"className":21798},[67],[15,21800],{"className":21801,"style":199},[77],[15,21803,21780],{"className":21804},[203],[15,21806],{"className":21807,"style":199},[77],[15,21809,21811,21814],{"className":21810},[58],[15,21812],{"className":21813,"style":3149},[62],[15,21815,20848],{"className":21816},[67],"）——因为洒水器在旱季更常开启，观测到它本身即构成「当前是旱季」的证据，进而压低降雨概率。这两个数字之间的差距，就是「相关」与「因果」在同一个模型内部的全部分量。",[11,21819,21820,21821,21996],{},"一般地，",[15,21822,21824,21870],{"className":21823,"translate":19},[18],[15,21825,21827],{"className":21826},[23],[25,21828,21829],{"xmlns":27},[29,21830,21831,21867],{},[32,21832,21833,21835,21837,21839,21841,21843,21845,21847,21849,21851,21853,21855,21857,21859,21861,21863,21865],{},[35,21834,98],{},[39,21836,102],{"stretchy":101},[35,21838,534],{},[39,21840,170],{},[35,21842,539],{},[39,21844,111],{"stretchy":101},[39,21846,18888],{"mathvariant":878},[35,21848,98],{},[39,21850,102],{"stretchy":101},[35,21852,534],{},[39,21854,170],{},[35,21856,696],{},[35,21858,699],{},[39,21860,102],{"stretchy":101},[35,21862,539],{},[39,21864,111],{"stretchy":101},[39,21866,111],{"stretchy":101},[47,21868,21869],{"encoding":49},"P(y\\mid x) \\neq P(y \\mid do(x))",[15,21871,21873,21897,21951,21975],{"className":21872,"ariaHidden":41},[54],[15,21874,21876,21879,21882,21885,21888,21891,21894],{"className":21875},[58],[15,21877],{"className":21878,"style":124},[62],[15,21880,98],{"className":21881,"style":128},[67,68],[15,21883,102],{"className":21884},[132],[15,21886,534],{"className":21887,"style":563},[67,68],[15,21889],{"className":21890,"style":199},[77],[15,21892,170],{"className":21893},[203],[15,21895],{"className":21896,"style":199},[77],[15,21898,21900,21903,21906,21909,21912,21948],{"className":21899},[58],[15,21901],{"className":21902,"style":124},[62],[15,21904,539],{"className":21905},[67,68],[15,21907,111],{"className":21908},[148],[15,21910],{"className":21911,"style":199},[77],[15,21913,21915,21942,21945],{"className":21914},[203],[15,21916,21918],{"className":21917},[203],[15,21919,21921],{"className":21920},[67,4469],[15,21922,21924],{"className":21923},[4473],[15,21925,21927,21930,21939],{"className":21926},[4477],[15,21928],{"className":21929,"style":4456},[62],[15,21931,21933],{"className":21932},[4484],[15,21934,21936],{"className":21935},[67],[15,21937,4491],{"className":21938},[203],[15,21940],{"className":21941},[4495],[15,21943],{"className":21944},[77,4499],[15,21946,602],{"className":21947},[203],[15,21949],{"className":21950,"style":199},[77],[15,21952,21954,21957,21960,21963,21966,21969,21972],{"className":21953},[58],[15,21955],{"className":21956,"style":124},[62],[15,21958,98],{"className":21959,"style":128},[67,68],[15,21961,102],{"className":21962},[132],[15,21964,534],{"className":21965,"style":563},[67,68],[15,21967],{"className":21968,"style":199},[77],[15,21970,170],{"className":21971},[203],[15,21973],{"className":21974,"style":199},[77],[15,21976,21978,21981,21984,21987,21990,21993],{"className":21977},[58],[15,21979],{"className":21980,"style":124},[62],[15,21982,696],{"className":21983},[67,68],[15,21985,699],{"className":21986},[67,68],[15,21988,102],{"className":21989},[132],[15,21991,539],{"className":21992},[67,68],[15,21994,759],{"className":21995},[148],"，二者的差异正是「相关不蕴含因果」这一箴言在结构方程框架下的精确定量表述：前者包含了通过混杂路径（如叉结构）传递的虚假信息，后者则通过对结构方程的手术式修改将其剔除。",[1309,21998,22000],{"id":21999},"_33-反事实从群体到个体","3.3 反事实：从群体到个体",[11,22002,22003,22004,22087,22088,22091,22092,811,22142,22170,22171,22174,22175,22326,22327,1239,22355,22484,22485,22513],{},"干预分布 ",[15,22005,22007,22039],{"className":22006,"translate":19},[18],[15,22008,22010],{"className":22009},[23],[25,22011,22012],{"xmlns":27},[29,22013,22014,22036],{},[32,22015,22016,22018,22020,22022,22024,22026,22028,22030,22032,22034],{},[35,22017,98],{},[39,22019,102],{"stretchy":101},[35,22021,534],{},[39,22023,170],{},[35,22025,696],{},[35,22027,699],{},[39,22029,102],{"stretchy":101},[35,22031,539],{},[39,22033,111],{"stretchy":101},[39,22035,111],{"stretchy":101},[47,22037,22038],{"encoding":49},"P(y \\mid do(x))",[15,22040,22042,22066],{"className":22041,"ariaHidden":41},[54],[15,22043,22045,22048,22051,22054,22057,22060,22063],{"className":22044},[58],[15,22046],{"className":22047,"style":124},[62],[15,22049,98],{"className":22050,"style":128},[67,68],[15,22052,102],{"className":22053},[132],[15,22055,534],{"className":22056,"style":563},[67,68],[15,22058],{"className":22059,"style":199},[77],[15,22061,170],{"className":22062},[203],[15,22064],{"className":22065,"style":199},[77],[15,22067,22069,22072,22075,22078,22081,22084],{"className":22068},[58],[15,22070],{"className":22071,"style":124},[62],[15,22073,696],{"className":22074},[67,68],[15,22076,699],{"className":22077},[67,68],[15,22079,102],{"className":22080},[132],[15,22082,539],{"className":22083},[67,68],[15,22085,759],{"className":22086},[148]," 回答的是",[305,22089,22090],{},"群体或总体层面","的问题：「若对某个（服从既定分布的）个体施加干预 ",[15,22093,22095,22112],{"className":22094,"translate":19},[18],[15,22096,22098],{"className":22097},[23],[25,22099,22100],{"xmlns":27},[29,22101,22102,22110],{},[32,22103,22104,22106,22108],{},[35,22105,37],{},[39,22107,602],{},[35,22109,539],{},[47,22111,607],{"encoding":49},[15,22113,22115,22133],{"className":22114,"ariaHidden":41},[54],[15,22116,22118,22121,22124,22127,22130],{"className":22117},[58],[15,22119],{"className":22120,"style":299},[62],[15,22122,37],{"className":22123,"style":69},[67,68],[15,22125],{"className":22126,"style":199},[77],[15,22128,602],{"className":22129},[203],[15,22131],{"className":22132,"style":199},[77],[15,22134,22136,22139],{"className":22135},[58],[15,22137],{"className":22138,"style":635},[62],[15,22140,539],{"className":22141},[67,68],[15,22143,22145,22158],{"className":22144,"translate":19},[18],[15,22146,22148],{"className":22147},[23],[25,22149,22150],{"xmlns":27},[29,22151,22152,22156],{},[32,22153,22154],{},[35,22155,45],{},[47,22157,45],{"encoding":49},[15,22159,22161],{"className":22160,"ariaHidden":41},[54],[15,22162,22164,22167],{"className":22163},[58],[15,22165],{"className":22166,"style":299},[62],[15,22168,45],{"className":22169,"style":82},[67,68]," 的分布会是什么」。而反事实推理进一步追问",[305,22172,22173],{},"特定已观测个体","层面的问题：「对于这个已经观测到 ",[15,22176,22178,22211],{"className":22177,"translate":19},[18],[15,22179,22181],{"className":22180},[23],[25,22182,22183],{"xmlns":27},[29,22184,22185,22209],{},[32,22186,22187,22189,22191,22197,22199,22201,22203],{},[35,22188,37],{},[39,22190,602],{},[872,22192,22193,22195],{},[35,22194,539],{},[39,22196,880],{"mathvariant":878,"lspace":879,"rspace":879},[39,22198,42],{"separator":41},[35,22200,45],{},[39,22202,602],{},[872,22204,22205,22207],{},[35,22206,534],{},[39,22208,880],{"mathvariant":878,"lspace":879,"rspace":879},[47,22210,1093],{"encoding":49},[15,22212,22214,22232,22288],{"className":22213,"ariaHidden":41},[54],[15,22215,22217,22220,22223,22226,22229],{"className":22216},[58],[15,22218],{"className":22219,"style":299},[62],[15,22221,37],{"className":22222,"style":69},[67,68],[15,22224],{"className":22225,"style":199},[77],[15,22227,602],{"className":22228},[203],[15,22230],{"className":22231,"style":199},[77],[15,22233,22235,22238,22270,22273,22276,22279,22282,22285],{"className":22234},[58],[15,22236],{"className":22237,"style":1121},[62],[15,22239,22241,22244],{"className":22240},[67],[15,22242,539],{"className":22243},[67,68],[15,22245,22247],{"className":22246},[918],[15,22248,22250],{"className":22249},[922],[15,22251,22253],{"className":22252},[927],[15,22254,22256],{"className":22255,"style":999},[931],[15,22257,22258,22261],{"style":1002},[15,22259],{"className":22260,"style":940},[939],[15,22262,22264],{"className":22263},[944,945,946,947],[15,22265,22267],{"className":22266},[67,947],[15,22268,880],{"className":22269},[67,947],[15,22271,42],{"className":22272},[73],[15,22274],{"className":22275,"style":78},[77],[15,22277,45],{"className":22278,"style":82},[67,68],[15,22280],{"className":22281,"style":199},[77],[15,22283,602],{"className":22284},[203],[15,22286],{"className":22287,"style":199},[77],[15,22289,22291,22294],{"className":22290},[58],[15,22292],{"className":22293,"style":1121},[62],[15,22295,22297,22300],{"className":22296},[67],[15,22298,534],{"className":22299,"style":563},[67,68],[15,22301,22303],{"className":22302},[918],[15,22304,22306],{"className":22305},[922],[15,22307,22309],{"className":22308},[927],[15,22310,22312],{"className":22311,"style":999},[931],[15,22313,22314,22317],{"style":1002},[15,22315],{"className":22316,"style":940},[939],[15,22318,22320],{"className":22319},[944,945,946,947],[15,22321,22323],{"className":22322},[67,947],[15,22324,880],{"className":22325},[67,947]," 的具体个体，若当初 ",[15,22328,22330,22343],{"className":22329,"translate":19},[18],[15,22331,22333],{"className":22332},[23],[25,22334,22335],{"xmlns":27},[29,22336,22337,22341],{},[32,22338,22339],{},[35,22340,37],{},[47,22342,37],{"encoding":49},[15,22344,22346],{"className":22345,"ariaHidden":41},[54],[15,22347,22349,22352],{"className":22348},[58],[15,22350],{"className":22351,"style":299},[62],[15,22353,37],{"className":22354,"style":69},[67,68],[15,22356,22358,22386],{"className":22357,"translate":19},[18],[15,22359,22361],{"className":22360},[23],[25,22362,22363],{"xmlns":27},[29,22364,22365,22383],{},[32,22366,22367,22369,22371,22373,22375,22381],{},[35,22368,539],{},[238,22370,3926],{},[39,22372,102],{"stretchy":101},[39,22374,18888],{"mathvariant":878},[872,22376,22377,22379],{},[35,22378,539],{},[39,22380,880],{"mathvariant":878,"lspace":879,"rspace":879},[39,22382,111],{"stretchy":101},[47,22384,22385],{"encoding":49},"x \\ (\\neq x')",[15,22387,22389,22443],{"className":22388,"ariaHidden":41},[54],[15,22390,22392,22395,22398,22401,22404,22440],{"className":22391},[58],[15,22393],{"className":22394,"style":124},[62],[15,22396,539],{"className":22397},[67,68],[15,22399,3926],{"className":22400},[77],[15,22402,102],{"className":22403},[132],[15,22405,22407,22434,22437],{"className":22406},[203],[15,22408,22410],{"className":22409},[203],[15,22411,22413],{"className":22412},[67,4469],[15,22414,22416],{"className":22415},[4473],[15,22417,22419,22422,22431],{"className":22418},[4477],[15,22420],{"className":22421,"style":4456},[62],[15,22423,22425],{"className":22424},[4484],[15,22426,22428],{"className":22427},[67],[15,22429,4491],{"className":22430},[203],[15,22432],{"className":22433},[4495],[15,22435],{"className":22436},[77,4499],[15,22438,602],{"className":22439},[203],[15,22441],{"className":22442,"style":199},[77],[15,22444,22446,22449,22481],{"className":22445},[58],[15,22447],{"className":22448,"style":980},[62],[15,22450,22452,22455],{"className":22451},[67],[15,22453,539],{"className":22454},[67,68],[15,22456,22458],{"className":22457},[918],[15,22459,22461],{"className":22460},[922],[15,22462,22464],{"className":22463},[927],[15,22465,22467],{"className":22466,"style":999},[931],[15,22468,22469,22472],{"style":1002},[15,22470],{"className":22471,"style":940},[939],[15,22473,22475],{"className":22474},[944,945,946,947],[15,22476,22478],{"className":22477},[67,947],[15,22479,880],{"className":22480},[67,947],[15,22482,111],{"className":22483},[148],"，其 ",[15,22486,22488,22501],{"className":22487,"translate":19},[18],[15,22489,22491],{"className":22490},[23],[25,22492,22493],{"xmlns":27},[29,22494,22495,22499],{},[32,22496,22497],{},[35,22498,45],{},[47,22500,45],{"encoding":49},[15,22502,22504],{"className":22503,"ariaHidden":41},[54],[15,22505,22507,22510],{"className":22506},[58],[15,22508],{"className":22509,"style":299},[62],[15,22511,45],{"className":22512,"style":82},[67,68]," 会是什么」。这需要更精细的结构。",[1314,22515,22516],{},[11,22517,22518,11065,22521,22549,22550,22601,22602,22630,22631,22681,22682,22685,22686,6696,22755,22805,22806],{},[305,22519,22520],{},"定义 3.4（潜在结果，Potential Outcome）",[15,22522,22524,22537],{"className":22523,"translate":19},[18],[15,22525,22527],{"className":22526},[23],[25,22528,22529],{"xmlns":27},[29,22530,22531,22535],{},[32,22532,22533],{},[35,22534,9469],{},[47,22536,9469],{"encoding":49},[15,22538,22540],{"className":22539,"ariaHidden":41},[54],[15,22541,22543,22546],{"className":22542},[58],[15,22544],{"className":22545,"style":299},[62],[15,22547,9469],{"className":22548,"style":2570},[67,68]," 与其外生变量的一次具体实现 ",[15,22551,22553,22571],{"className":22552,"translate":19},[18],[15,22554,22556],{"className":22555},[23],[25,22557,22558],{"xmlns":27},[29,22559,22560,22568],{},[32,22561,22562,22564,22566],{},[35,22563,2458],{},[39,22565,602],{},[35,22567,13778],{},[47,22569,22570],{"encoding":49},"U=u",[15,22572,22574,22592],{"className":22573,"ariaHidden":41},[54],[15,22575,22577,22580,22583,22586,22589],{"className":22576},[58],[15,22578],{"className":22579,"style":299},[62],[15,22581,2458],{"className":22582,"style":2570},[67,68],[15,22584],{"className":22585,"style":199},[77],[15,22587,602],{"className":22588},[203],[15,22590],{"className":22591,"style":199},[77],[15,22593,22595,22598],{"className":22594},[58],[15,22596],{"className":22597,"style":635},[62],[15,22599,13778],{"className":22600},[67,68],"（对应一个特定「个体」或「世界状态」），变量 ",[15,22603,22605,22618],{"className":22604,"translate":19},[18],[15,22606,22608],{"className":22607},[23],[25,22609,22610],{"xmlns":27},[29,22611,22612,22616],{},[32,22613,22614],{},[35,22615,45],{},[47,22617,45],{"encoding":49},[15,22619,22621],{"className":22620,"ariaHidden":41},[54],[15,22622,22624,22627],{"className":22623},[58],[15,22625],{"className":22626,"style":299},[62],[15,22628,45],{"className":22629,"style":82},[67,68]," 在假设 ",[15,22632,22634,22651],{"className":22633,"translate":19},[18],[15,22635,22637],{"className":22636},[23],[25,22638,22639],{"xmlns":27},[29,22640,22641,22649],{},[32,22642,22643,22645,22647],{},[35,22644,37],{},[39,22646,602],{},[35,22648,539],{},[47,22650,607],{"encoding":49},[15,22652,22654,22672],{"className":22653,"ariaHidden":41},[54],[15,22655,22657,22660,22663,22666,22669],{"className":22656},[58],[15,22658],{"className":22659,"style":299},[62],[15,22661,37],{"className":22662,"style":69},[67,68],[15,22664],{"className":22665,"style":199},[77],[15,22667,602],{"className":22668},[203],[15,22670],{"className":22671,"style":199},[77],[15,22673,22675,22678],{"className":22674},[58],[15,22676],{"className":22677,"style":635},[62],[15,22679,539],{"className":22680},[67,68]," 下的",[305,22683,22684],{},"潜在结果","定义为子模型 ",[15,22687,22689,22706],{"className":22688,"translate":19},[18],[15,22690,22692],{"className":22691},[23],[25,22693,22694],{"xmlns":27},[29,22695,22696,22704],{},[32,22697,22698],{},[863,22699,22700,22702],{},[35,22701,9469],{},[35,22703,539],{},[47,22705,18193],{"encoding":49},[15,22707,22709],{"className":22708,"ariaHidden":41},[54],[15,22710,22712,22715],{"className":22711},[58],[15,22713],{"className":22714,"style":1865},[62],[15,22716,22718,22721],{"className":22717},[67],[15,22719,9469],{"className":22720,"style":2570},[67,68],[15,22722,22724],{"className":22723},[918],[15,22725,22727,22747],{"className":22726},[922,923],[15,22728,22730,22744],{"className":22729},[927],[15,22731,22733],{"className":22732,"style":932},[931],[15,22734,22735,22738],{"style":2585},[15,22736],{"className":22737,"style":940},[939],[15,22739,22741],{"className":22740},[944,945,946,947],[15,22742,539],{"className":22743},[67,68,947],[15,22745,955],{"className":22746},[954],[15,22748,22750],{"className":22749},[927],[15,22751,22753],{"className":22752,"style":962},[931],[15,22754],{},[15,22756,22758,22775],{"className":22757,"translate":19},[18],[15,22759,22761],{"className":22760},[23],[25,22762,22763],{"xmlns":27},[29,22764,22765,22773],{},[32,22766,22767,22769,22771],{},[35,22768,2458],{},[39,22770,602],{},[35,22772,13778],{},[47,22774,22570],{"encoding":49},[15,22776,22778,22796],{"className":22777,"ariaHidden":41},[54],[15,22779,22781,22784,22787,22790,22793],{"className":22780},[58],[15,22782],{"className":22783,"style":299},[62],[15,22785,2458],{"className":22786,"style":2570},[67,68],[15,22788],{"className":22789,"style":199},[77],[15,22791,602],{"className":22792},[203],[15,22794],{"className":22795,"style":199},[77],[15,22797,22799,22802],{"className":22798},[58],[15,22800],{"className":22801,"style":635},[62],[15,22803,13778],{"className":22804},[67,68]," 下的取值：\n",[15,22807,22809,22853],{"className":22808,"translate":19},[18],[15,22810,22812],{"className":22811},[23],[25,22813,22814],{"xmlns":27},[29,22815,22816,22850],{},[32,22817,22818,22824,22826,22828,22830,22832,22834,22844,22846,22848],{},[863,22819,22820,22822],{},[35,22821,45],{},[35,22823,539],{},[39,22825,102],{"stretchy":101},[35,22827,13778],{},[39,22829,111],{"stretchy":101},[39,22831,8863],{},[39,22833,602],{},[863,22835,22836,22838],{},[35,22837,45],{},[863,22839,22840,22842],{},[35,22841,9469],{},[35,22843,539],{},[39,22845,102],{"stretchy":101},[35,22847,13778],{},[39,22849,111],{"stretchy":101},[47,22851,22852],{"encoding":49},"Y_x(u) := Y_{M_x}(u)",[15,22854,22856,22920],{"className":22855,"ariaHidden":41},[54],[15,22857,22859,22862,22902,22905,22908,22911,22914,22917],{"className":22858},[58],[15,22860],{"className":22861,"style":124},[62],[15,22863,22865,22868],{"className":22864},[67],[15,22866,45],{"className":22867,"style":82},[67,68],[15,22869,22871],{"className":22870},[918],[15,22872,22874,22894],{"className":22873},[922,923],[15,22875,22877,22891],{"className":22876},[927],[15,22878,22880],{"className":22879,"style":932},[931],[15,22881,22882,22885],{"style":1499},[15,22883],{"className":22884,"style":940},[939],[15,22886,22888],{"className":22887},[944,945,946,947],[15,22889,539],{"className":22890},[67,68,947],[15,22892,955],{"className":22893},[954],[15,22895,22897],{"className":22896},[927],[15,22898,22900],{"className":22899,"style":962},[931],[15,22901],{},[15,22903,102],{"className":22904},[132],[15,22906,13778],{"className":22907},[67,68],[15,22909,111],{"className":22910},[148],[15,22912],{"className":22913,"style":199},[77],[15,22915,8899],{"className":22916},[203],[15,22918],{"className":22919,"style":199},[77],[15,22921,22923,22926,23006,23009,23012],{"className":22922},[58],[15,22924],{"className":22925,"style":18362},[62],[15,22927,22929,22932],{"className":22928},[67],[15,22930,45],{"className":22931,"style":82},[67,68],[15,22933,22935],{"className":22934},[918],[15,22936,22938,22998],{"className":22937},[922,923],[15,22939,22941,22995],{"className":22940},[927],[15,22942,22944],{"className":22943,"style":7358},[931],[15,22945,22946,22949],{"style":1499},[15,22947],{"className":22948,"style":940},[939],[15,22950,22952],{"className":22951},[944,945,946,947],[15,22953,22955],{"className":22954},[67,947],[15,22956,22958,22961],{"className":22957},[67,947],[15,22959,9469],{"className":22960,"style":2570},[67,68,947],[15,22962,22964],{"className":22963},[918],[15,22965,22967,22987],{"className":22966},[922,923],[15,22968,22970,22984],{"className":22969},[927],[15,22971,22973],{"className":22972,"style":18410},[931],[15,22974,22975,22978],{"style":18413},[15,22976],{"className":22977,"style":18417},[939],[15,22979,22981],{"className":22980},[944,18421,15089,947],[15,22982,539],{"className":22983},[67,68,947],[15,22985,955],{"className":22986},[954],[15,22988,22990],{"className":22989},[927],[15,22991,22993],{"className":22992,"style":18434},[931],[15,22994],{},[15,22996,955],{"className":22997},[954],[15,22999,23001],{"className":23000},[927],[15,23002,23004],{"className":23003,"style":18446},[931],[15,23005],{},[15,23007,102],{"className":23008},[132],[15,23010,13778],{"className":23011},[67,68],[15,23013,111],{"className":23014},[148],[1314,23016,23017,23379],{},[11,23018,23019,23022,23023,23074,23075,23226,23227,23378],{},[305,23020,23021],{},"算法 3.1（反事实查询的三步算法）"," 给定观测证据 ",[15,23024,23026,23044],{"className":23025,"translate":19},[18],[15,23027,23029],{"className":23028},[23],[25,23030,23031],{"xmlns":27},[29,23032,23033,23041],{},[32,23034,23035,23037,23039],{},[35,23036,1348],{},[39,23038,602],{},[35,23040,13768],{},[47,23042,23043],{"encoding":49},"E=e",[15,23045,23047,23065],{"className":23046,"ariaHidden":41},[54],[15,23048,23050,23053,23056,23059,23062],{"className":23049},[58],[15,23051],{"className":23052,"style":299},[62],[15,23054,1348],{"className":23055,"style":1396},[67,68],[15,23057],{"className":23058,"style":199},[77],[15,23060,602],{"className":23061},[203],[15,23063],{"className":23064,"style":199},[77],[15,23066,23068,23071],{"className":23067},[58],[15,23069],{"className":23070,"style":635},[62],[15,23072,13768],{"className":23073},[67,68],"（例如 ",[15,23076,23078,23111],{"className":23077,"translate":19},[18],[15,23079,23081],{"className":23080},[23],[25,23082,23083],{"xmlns":27},[29,23084,23085,23109],{},[32,23086,23087,23089,23091,23097,23099,23101,23103],{},[35,23088,37],{},[39,23090,602],{},[872,23092,23093,23095],{},[35,23094,539],{},[39,23096,880],{"mathvariant":878,"lspace":879,"rspace":879},[39,23098,42],{"separator":41},[35,23100,45],{},[39,23102,602],{},[872,23104,23105,23107],{},[35,23106,534],{},[39,23108,880],{"mathvariant":878,"lspace":879,"rspace":879},[47,23110,1093],{"encoding":49},[15,23112,23114,23132,23188],{"className":23113,"ariaHidden":41},[54],[15,23115,23117,23120,23123,23126,23129],{"className":23116},[58],[15,23118],{"className":23119,"style":299},[62],[15,23121,37],{"className":23122,"style":69},[67,68],[15,23124],{"className":23125,"style":199},[77],[15,23127,602],{"className":23128},[203],[15,23130],{"className":23131,"style":199},[77],[15,23133,23135,23138,23170,23173,23176,23179,23182,23185],{"className":23134},[58],[15,23136],{"className":23137,"style":1121},[62],[15,23139,23141,23144],{"className":23140},[67],[15,23142,539],{"className":23143},[67,68],[15,23145,23147],{"className":23146},[918],[15,23148,23150],{"className":23149},[922],[15,23151,23153],{"className":23152},[927],[15,23154,23156],{"className":23155,"style":999},[931],[15,23157,23158,23161],{"style":1002},[15,23159],{"className":23160,"style":940},[939],[15,23162,23164],{"className":23163},[944,945,946,947],[15,23165,23167],{"className":23166},[67,947],[15,23168,880],{"className":23169},[67,947],[15,23171,42],{"className":23172},[73],[15,23174],{"className":23175,"style":78},[77],[15,23177,45],{"className":23178,"style":82},[67,68],[15,23180],{"className":23181,"style":199},[77],[15,23183,602],{"className":23184},[203],[15,23186],{"className":23187,"style":199},[77],[15,23189,23191,23194],{"className":23190},[58],[15,23192],{"className":23193,"style":1121},[62],[15,23195,23197,23200],{"className":23196},[67],[15,23198,534],{"className":23199,"style":563},[67,68],[15,23201,23203],{"className":23202},[918],[15,23204,23206],{"className":23205},[922],[15,23207,23209],{"className":23208},[927],[15,23210,23212],{"className":23211,"style":999},[931],[15,23213,23214,23217],{"style":1002},[15,23215],{"className":23216,"style":940},[939],[15,23218,23220],{"className":23219},[944,945,946,947],[15,23221,23223],{"className":23222},[67,947],[15,23224,880],{"className":23225},[67,947],"），欲计算反事实量 ",[15,23228,23230,23266],{"className":23229,"translate":19},[18],[15,23231,23233],{"className":23232},[23],[25,23234,23235],{"xmlns":27},[29,23236,23237,23263],{},[32,23238,23239,23241,23243,23249,23251,23253,23255,23257,23259,23261],{},[35,23240,98],{},[39,23242,102],{"stretchy":101},[863,23244,23245,23247],{},[35,23246,45],{},[35,23248,539],{},[39,23250,602],{},[35,23252,534],{},[39,23254,170],{},[35,23256,1348],{},[39,23258,602],{},[35,23260,13768],{},[39,23262,111],{"stretchy":101},[47,23264,23265],{"encoding":49},"P(Y_x = y \\mid E=e)",[15,23267,23269,23330,23348,23366],{"className":23268,"ariaHidden":41},[54],[15,23270,23272,23275,23278,23281,23321,23324,23327],{"className":23271},[58],[15,23273],{"className":23274,"style":124},[62],[15,23276,98],{"className":23277,"style":128},[67,68],[15,23279,102],{"className":23280},[132],[15,23282,23284,23287],{"className":23283},[67],[15,23285,45],{"className":23286,"style":82},[67,68],[15,23288,23290],{"className":23289},[918],[15,23291,23293,23313],{"className":23292},[922,923],[15,23294,23296,23310],{"className":23295},[927],[15,23297,23299],{"className":23298,"style":932},[931],[15,23300,23301,23304],{"style":1499},[15,23302],{"className":23303,"style":940},[939],[15,23305,23307],{"className":23306},[944,945,946,947],[15,23308,539],{"className":23309},[67,68,947],[15,23311,955],{"className":23312},[954],[15,23314,23316],{"className":23315},[927],[15,23317,23319],{"className":23318,"style":962},[931],[15,23320],{},[15,23322],{"className":23323,"style":199},[77],[15,23325,602],{"className":23326},[203],[15,23328],{"className":23329,"style":199},[77],[15,23331,23333,23336,23339,23342,23345],{"className":23332},[58],[15,23334],{"className":23335,"style":124},[62],[15,23337,534],{"className":23338,"style":563},[67,68],[15,23340],{"className":23341,"style":199},[77],[15,23343,170],{"className":23344},[203],[15,23346],{"className":23347,"style":199},[77],[15,23349,23351,23354,23357,23360,23363],{"className":23350},[58],[15,23352],{"className":23353,"style":299},[62],[15,23355,1348],{"className":23356,"style":1396},[67,68],[15,23358],{"className":23359,"style":199},[77],[15,23361,602],{"className":23362},[203],[15,23364],{"className":23365,"style":199},[77],[15,23367,23369,23372,23375],{"className":23368},[58],[15,23370],{"className":23371,"style":124},[62],[15,23373,13768],{"className":23374},[67,68],[15,23376,111],{"className":23377},[148],"，分三步进行：",[7923,23380,23381,23527,23674],{},[510,23382,23383,23386,23387,23415,23416,23459,23460,23526],{},[305,23384,23385],{},"溯因（Abduction）","：利用观测证据 ",[15,23388,23390,23403],{"className":23389,"translate":19},[18],[15,23391,23393],{"className":23392},[23],[25,23394,23395],{"xmlns":27},[29,23396,23397,23401],{},[32,23398,23399],{},[35,23400,13768],{},[47,23402,13768],{"encoding":49},[15,23404,23406],{"className":23405,"ariaHidden":41},[54],[15,23407,23409,23412],{"className":23408},[58],[15,23410],{"className":23411,"style":635},[62],[15,23413,13768],{"className":23414},[67,68],"，将外生变量的先验分布 ",[15,23417,23419,23438],{"className":23418,"translate":19},[18],[15,23420,23422],{"className":23421},[23],[25,23423,23424],{"xmlns":27},[29,23425,23426,23436],{},[32,23427,23428,23430,23432,23434],{},[35,23429,98],{},[39,23431,102],{"stretchy":101},[35,23433,2458],{},[39,23435,111],{"stretchy":101},[47,23437,11006],{"encoding":49},[15,23439,23441],{"className":23440,"ariaHidden":41},[54],[15,23442,23444,23447,23450,23453,23456],{"className":23443},[58],[15,23445],{"className":23446,"style":124},[62],[15,23448,98],{"className":23449,"style":128},[67,68],[15,23451,102],{"className":23452},[132],[15,23454,2458],{"className":23455,"style":2570},[67,68],[15,23457,111],{"className":23458},[148]," 更新为后验分布 ",[15,23461,23463,23487],{"className":23462,"translate":19},[18],[15,23464,23466],{"className":23465},[23],[25,23467,23468],{"xmlns":27},[29,23469,23470,23484],{},[32,23471,23472,23474,23476,23478,23480,23482],{},[35,23473,98],{},[39,23475,102],{"stretchy":101},[35,23477,2458],{},[39,23479,170],{},[35,23481,13768],{},[39,23483,111],{"stretchy":101},[47,23485,23486],{"encoding":49},"P(U \\mid e)",[15,23488,23490,23514],{"className":23489,"ariaHidden":41},[54],[15,23491,23493,23496,23499,23502,23505,23508,23511],{"className":23492},[58],[15,23494],{"className":23495,"style":124},[62],[15,23497,98],{"className":23498,"style":128},[67,68],[15,23500,102],{"className":23501},[132],[15,23503,2458],{"className":23504,"style":2570},[67,68],[15,23506],{"className":23507,"style":199},[77],[15,23509,170],{"className":23510},[203],[15,23512],{"className":23513,"style":199},[77],[15,23515,23517,23520,23523],{"className":23516},[58],[15,23518],{"className":23519,"style":124},[62],[15,23521,13768],{"className":23522},[67,68],[15,23524,111],{"className":23525},[148],"，即根据「结果倒推该个体所处的具体随机情境」；",[510,23528,23529,23532,23533,23603,23604,23673],{},[305,23530,23531],{},"行动（Action）","：对结构方程集合施加 ",[15,23534,23536,23561],{"className":23535,"translate":19},[18],[15,23537,23539],{"className":23538},[23],[25,23540,23541],{"xmlns":27},[29,23542,23543,23559],{},[32,23544,23545,23547,23549,23551,23553,23555,23557],{},[35,23546,696],{},[35,23548,699],{},[39,23550,102],{"stretchy":101},[35,23552,37],{},[39,23554,602],{},[35,23556,539],{},[39,23558,111],{"stretchy":101},[47,23560,8079],{"encoding":49},[15,23562,23564,23591],{"className":23563,"ariaHidden":41},[54],[15,23565,23567,23570,23573,23576,23579,23582,23585,23588],{"className":23566},[58],[15,23568],{"className":23569,"style":124},[62],[15,23571,696],{"className":23572},[67,68],[15,23574,699],{"className":23575},[67,68],[15,23577,102],{"className":23578},[132],[15,23580,37],{"className":23581,"style":69},[67,68],[15,23583],{"className":23584,"style":199},[77],[15,23586,602],{"className":23587},[203],[15,23589],{"className":23590,"style":199},[77],[15,23592,23594,23597,23600],{"className":23593},[58],[15,23595],{"className":23596,"style":124},[62],[15,23598,539],{"className":23599},[67,68],[15,23601,111],{"className":23602},[148],"，得到子模型 ",[15,23605,23607,23624],{"className":23606,"translate":19},[18],[15,23608,23610],{"className":23609},[23],[25,23611,23612],{"xmlns":27},[29,23613,23614,23622],{},[32,23615,23616],{},[863,23617,23618,23620],{},[35,23619,9469],{},[35,23621,539],{},[47,23623,18193],{"encoding":49},[15,23625,23627],{"className":23626,"ariaHidden":41},[54],[15,23628,23630,23633],{"className":23629},[58],[15,23631],{"className":23632,"style":1865},[62],[15,23634,23636,23639],{"className":23635},[67],[15,23637,9469],{"className":23638,"style":2570},[67,68],[15,23640,23642],{"className":23641},[918],[15,23643,23645,23665],{"className":23644},[922,923],[15,23646,23648,23662],{"className":23647},[927],[15,23649,23651],{"className":23650,"style":932},[931],[15,23652,23653,23656],{"style":2585},[15,23654],{"className":23655,"style":940},[939],[15,23657,23659],{"className":23658},[944,945,946,947],[15,23660,539],{"className":23661},[67,68,947],[15,23663,955],{"className":23664},[954],[15,23666,23668],{"className":23667},[927],[15,23669,23671],{"className":23670,"style":962},[931],[15,23672],{},"（同定义 3.2）；",[510,23675,23676,23679,23680,23749,23750,23816,23817,23845,23846],{},[305,23677,23678],{},"预测（Prediction）","：在子模型 ",[15,23681,23683,23700],{"className":23682,"translate":19},[18],[15,23684,23686],{"className":23685},[23],[25,23687,23688],{"xmlns":27},[29,23689,23690,23698],{},[32,23691,23692],{},[863,23693,23694,23696],{},[35,23695,9469],{},[35,23697,539],{},[47,23699,18193],{"encoding":49},[15,23701,23703],{"className":23702,"ariaHidden":41},[54],[15,23704,23706,23709],{"className":23705},[58],[15,23707],{"className":23708,"style":1865},[62],[15,23710,23712,23715],{"className":23711},[67],[15,23713,9469],{"className":23714,"style":2570},[67,68],[15,23716,23718],{"className":23717},[918],[15,23719,23721,23741],{"className":23720},[922,923],[15,23722,23724,23738],{"className":23723},[927],[15,23725,23727],{"className":23726,"style":932},[931],[15,23728,23729,23732],{"style":2585},[15,23730],{"className":23731,"style":940},[939],[15,23733,23735],{"className":23734},[944,945,946,947],[15,23736,539],{"className":23737},[67,68,947],[15,23739,955],{"className":23740},[954],[15,23742,23744],{"className":23743},[927],[15,23745,23747],{"className":23746,"style":962},[931],[15,23748],{}," 中，用第一步得到的后验分布 ",[15,23751,23753,23777],{"className":23752,"translate":19},[18],[15,23754,23756],{"className":23755},[23],[25,23757,23758],{"xmlns":27},[29,23759,23760,23774],{},[32,23761,23762,23764,23766,23768,23770,23772],{},[35,23763,98],{},[39,23765,102],{"stretchy":101},[35,23767,2458],{},[39,23769,170],{},[35,23771,13768],{},[39,23773,111],{"stretchy":101},[47,23775,23776],{"encoding":49},"P(U\\mid e)",[15,23778,23780,23804],{"className":23779,"ariaHidden":41},[54],[15,23781,23783,23786,23789,23792,23795,23798,23801],{"className":23782},[58],[15,23784],{"className":23785,"style":124},[62],[15,23787,98],{"className":23788,"style":128},[67,68],[15,23790,102],{"className":23791},[132],[15,23793,2458],{"className":23794,"style":2570},[67,68],[15,23796],{"className":23797,"style":199},[77],[15,23799,170],{"className":23800},[203],[15,23802],{"className":23803,"style":199},[77],[15,23805,23807,23810,23813],{"className":23806},[58],[15,23808],{"className":23809,"style":124},[62],[15,23811,13768],{"className":23812},[67,68],[15,23814,111],{"className":23815},[148]," 计算 ",[15,23818,23820,23833],{"className":23819,"translate":19},[18],[15,23821,23823],{"className":23822},[23],[25,23824,23825],{"xmlns":27},[29,23826,23827,23831],{},[32,23828,23829],{},[35,23830,45],{},[47,23832,45],{"encoding":49},[15,23834,23836],{"className":23835,"ariaHidden":41},[54],[15,23837,23839,23842],{"className":23838},[58],[15,23840],{"className":23841,"style":299},[62],[15,23843,45],{"className":23844,"style":82},[67,68]," 的分布，即为所求反事实分布：\n",[15,23847,23849,23929],{"className":23848,"translate":19},[18],[15,23850,23852],{"className":23851},[23],[25,23853,23854],{"xmlns":27},[29,23855,23856,23926],{},[32,23857,23858,23860,23862,23868,23870,23872,23874,23876,23878,23880,23886,23888,23890,23900,23902,23904,23906,23908,23910,23912,23914,23916,23918,23920,23922,23924],{},[35,23859,98],{},[39,23861,102],{"stretchy":101},[863,23863,23864,23866],{},[35,23865,45],{},[35,23867,539],{},[39,23869,602],{},[35,23871,534],{},[39,23873,170],{},[35,23875,13768],{},[39,23877,111],{"stretchy":101},[39,23879,602],{},[863,23881,23882,23884],{},[39,23883,20423],{},[35,23885,13778],{},[35,23887,98],{},[39,23889,102],{"stretchy":101},[863,23891,23892,23894],{},[35,23893,45],{},[863,23895,23896,23898],{},[35,23897,9469],{},[35,23899,539],{},[39,23901,102],{"stretchy":101},[35,23903,13778],{},[39,23905,111],{"stretchy":101},[39,23907,602],{},[35,23909,534],{},[39,23911,111],{"stretchy":101},[39,23913,13830],{},[35,23915,98],{},[39,23917,102],{"stretchy":101},[35,23919,13778],{},[39,23921,170],{},[35,23923,13768],{},[39,23925,111],{"stretchy":101},[47,23927,23928],{"encoding":49},"P(Y_x = y \\mid e) = \\sum_u P(Y_{M_x}(u) = y) \\cdot P(u \\mid e)",[15,23930,23932,23993,24011,24032,24185,24206,24230],{"className":23931,"ariaHidden":41},[54],[15,23933,23935,23938,23941,23944,23984,23987,23990],{"className":23934},[58],[15,23936],{"className":23937,"style":124},[62],[15,23939,98],{"className":23940,"style":128},[67,68],[15,23942,102],{"className":23943},[132],[15,23945,23947,23950],{"className":23946},[67],[15,23948,45],{"className":23949,"style":82},[67,68],[15,23951,23953],{"className":23952},[918],[15,23954,23956,23976],{"className":23955},[922,923],[15,23957,23959,23973],{"className":23958},[927],[15,23960,23962],{"className":23961,"style":932},[931],[15,23963,23964,23967],{"style":1499},[15,23965],{"className":23966,"style":940},[939],[15,23968,23970],{"className":23969},[944,945,946,947],[15,23971,539],{"className":23972},[67,68,947],[15,23974,955],{"className":23975},[954],[15,23977,23979],{"className":23978},[927],[15,23980,23982],{"className":23981,"style":962},[931],[15,23983],{},[15,23985],{"className":23986,"style":199},[77],[15,23988,602],{"className":23989},[203],[15,23991],{"className":23992,"style":199},[77],[15,23994,23996,23999,24002,24005,24008],{"className":23995},[58],[15,23997],{"className":23998,"style":124},[62],[15,24000,534],{"className":24001,"style":563},[67,68],[15,24003],{"className":24004,"style":199},[77],[15,24006,170],{"className":24007},[203],[15,24009],{"className":24010,"style":199},[77],[15,24012,24014,24017,24020,24023,24026,24029],{"className":24013},[58],[15,24015],{"className":24016,"style":124},[62],[15,24018,13768],{"className":24019},[67,68],[15,24021,111],{"className":24022},[148],[15,24024],{"className":24025,"style":199},[77],[15,24027,602],{"className":24028},[203],[15,24030],{"className":24031,"style":199},[77],[15,24033,24035,24038,24078,24081,24084,24087,24167,24170,24173,24176,24179,24182],{"className":24034},[58],[15,24036],{"className":24037,"style":20601},[62],[15,24039,24041,24044],{"className":24040},[12772],[15,24042,20423],{"className":24043,"style":12778},[12772,12776,12777],[15,24045,24047],{"className":24046},[918],[15,24048,24050,24070],{"className":24049},[922,923],[15,24051,24053,24067],{"className":24052},[927],[15,24054,24056],{"className":24055,"style":20620},[931],[15,24057,24058,24061],{"style":12794},[15,24059],{"className":24060,"style":940},[939],[15,24062,24064],{"className":24063},[944,945,946,947],[15,24065,13778],{"className":24066},[67,68,947],[15,24068,955],{"className":24069},[954],[15,24071,24073],{"className":24072},[927],[15,24074,24076],{"className":24075,"style":12834},[931],[15,24077],{},[15,24079],{"className":24080,"style":78},[77],[15,24082,98],{"className":24083,"style":128},[67,68],[15,24085,102],{"className":24086},[132],[15,24088,24090,24093],{"className":24089},[67],[15,24091,45],{"className":24092,"style":82},[67,68],[15,24094,24096],{"className":24095},[918],[15,24097,24099,24159],{"className":24098},[922,923],[15,24100,24102,24156],{"className":24101},[927],[15,24103,24105],{"className":24104,"style":7358},[931],[15,24106,24107,24110],{"style":1499},[15,24108],{"className":24109,"style":940},[939],[15,24111,24113],{"className":24112},[944,945,946,947],[15,24114,24116],{"className":24115},[67,947],[15,24117,24119,24122],{"className":24118},[67,947],[15,24120,9469],{"className":24121,"style":2570},[67,68,947],[15,24123,24125],{"className":24124},[918],[15,24126,24128,24148],{"className":24127},[922,923],[15,24129,24131,24145],{"className":24130},[927],[15,24132,24134],{"className":24133,"style":18410},[931],[15,24135,24136,24139],{"style":18413},[15,24137],{"className":24138,"style":18417},[939],[15,24140,24142],{"className":24141},[944,18421,15089,947],[15,24143,539],{"className":24144},[67,68,947],[15,24146,955],{"className":24147},[954],[15,24149,24151],{"className":24150},[927],[15,24152,24154],{"className":24153,"style":18434},[931],[15,24155],{},[15,24157,955],{"className":24158},[954],[15,24160,24162],{"className":24161},[927],[15,24163,24165],{"className":24164,"style":18446},[931],[15,24166],{},[15,24168,102],{"className":24169},[132],[15,24171,13778],{"className":24172},[67,68],[15,24174,111],{"className":24175},[148],[15,24177],{"className":24178,"style":199},[77],[15,24180,602],{"className":24181},[203],[15,24183],{"className":24184,"style":199},[77],[15,24186,24188,24191,24194,24197,24200,24203],{"className":24187},[58],[15,24189],{"className":24190,"style":124},[62],[15,24192,534],{"className":24193,"style":563},[67,68],[15,24195,111],{"className":24196},[148],[15,24198],{"className":24199,"style":82},[77],[15,24201,13830],{"className":24202},[1648],[15,24204],{"className":24205,"style":82},[77],[15,24207,24209,24212,24215,24218,24221,24224,24227],{"className":24208},[58],[15,24210],{"className":24211,"style":124},[62],[15,24213,98],{"className":24214,"style":128},[67,68],[15,24216,102],{"className":24217},[132],[15,24219,13778],{"className":24220},[67,68],[15,24222],{"className":24223,"style":199},[77],[15,24225,170],{"className":24226},[203],[15,24228],{"className":24229,"style":199},[77],[15,24231,24233,24236,24239],{"className":24232},[58],[15,24234],{"className":24235,"style":124},[62],[15,24237,13768],{"className":24238},[67,68],[15,24240,111],{"className":24241},[148],[1314,24243,24244],{},[11,24245,24246,24249,24250,24301,24302,24353,24354,24405,24406,24592,24593,24596,24597,24724,24725,24728,24729,24757,24758,24811,24812,24840,24841,24869,24870,25056,25057,25060,25061,25188],{},[305,24247,24248],{},"例 3.3（反事实的具体计算）"," 设某病人服用了某药（",[15,24251,24253,24271],{"className":24252,"translate":19},[18],[15,24254,24256],{"className":24255},[23],[25,24257,24258],{"xmlns":27},[29,24259,24260,24268],{},[32,24261,24262,24264,24266],{},[35,24263,37],{},[39,24265,602],{},[1425,24267,1427],{},[47,24269,24270],{"encoding":49},"X=1",[15,24272,24274,24292],{"className":24273,"ariaHidden":41},[54],[15,24275,24277,24280,24283,24286,24289],{"className":24276},[58],[15,24278],{"className":24279,"style":299},[62],[15,24281,37],{"className":24282,"style":69},[67,68],[15,24284],{"className":24285,"style":199},[77],[15,24287,602],{"className":24288},[203],[15,24290],{"className":24291,"style":199},[77],[15,24293,24295,24298],{"className":24294},[58],[15,24296],{"className":24297,"style":3149},[62],[15,24299,1427],{"className":24300},[67],"）后康复（",[15,24303,24305,24323],{"className":24304,"translate":19},[18],[15,24306,24308],{"className":24307},[23],[25,24309,24310],{"xmlns":27},[29,24311,24312,24320],{},[32,24313,24314,24316,24318],{},[35,24315,45],{},[39,24317,602],{},[1425,24319,1427],{},[47,24321,24322],{"encoding":49},"Y=1",[15,24324,24326,24344],{"className":24325,"ariaHidden":41},[54],[15,24327,24329,24332,24335,24338,24341],{"className":24328},[58],[15,24330],{"className":24331,"style":299},[62],[15,24333,45],{"className":24334,"style":82},[67,68],[15,24336],{"className":24337,"style":199},[77],[15,24339,602],{"className":24340},[203],[15,24342],{"className":24343,"style":199},[77],[15,24345,24347,24350],{"className":24346},[58],[15,24348],{"className":24349,"style":3149},[62],[15,24351,1427],{"className":24352},[67],"）。欲问：「若该病人当初未服药（",[15,24355,24357,24375],{"className":24356,"translate":19},[18],[15,24358,24360],{"className":24359},[23],[25,24361,24362],{"xmlns":27},[29,24363,24364,24372],{},[32,24365,24366,24368,24370],{},[35,24367,37],{},[39,24369,602],{},[1425,24371,2461],{},[47,24373,24374],{"encoding":49},"X=0",[15,24376,24378,24396],{"className":24377,"ariaHidden":41},[54],[15,24379,24381,24384,24387,24390,24393],{"className":24380},[58],[15,24382],{"className":24383,"style":299},[62],[15,24385,37],{"className":24386,"style":69},[67,68],[15,24388],{"className":24389,"style":199},[77],[15,24391,602],{"className":24392},[203],[15,24394],{"className":24395,"style":199},[77],[15,24397,24399,24402],{"className":24398},[58],[15,24400],{"className":24401,"style":3149},[62],[15,24403,2461],{"className":24404},[67],"），是否仍会康复？」——即求 ",[15,24407,24409,24453],{"className":24408,"translate":19},[18],[15,24410,24412],{"className":24411},[23],[25,24413,24414],{"xmlns":27},[29,24415,24416,24450],{},[32,24417,24418,24420,24422,24428,24430,24432,24434,24436,24438,24440,24442,24444,24446,24448],{},[35,24419,98],{},[39,24421,102],{"stretchy":101},[863,24423,24424,24426],{},[35,24425,45],{},[1425,24427,2461],{},[39,24429,602],{},[1425,24431,1427],{},[39,24433,170],{},[35,24435,37],{},[39,24437,602],{},[1425,24439,1427],{},[39,24441,42],{"separator":41},[35,24443,45],{},[39,24445,602],{},[1425,24447,1427],{},[39,24449,111],{"stretchy":101},[47,24451,24452],{"encoding":49},"P(Y_0 = 1 \\mid X=1, Y=1)",[15,24454,24456,24517,24535,24553,24580],{"className":24455,"ariaHidden":41},[54],[15,24457,24459,24462,24465,24468,24508,24511,24514],{"className":24458},[58],[15,24460],{"className":24461,"style":124},[62],[15,24463,98],{"className":24464,"style":128},[67,68],[15,24466,102],{"className":24467},[132],[15,24469,24471,24474],{"className":24470},[67],[15,24472,45],{"className":24473,"style":82},[67,68],[15,24475,24477],{"className":24476},[918],[15,24478,24480,24500],{"className":24479},[922,923],[15,24481,24483,24497],{"className":24482},[927],[15,24484,24486],{"className":24485,"style":1496},[931],[15,24487,24488,24491],{"style":1499},[15,24489],{"className":24490,"style":940},[939],[15,24492,24494],{"className":24493},[944,945,946,947],[15,24495,2461],{"className":24496},[67,947],[15,24498,955],{"className":24499},[954],[15,24501,24503],{"className":24502},[927],[15,24504,24506],{"className":24505,"style":962},[931],[15,24507],{},[15,24509],{"className":24510,"style":199},[77],[15,24512,602],{"className":24513},[203],[15,24515],{"className":24516,"style":199},[77],[15,24518,24520,24523,24526,24529,24532],{"className":24519},[58],[15,24521],{"className":24522,"style":124},[62],[15,24524,1427],{"className":24525},[67],[15,24527],{"className":24528,"style":199},[77],[15,24530,170],{"className":24531},[203],[15,24533],{"className":24534,"style":199},[77],[15,24536,24538,24541,24544,24547,24550],{"className":24537},[58],[15,24539],{"className":24540,"style":299},[62],[15,24542,37],{"className":24543,"style":69},[67,68],[15,24545],{"className":24546,"style":199},[77],[15,24548,602],{"className":24549},[203],[15,24551],{"className":24552,"style":199},[77],[15,24554,24556,24559,24562,24565,24568,24571,24574,24577],{"className":24555},[58],[15,24557],{"className":24558,"style":63},[62],[15,24560,1427],{"className":24561},[67],[15,24563,42],{"className":24564},[73],[15,24566],{"className":24567,"style":78},[77],[15,24569,45],{"className":24570,"style":82},[67,68],[15,24572],{"className":24573,"style":199},[77],[15,24575,602],{"className":24576},[203],[15,24578],{"className":24579,"style":199},[77],[15,24581,24583,24586,24589],{"className":24582},[58],[15,24584],{"className":24585,"style":124},[62],[15,24587,1427],{"className":24588},[67],[15,24590,111],{"className":24591},[148],"。这一问题",[305,24594,24595],{},"不能","简单地用干预分布 ",[15,24598,24600,24640],{"className":24599,"translate":19},[18],[15,24601,24603],{"className":24602},[23],[25,24604,24605],{"xmlns":27},[29,24606,24607,24637],{},[32,24608,24609,24611,24613,24615,24617,24619,24621,24623,24625,24627,24629,24631,24633,24635],{},[35,24610,98],{},[39,24612,102],{"stretchy":101},[35,24614,45],{},[39,24616,602],{},[1425,24618,1427],{},[39,24620,170],{},[35,24622,696],{},[35,24624,699],{},[39,24626,102],{"stretchy":101},[35,24628,37],{},[39,24630,602],{},[1425,24632,2461],{},[39,24634,111],{"stretchy":101},[39,24636,111],{"stretchy":101},[47,24638,24639],{"encoding":49},"P(Y=1 \\mid do(X=0))",[15,24641,24643,24667,24685,24712],{"className":24642,"ariaHidden":41},[54],[15,24644,24646,24649,24652,24655,24658,24661,24664],{"className":24645},[58],[15,24647],{"className":24648,"style":124},[62],[15,24650,98],{"className":24651,"style":128},[67,68],[15,24653,102],{"className":24654},[132],[15,24656,45],{"className":24657,"style":82},[67,68],[15,24659],{"className":24660,"style":199},[77],[15,24662,602],{"className":24663},[203],[15,24665],{"className":24666,"style":199},[77],[15,24668,24670,24673,24676,24679,24682],{"className":24669},[58],[15,24671],{"className":24672,"style":124},[62],[15,24674,1427],{"className":24675},[67],[15,24677],{"className":24678,"style":199},[77],[15,24680,170],{"className":24681},[203],[15,24683],{"className":24684,"style":199},[77],[15,24686,24688,24691,24694,24697,24700,24703,24706,24709],{"className":24687},[58],[15,24689],{"className":24690,"style":124},[62],[15,24692,696],{"className":24693},[67,68],[15,24695,699],{"className":24696},[67,68],[15,24698,102],{"className":24699},[132],[15,24701,37],{"className":24702,"style":69},[67,68],[15,24704],{"className":24705,"style":199},[77],[15,24707,602],{"className":24708},[203],[15,24710],{"className":24711,"style":199},[77],[15,24713,24715,24718,24721],{"className":24714},[58],[15,24716],{"className":24717,"style":124},[62],[15,24719,2461],{"className":24720},[67],[15,24722,759],{"className":24723},[148],"（总体中未服药者的康复率）来回答，因为后者描述的是「随机抽取一个未服药个体」的康复概率，而反事实问题问的是",[305,24726,24727],{},"这同一个","已知服药后康复的病人。按照三步算法：首先根据「该病人服药后康复」这一证据，对可能导致其康复的外生因素（如自身免疫力 ",[15,24730,24732,24745],{"className":24731,"translate":19},[18],[15,24733,24735],{"className":24734},[23],[25,24736,24737],{"xmlns":27},[29,24738,24739,24743],{},[32,24740,24741],{},[35,24742,2458],{},[47,24744,2458],{"encoding":49},[15,24746,24748],{"className":24747,"ariaHidden":41},[54],[15,24749,24751,24754],{"className":24750},[58],[15,24752],{"className":24753,"style":299},[62],[15,24755,2458],{"className":24756,"style":2570},[67,68],"）的分布进行后验更新——服药后康复的人群中，「体质本身较好、即使不服药也可能康复」的后验概率会高于总体先验；随后在 ",[15,24759,24761,24781],{"className":24760,"translate":19},[18],[15,24762,24764],{"className":24763},[23],[25,24765,24766],{"xmlns":27},[29,24767,24768,24778],{},[32,24769,24770,24772,24774,24776],{},[35,24771,37],{},[39,24773,8863],{},[39,24775,602],{},[1425,24777,2461],{},[47,24779,24780],{"encoding":49},"X:=0",[15,24782,24784,24802],{"className":24783,"ariaHidden":41},[54],[15,24785,24787,24790,24793,24796,24799],{"className":24786},[58],[15,24788],{"className":24789,"style":299},[62],[15,24791,37],{"className":24792,"style":69},[67,68],[15,24794],{"className":24795,"style":199},[77],[15,24797,8899],{"className":24798},[203],[15,24800],{"className":24801,"style":199},[77],[15,24803,24805,24808],{"className":24804},[58],[15,24806],{"className":24807,"style":3149},[62],[15,24809,2461],{"className":24810},[67]," 的子模型中，用这一更新后的 ",[15,24813,24815,24828],{"className":24814,"translate":19},[18],[15,24816,24818],{"className":24817},[23],[25,24819,24820],{"xmlns":27},[29,24821,24822,24826],{},[32,24823,24824],{},[35,24825,2458],{},[47,24827,2458],{"encoding":49},[15,24829,24831],{"className":24830,"ariaHidden":41},[54],[15,24832,24834,24837],{"className":24833},[58],[15,24835],{"className":24836,"style":299},[62],[15,24838,2458],{"className":24839,"style":2570},[67,68]," 分布重新计算 ",[15,24842,24844,24857],{"className":24843,"translate":19},[18],[15,24845,24847],{"className":24846},[23],[25,24848,24849],{"xmlns":27},[29,24850,24851,24855],{},[32,24852,24853],{},[35,24854,45],{},[47,24856,45],{"encoding":49},[15,24858,24860],{"className":24859,"ariaHidden":41},[54],[15,24861,24863,24866],{"className":24862},[58],[15,24864],{"className":24865,"style":299},[62],[15,24867,45],{"className":24868,"style":82},[67,68],"。这解释了为什么反事实概率 ",[15,24871,24873,24917],{"className":24872,"translate":19},[18],[15,24874,24876],{"className":24875},[23],[25,24877,24878],{"xmlns":27},[29,24879,24880,24914],{},[32,24881,24882,24884,24886,24892,24894,24896,24898,24900,24902,24904,24906,24908,24910,24912],{},[35,24883,98],{},[39,24885,102],{"stretchy":101},[863,24887,24888,24890],{},[35,24889,45],{},[1425,24891,2461],{},[39,24893,602],{},[1425,24895,1427],{},[39,24897,170],{},[35,24899,37],{},[39,24901,602],{},[1425,24903,1427],{},[39,24905,42],{"separator":41},[35,24907,45],{},[39,24909,602],{},[1425,24911,1427],{},[39,24913,111],{"stretchy":101},[47,24915,24916],{"encoding":49},"P(Y_0=1\\mid X=1,Y=1)",[15,24918,24920,24981,24999,25017,25044],{"className":24919,"ariaHidden":41},[54],[15,24921,24923,24926,24929,24932,24972,24975,24978],{"className":24922},[58],[15,24924],{"className":24925,"style":124},[62],[15,24927,98],{"className":24928,"style":128},[67,68],[15,24930,102],{"className":24931},[132],[15,24933,24935,24938],{"className":24934},[67],[15,24936,45],{"className":24937,"style":82},[67,68],[15,24939,24941],{"className":24940},[918],[15,24942,24944,24964],{"className":24943},[922,923],[15,24945,24947,24961],{"className":24946},[927],[15,24948,24950],{"className":24949,"style":1496},[931],[15,24951,24952,24955],{"style":1499},[15,24953],{"className":24954,"style":940},[939],[15,24956,24958],{"className":24957},[944,945,946,947],[15,24959,2461],{"className":24960},[67,947],[15,24962,955],{"className":24963},[954],[15,24965,24967],{"className":24966},[927],[15,24968,24970],{"className":24969,"style":962},[931],[15,24971],{},[15,24973],{"className":24974,"style":199},[77],[15,24976,602],{"className":24977},[203],[15,24979],{"className":24980,"style":199},[77],[15,24982,24984,24987,24990,24993,24996],{"className":24983},[58],[15,24985],{"className":24986,"style":124},[62],[15,24988,1427],{"className":24989},[67],[15,24991],{"className":24992,"style":199},[77],[15,24994,170],{"className":24995},[203],[15,24997],{"className":24998,"style":199},[77],[15,25000,25002,25005,25008,25011,25014],{"className":25001},[58],[15,25003],{"className":25004,"style":299},[62],[15,25006,37],{"className":25007,"style":69},[67,68],[15,25009],{"className":25010,"style":199},[77],[15,25012,602],{"className":25013},[203],[15,25015],{"className":25016,"style":199},[77],[15,25018,25020,25023,25026,25029,25032,25035,25038,25041],{"className":25019},[58],[15,25021],{"className":25022,"style":63},[62],[15,25024,1427],{"className":25025},[67],[15,25027,42],{"className":25028},[73],[15,25030],{"className":25031,"style":78},[77],[15,25033,45],{"className":25034,"style":82},[67,68],[15,25036],{"className":25037,"style":199},[77],[15,25039,602],{"className":25040},[203],[15,25042],{"className":25043,"style":199},[77],[15,25045,25047,25050,25053],{"className":25046},[58],[15,25048],{"className":25049,"style":124},[62],[15,25051,1427],{"className":25052},[67],[15,25054,111],{"className":25055},[148]," 一般会",[305,25058,25059],{},"高于","总体干预概率 ",[15,25062,25064,25104],{"className":25063,"translate":19},[18],[15,25065,25067],{"className":25066},[23],[25,25068,25069],{"xmlns":27},[29,25070,25071,25101],{},[32,25072,25073,25075,25077,25079,25081,25083,25085,25087,25089,25091,25093,25095,25097,25099],{},[35,25074,98],{},[39,25076,102],{"stretchy":101},[35,25078,45],{},[39,25080,602],{},[1425,25082,1427],{},[39,25084,170],{},[35,25086,696],{},[35,25088,699],{},[39,25090,102],{"stretchy":101},[35,25092,37],{},[39,25094,602],{},[1425,25096,2461],{},[39,25098,111],{"stretchy":101},[39,25100,111],{"stretchy":101},[47,25102,25103],{"encoding":49},"P(Y=1\\mid do(X=0))",[15,25105,25107,25131,25149,25176],{"className":25106,"ariaHidden":41},[54],[15,25108,25110,25113,25116,25119,25122,25125,25128],{"className":25109},[58],[15,25111],{"className":25112,"style":124},[62],[15,25114,98],{"className":25115,"style":128},[67,68],[15,25117,102],{"className":25118},[132],[15,25120,45],{"className":25121,"style":82},[67,68],[15,25123],{"className":25124,"style":199},[77],[15,25126,602],{"className":25127},[203],[15,25129],{"className":25130,"style":199},[77],[15,25132,25134,25137,25140,25143,25146],{"className":25133},[58],[15,25135],{"className":25136,"style":124},[62],[15,25138,1427],{"className":25139},[67],[15,25141],{"className":25142,"style":199},[77],[15,25144,170],{"className":25145},[203],[15,25147],{"className":25148,"style":199},[77],[15,25150,25152,25155,25158,25161,25164,25167,25170,25173],{"className":25151},[58],[15,25153],{"className":25154,"style":124},[62],[15,25156,696],{"className":25157},[67,68],[15,25159,699],{"className":25160},[67,68],[15,25162,102],{"className":25163},[132],[15,25165,37],{"className":25166,"style":69},[67,68],[15,25168],{"className":25169,"style":199},[77],[15,25171,602],{"className":25172},[203],[15,25174],{"className":25175,"style":199},[77],[15,25177,25179,25182,25185],{"className":25178},[58],[15,25180],{"className":25181,"style":124},[62],[15,25183,2461],{"className":25184},[67],[15,25186,759],{"className":25187},[148],"——因为前者的条件化过程已经通过溯因步骤「筛选」出了体质更好的子群体。这一细微但本质的差别，是反事实推理（第三层）无法被干预计算（第二层）替代的直接例证，也是「个体化处理效应（Individual Treatment Effect）」这一概念在医学与政策评估中难以精确估计、却又极具价值的理论根源。",[11,25190,25191,25194,25195,25198,25199,25227,25228,25271,25272,431,25300,25343],{},[305,25192,25193],{},"一个必须说清楚的边界：反事实的可识别性。"," 上述三步算法成立的前提是 SCM ",[305,25196,25197],{},"完全已知","——",[15,25200,25202,25215],{"className":25201,"translate":19},[18],[15,25203,25205],{"className":25204},[23],[25,25206,25207],{"xmlns":27},[29,25208,25209,25213],{},[32,25210,25211],{},[35,25212,9484],{},[47,25214,9484],{"encoding":49},[15,25216,25218],{"className":25217,"ariaHidden":41},[54],[15,25219,25221,25224],{"className":25220},[58],[15,25222],{"className":25223,"style":299},[62],[15,25225,9484],{"className":25226,"style":128},[67,68]," 中的函数形式与 ",[15,25229,25231,25250],{"className":25230,"translate":19},[18],[15,25232,25234],{"className":25233},[23],[25,25235,25236],{"xmlns":27},[29,25237,25238,25248],{},[32,25239,25240,25242,25244,25246],{},[35,25241,98],{},[39,25243,102],{"stretchy":101},[35,25245,2458],{},[39,25247,111],{"stretchy":101},[47,25249,11006],{"encoding":49},[15,25251,25253],{"className":25252,"ariaHidden":41},[54],[15,25254,25256,25259,25262,25265,25268],{"className":25255},[58],[15,25257],{"className":25258,"style":124},[62],[15,25260,98],{"className":25261,"style":128},[67,68],[15,25263,102],{"className":25264},[132],[15,25266,2458],{"className":25267,"style":2570},[67,68],[15,25269,111],{"className":25270},[148]," 的分布都已指定。而在现实中我们通常只有观测数据，",[15,25273,25275,25288],{"className":25274,"translate":19},[18],[15,25276,25278],{"className":25277},[23],[25,25279,25280],{"xmlns":27},[29,25281,25282,25286],{},[32,25283,25284],{},[35,25285,9484],{},[47,25287,9484],{"encoding":49},[15,25289,25291],{"className":25290,"ariaHidden":41},[54],[15,25292,25294,25297],{"className":25293},[58],[15,25295],{"className":25296,"style":299},[62],[15,25298,9484],{"className":25299,"style":128},[67,68],[15,25301,25303,25322],{"className":25302,"translate":19},[18],[15,25304,25306],{"className":25305},[23],[25,25307,25308],{"xmlns":27},[29,25309,25310,25320],{},[32,25311,25312,25314,25316,25318],{},[35,25313,98],{},[39,25315,102],{"stretchy":101},[35,25317,2458],{},[39,25319,111],{"stretchy":101},[47,25321,11006],{"encoding":49},[15,25323,25325],{"className":25324,"ariaHidden":41},[54],[15,25326,25328,25331,25334,25337,25340],{"className":25327},[58],[15,25329],{"className":25330,"style":124},[62],[15,25332,98],{"className":25333,"style":128},[67,68],[15,25335,102],{"className":25336},[132],[15,25338,2458],{"className":25339,"style":2570},[67,68],[15,25341,111],{"className":25342},[148]," 都是未知的。这一差别不是技术细节，而是第三层与第二层之间的一条硬边界：",[507,25345,25346,25436],{},[510,25347,25348,25349,25431,25432,25435],{},"第二层的量 ",[15,25350,25352,25383],{"className":25351,"translate":19},[18],[15,25353,25355],{"className":25354},[23],[25,25356,25357],{"xmlns":27},[29,25358,25359,25381],{},[32,25360,25361,25363,25365,25367,25369,25371,25373,25375,25377,25379],{},[35,25362,98],{},[39,25364,102],{"stretchy":101},[35,25366,534],{},[39,25368,170],{},[35,25370,696],{},[35,25372,699],{},[39,25374,102],{"stretchy":101},[35,25376,539],{},[39,25378,111],{"stretchy":101},[39,25380,111],{"stretchy":101},[47,25382,710],{"encoding":49},[15,25384,25386,25410],{"className":25385,"ariaHidden":41},[54],[15,25387,25389,25392,25395,25398,25401,25404,25407],{"className":25388},[58],[15,25390],{"className":25391,"style":124},[62],[15,25393,98],{"className":25394,"style":128},[67,68],[15,25396,102],{"className":25397},[132],[15,25399,534],{"className":25400,"style":563},[67,68],[15,25402],{"className":25403,"style":199},[77],[15,25405,170],{"className":25406},[203],[15,25408],{"className":25409,"style":199},[77],[15,25411,25413,25416,25419,25422,25425,25428],{"className":25412},[58],[15,25414],{"className":25415,"style":124},[62],[15,25417,696],{"className":25418},[67,68],[15,25420,699],{"className":25421},[67,68],[15,25423,102],{"className":25424},[132],[15,25426,539],{"className":25427},[67,68],[15,25429,759],{"className":25430},[148]," 在满足后门准则或前门准则（见 3.5 节）时，",[305,25433,25434],{},"可以","仅用观测分布表达出来，因而能够由数据估计；",[510,25437,25438,25439,25568,25569,25600,25601,25629,25630,25658,25659,2249],{},"第三层的量 ",[15,25440,25442,25474],{"className":25441,"translate":19},[18],[15,25443,25445],{"className":25444},[23],[25,25446,25447],{"xmlns":27},[29,25448,25449,25471],{},[32,25450,25451,25453,25455,25461,25463,25465,25467,25469],{},[35,25452,98],{},[39,25454,102],{"stretchy":101},[863,25456,25457,25459],{},[35,25458,45],{},[35,25460,539],{},[39,25462,602],{},[35,25464,534],{},[39,25466,170],{},[35,25468,13768],{},[39,25470,111],{"stretchy":101},[47,25472,25473],{"encoding":49},"P(Y_x = y \\mid e)",[15,25475,25477,25538,25556],{"className":25476,"ariaHidden":41},[54],[15,25478,25480,25483,25486,25489,25529,25532,25535],{"className":25479},[58],[15,25481],{"className":25482,"style":124},[62],[15,25484,98],{"className":25485,"style":128},[67,68],[15,25487,102],{"className":25488},[132],[15,25490,25492,25495],{"className":25491},[67],[15,25493,45],{"className":25494,"style":82},[67,68],[15,25496,25498],{"className":25497},[918],[15,25499,25501,25521],{"className":25500},[922,923],[15,25502,25504,25518],{"className":25503},[927],[15,25505,25507],{"className":25506,"style":932},[931],[15,25508,25509,25512],{"style":1499},[15,25510],{"className":25511,"style":940},[939],[15,25513,25515],{"className":25514},[944,945,946,947],[15,25516,539],{"className":25517},[67,68,947],[15,25519,955],{"className":25520},[954],[15,25522,25524],{"className":25523},[927],[15,25525,25527],{"className":25526,"style":962},[931],[15,25528],{},[15,25530],{"className":25531,"style":199},[77],[15,25533,602],{"className":25534},[203],[15,25536],{"className":25537,"style":199},[77],[15,25539,25541,25544,25547,25550,25553],{"className":25540},[58],[15,25542],{"className":25543,"style":124},[62],[15,25545,534],{"className":25546,"style":563},[67,68],[15,25548],{"className":25549,"style":199},[77],[15,25551,170],{"className":25552},[203],[15,25554],{"className":25555,"style":199},[77],[15,25557,25559,25562,25565],{"className":25558},[58],[15,25560],{"className":25561,"style":124},[62],[15,25563,13768],{"className":25564},[67,68],[15,25566,111],{"className":25567},[148]," 则要求「同一个体在另一个可能世界中的取值」，也就是要求",[305,25570,25571,25572],{},"同一个 ",[15,25573,25575,25588],{"className":25574,"translate":19},[18],[15,25576,25578],{"className":25577},[23],[25,25579,25580],{"xmlns":27},[29,25581,25582,25586],{},[32,25583,25584],{},[35,25585,13778],{},[47,25587,13778],{"encoding":49},[15,25589,25591],{"className":25590,"ariaHidden":41},[54],[15,25592,25594,25597],{"className":25593},[58],[15,25595],{"className":25596,"style":635},[62],[15,25598,13778],{"className":25599},[67,68],"，而 ",[15,25602,25604,25617],{"className":25603,"translate":19},[18],[15,25605,25607],{"className":25606},[23],[25,25608,25609],{"xmlns":27},[29,25610,25611,25615],{},[32,25612,25613],{},[35,25614,13778],{},[47,25616,13778],{"encoding":49},[15,25618,25620],{"className":25619,"ariaHidden":41},[54],[15,25621,25623,25626],{"className":25622},[58],[15,25624],{"className":25625,"style":635},[62],[15,25627,13778],{"className":25628},[67,68]," 本身不可观测。观测数据只能给出内生变量 ",[15,25631,25633,25646],{"className":25632,"translate":19},[18],[15,25634,25636],{"className":25635},[23],[25,25637,25638],{"xmlns":27},[29,25639,25640,25644],{},[32,25641,25642],{},[35,25643,1343],{},[47,25645,1343],{"encoding":49},[15,25647,25649],{"className":25648,"ariaHidden":41},[54],[15,25650,25652,25655],{"className":25651},[58],[15,25653],{"className":25654,"style":299},[62],[15,25656,1343],{"className":25657,"style":82},[67,68]," 的联合分布，一般无法唯一反解出 ",[15,25660,25662,25686],{"className":25661,"translate":19},[18],[15,25663,25665],{"className":25664},[23],[25,25666,25667],{"xmlns":27},[29,25668,25669,25683],{},[32,25670,25671,25673,25675,25677,25679,25681],{},[35,25672,98],{},[39,25674,102],{"stretchy":101},[35,25676,13778],{},[39,25678,170],{},[35,25680,13768],{},[39,25682,111],{"stretchy":101},[47,25684,25685],{"encoding":49},"P(u\\mid e)",[15,25687,25689,25713],{"className":25688,"ariaHidden":41},[54],[15,25690,25692,25695,25698,25701,25704,25707,25710],{"className":25691},[58],[15,25693],{"className":25694,"style":124},[62],[15,25696,98],{"className":25697,"style":128},[67,68],[15,25699,102],{"className":25700},[132],[15,25702,13778],{"className":25703},[67,68],[15,25705],{"className":25706,"style":199},[77],[15,25708,170],{"className":25709},[203],[15,25711],{"className":25712,"style":199},[77],[15,25714,25716,25719,25722],{"className":25715},[58],[15,25717],{"className":25718,"style":124},[62],[15,25720,13768],{"className":25721},[67,68],[15,25723,111],{"className":25724},[148],[11,25726,25727,25728],{},"由此可以得到一个一般性判断：",[305,25729,25730],{},"反事实量在一般情形下不可从观测数据识别，只有在 SCM 被完整指定、或引入足够强的额外假设时才可计算。",[11,25732,25733,25734,25813,25814,25902,25903,811,25931,25959,25960,25962,25963,25991],{},"一个极端而富有启发的例子是线性 SCM：此时 ",[15,25735,25737,25761],{"className":25736,"translate":19},[18],[15,25738,25740],{"className":25739},[23],[25,25741,25742],{"xmlns":27},[29,25743,25744,25758],{},[32,25745,25746,25748,25750,25752,25754,25756],{},[35,25747,1343],{},[39,25749,602],{},[35,25751,13765],{},[35,25753,1343],{},[39,25755,2894],{},[35,25757,2458],{},[47,25759,25760],{"encoding":49},"V = BV + U",[15,25762,25764,25782,25804],{"className":25763,"ariaHidden":41},[54],[15,25765,25767,25770,25773,25776,25779],{"className":25766},[58],[15,25768],{"className":25769,"style":299},[62],[15,25771,1343],{"className":25772,"style":82},[67,68],[15,25774],{"className":25775,"style":199},[77],[15,25777,602],{"className":25778},[203],[15,25780],{"className":25781,"style":199},[77],[15,25783,25785,25788,25792,25795,25798,25801],{"className":25784},[58],[15,25786],{"className":25787,"style":1638},[62],[15,25789,13765],{"className":25790,"style":25791},[67,68],"margin-right:0.0502em;",[15,25793,1343],{"className":25794,"style":82},[67,68],[15,25796],{"className":25797,"style":82},[77],[15,25799,2894],{"className":25800},[1648],[15,25802],{"className":25803,"style":82},[77],[15,25805,25807,25810],{"className":25806},[58],[15,25808],{"className":25809,"style":299},[62],[15,25811,2458],{"className":25812,"style":2570},[67,68]," 蕴含 ",[15,25815,25817,25845],{"className":25816,"translate":19},[18],[15,25818,25820],{"className":25819},[23],[25,25821,25822],{"xmlns":27},[29,25823,25824,25842],{},[32,25825,25826,25828,25830,25832,25834,25836,25838,25840],{},[35,25827,2458],{},[39,25829,602],{},[39,25831,102],{"stretchy":101},[35,25833,16674],{},[39,25835,14235],{},[35,25837,13765],{},[39,25839,111],{"stretchy":101},[35,25841,1343],{},[47,25843,25844],{"encoding":49},"U = (I-B)V",[15,25846,25848,25866,25887],{"className":25847,"ariaHidden":41},[54],[15,25849,25851,25854,25857,25860,25863],{"className":25850},[58],[15,25852],{"className":25853,"style":299},[62],[15,25855,2458],{"className":25856,"style":2570},[67,68],[15,25858],{"className":25859,"style":199},[77],[15,25861,602],{"className":25862},[203],[15,25864],{"className":25865,"style":199},[77],[15,25867,25869,25872,25875,25878,25881,25884],{"className":25868},[58],[15,25870],{"className":25871,"style":124},[62],[15,25873,102],{"className":25874},[132],[15,25876,16674],{"className":25877,"style":69},[67,68],[15,25879],{"className":25880,"style":82},[77],[15,25882,14235],{"className":25883},[1648],[15,25885],{"className":25886,"style":82},[77],[15,25888,25890,25893,25896,25899],{"className":25889},[58],[15,25891],{"className":25892,"style":124},[62],[15,25894,13765],{"className":25895,"style":25791},[67,68],[15,25897,111],{"className":25898},[148],[15,25900,1343],{"className":25901,"style":82},[67,68],"，于是给定任一观测到的 ",[15,25904,25906,25919],{"className":25905,"translate":19},[18],[15,25907,25909],{"className":25908},[23],[25,25910,25911],{"xmlns":27},[29,25912,25913,25917],{},[32,25914,25915],{},[35,25916,12538],{},[47,25918,12538],{"encoding":49},[15,25920,25922],{"className":25921,"ariaHidden":41},[54],[15,25923,25925,25928],{"className":25924},[58],[15,25926],{"className":25927,"style":635},[62],[15,25929,12538],{"className":25930,"style":563},[67,68],[15,25932,25934,25947],{"className":25933,"translate":19},[18],[15,25935,25937],{"className":25936},[23],[25,25938,25939],{"xmlns":27},[29,25940,25941,25945],{},[32,25942,25943],{},[35,25944,13778],{},[47,25946,13778],{"encoding":49},[15,25948,25950],{"className":25949,"ariaHidden":41},[54],[15,25951,25953,25956],{"className":25952},[58],[15,25954],{"className":25955,"style":635},[62],[15,25957,13778],{"className":25958},[67,68]," 被",[305,25961,15985],{},"，反事实分布退化为一个点质量，个体处理效应似乎唾手可得。但这一「可得」完全是线性与可加假设的产物，而非数据所提供的信息——一旦允许非线性或非高斯，「同一个 ",[15,25964,25966,25979],{"className":25965,"translate":19},[18],[15,25967,25969],{"className":25968},[23],[25,25970,25971],{"xmlns":27},[29,25972,25973,25977],{},[32,25974,25975],{},[35,25976,13778],{},[47,25978,13778],{"encoding":49},[15,25980,25982],{"className":25981,"ariaHidden":41},[54],[15,25983,25985,25988],{"className":25984},[58],[15,25986],{"className":25987,"style":635},[62],[15,25989,13778],{"className":25990},[67,68],"」便重新变得不可复原。这也正是经典 SEM 传统（见 4.2 节）能够讨论「个体效应」、而现代因果推断对此极为谨慎的原因所在。",[11,25993,25994],{},"因此第三层虽然在形式上已被定义清楚，其实践可达性却最弱。本文余下部分把重点放在第二层的可识别性上，这并非理论上的偏好，而是数据所能支撑的边界所在。",[1309,25996,25998],{"id":25997},"_34-中介分析从总效应到直接效应与间接效应","3.4 中介分析：从总效应到直接效应与间接效应",[11,26000,26001,26002,26074],{},"第一部分曾用链结构 ",[15,26003,26005,26026],{"className":26004,"translate":19},[18],[15,26006,26008],{"className":26007},[23],[25,26009,26010],{"xmlns":27},[29,26011,26012,26024],{},[32,26013,26014,26016,26018,26020,26022],{},[35,26015,37],{},[39,26017,1846],{},[35,26019,4214],{},[39,26021,1846],{},[35,26023,45],{},[47,26025,4360],{"encoding":49},[15,26027,26029,26047,26065],{"className":26028,"ariaHidden":41},[54],[15,26030,26032,26035,26038,26041,26044],{"className":26031},[58],[15,26033],{"className":26034,"style":299},[62],[15,26036,37],{"className":26037,"style":69},[67,68],[15,26039],{"className":26040,"style":199},[77],[15,26042,1846],{"className":26043},[203],[15,26045],{"className":26046,"style":199},[77],[15,26048,26050,26053,26056,26059,26062],{"className":26049},[58],[15,26051],{"className":26052,"style":299},[62],[15,26054,4214],{"className":26055,"style":4243},[67,68],[15,26057],{"className":26058,"style":199},[77],[15,26060,1846],{"className":26061},[203],[15,26063],{"className":26064,"style":199},[77],[15,26066,26068,26071],{"className":26067},[58],[15,26069],{"className":26070,"style":299},[62],[15,26072,45],{"className":26073,"style":82},[67,68]," 说明「控制中介会切断全部影响」。当时给出的只是定性结论，现在有了 do-算子与反事实的语言，可以把「影响如何被分解」这件事精确化。",[11,26076,26077,26078,26106,26107,26135,26136,26164,26165,4697,26193,26221,26222,26295,26296,2249],{},"设 ",[15,26079,26081,26094],{"className":26080,"translate":19},[18],[15,26082,26084],{"className":26083},[23],[25,26085,26086],{"xmlns":27},[29,26087,26088,26092],{},[32,26089,26090],{},[35,26091,37],{},[47,26093,37],{"encoding":49},[15,26095,26097],{"className":26096,"ariaHidden":41},[54],[15,26098,26100,26103],{"className":26099},[58],[15,26101],{"className":26102,"style":299},[62],[15,26104,37],{"className":26105,"style":69},[67,68]," 为处理变量，",[15,26108,26110,26123],{"className":26109,"translate":19},[18],[15,26111,26113],{"className":26112},[23],[25,26114,26115],{"xmlns":27},[29,26116,26117,26121],{},[32,26118,26119],{},[35,26120,45],{},[47,26122,45],{"encoding":49},[15,26124,26126],{"className":26125,"ariaHidden":41},[54],[15,26127,26129,26132],{"className":26128},[58],[15,26130],{"className":26131,"style":299},[62],[15,26133,45],{"className":26134,"style":82},[67,68]," 为结果，",[15,26137,26139,26152],{"className":26138,"translate":19},[18],[15,26140,26142],{"className":26141},[23],[25,26143,26144],{"xmlns":27},[29,26145,26146,26150],{},[32,26147,26148],{},[35,26149,9469],{},[47,26151,9469],{"encoding":49},[15,26153,26155],{"className":26154,"ariaHidden":41},[54],[15,26156,26158,26161],{"className":26157},[58],[15,26159],{"className":26160,"style":299},[62],[15,26162,9469],{"className":26163,"style":2570},[67,68]," 为介于二者之间的中介变量。",[15,26166,26168,26181],{"className":26167,"translate":19},[18],[15,26169,26171],{"className":26170},[23],[25,26172,26173],{"xmlns":27},[29,26174,26175,26179],{},[32,26176,26177],{},[35,26178,37],{},[47,26180,37],{"encoding":49},[15,26182,26184],{"className":26183,"ariaHidden":41},[54],[15,26185,26187,26190],{"className":26186},[58],[15,26188],{"className":26189,"style":299},[62],[15,26191,37],{"className":26192,"style":69},[67,68],[15,26194,26196,26209],{"className":26195,"translate":19},[18],[15,26197,26199],{"className":26198},[23],[25,26200,26201],{"xmlns":27},[29,26202,26203,26207],{},[32,26204,26205],{},[35,26206,45],{},[47,26208,45],{"encoding":49},[15,26210,26212],{"className":26211,"ariaHidden":41},[54],[15,26213,26215,26218],{"className":26214},[58],[15,26216],{"className":26217,"style":299},[62],[15,26219,45],{"className":26220,"style":82},[67,68]," 的作用只可能经过两条通道：中介通道 ",[15,26223,26225,26247],{"className":26224,"translate":19},[18],[15,26226,26228],{"className":26227},[23],[25,26229,26230],{"xmlns":27},[29,26231,26232,26244],{},[32,26233,26234,26236,26238,26240,26242],{},[35,26235,37],{},[39,26237,1846],{},[35,26239,9469],{},[39,26241,1846],{},[35,26243,45],{},[47,26245,26246],{"encoding":49},"X \\to M \\to Y",[15,26248,26250,26268,26286],{"className":26249,"ariaHidden":41},[54],[15,26251,26253,26256,26259,26262,26265],{"className":26252},[58],[15,26254],{"className":26255,"style":299},[62],[15,26257,37],{"className":26258,"style":69},[67,68],[15,26260],{"className":26261,"style":199},[77],[15,26263,1846],{"className":26264},[203],[15,26266],{"className":26267,"style":199},[77],[15,26269,26271,26274,26277,26280,26283],{"className":26270},[58],[15,26272],{"className":26273,"style":299},[62],[15,26275,9469],{"className":26276,"style":2570},[67,68],[15,26278],{"className":26279,"style":199},[77],[15,26281,1846],{"className":26282},[203],[15,26284],{"className":26285,"style":199},[77],[15,26287,26289,26292],{"className":26288},[58],[15,26290],{"className":26291,"style":299},[62],[15,26293,45],{"className":26294,"style":82},[67,68]," 与直接通道 ",[15,26297,26299,26316],{"className":26298,"translate":19},[18],[15,26300,26302],{"className":26301},[23],[25,26303,26304],{"xmlns":27},[29,26305,26306,26314],{},[32,26307,26308,26310,26312],{},[35,26309,37],{},[39,26311,1846],{},[35,26313,45],{},[47,26315,9037],{"encoding":49},[15,26317,26319,26337],{"className":26318,"ariaHidden":41},[54],[15,26320,26322,26325,26328,26331,26334],{"className":26321},[58],[15,26323],{"className":26324,"style":299},[62],[15,26326,37],{"className":26327,"style":69},[67,68],[15,26329],{"className":26330,"style":199},[77],[15,26332,1846],{"className":26333},[203],[15,26335],{"className":26336,"style":199},[77],[15,26338,26340,26343],{"className":26339},[58],[15,26341],{"className":26342,"style":299},[62],[15,26344,45],{"className":26345,"style":82},[67,68],[4118,26347,26350],{"className":26348,"code":26349,"language":4123},[4121],"      X ──→ M ──→ Y\n      │           ↑\n      └───────────┘\n",[4125,26351,26349],{"__ignoreMap":4127},[11,26353,26354,26355,26358,26359,17847,26594,26622,26623,26683,26684,26712],{},"先定义",[305,26356,26357],{},"总效应（Average Total Effect）","：\n",[15,26360,26362,26414],{"className":26361,"translate":19},[18],[15,26363,26365],{"className":26364},[23],[25,26366,26367],{"xmlns":27},[29,26368,26369,26411],{},[32,26370,26371,26378,26380,26382,26384,26390,26392,26394,26396,26398,26409],{},[32,26372,26373,26376],{},[35,26374,26375],{"mathvariant":878},"T",[35,26377,1348],{"mathvariant":878},[39,26379,602],{},[35,26381,1348],{"mathvariant":13815},[39,26383,13818],{"stretchy":101},[863,26385,26386,26388],{},[35,26387,45],{},[35,26389,539],{},[39,26391,13827],{"stretchy":101},[39,26393,14235],{},[35,26395,1348],{"mathvariant":13815},[39,26397,13818],{"stretchy":101},[863,26399,26400,26402],{},[35,26401,45],{},[872,26403,26404,26406],{},[35,26405,539],{},[39,26407,26408],{},"∗",[39,26410,13827],{"stretchy":101},[47,26412,26413],{"encoding":49},"\\mathrm{TE} = \\mathbb{E}[Y_{x}] - \\mathbb{E}[Y_{x^*}]",[15,26415,26417,26439,26507],{"className":26416,"ariaHidden":41},[54],[15,26418,26420,26423,26430,26433,26436],{"className":26419},[58],[15,26421],{"className":26422,"style":299},[62],[15,26424,26426],{"className":26425},[67],[15,26427,26429],{"className":26428},[67,10382],"TE",[15,26431],{"className":26432,"style":199},[77],[15,26434,602],{"className":26435},[203],[15,26437],{"className":26438,"style":199},[77],[15,26440,26442,26445,26449,26452,26495,26498,26501,26504],{"className":26441},[58],[15,26443],{"className":26444,"style":124},[62],[15,26446,1348],{"className":26447},[67,26448],"mathbb",[15,26450,13818],{"className":26451},[132],[15,26453,26455,26458],{"className":26454},[67],[15,26456,45],{"className":26457,"style":82},[67,68],[15,26459,26461],{"className":26460},[918],[15,26462,26464,26487],{"className":26463},[922,923],[15,26465,26467,26484],{"className":26466},[927],[15,26468,26470],{"className":26469,"style":932},[931],[15,26471,26472,26475],{"style":1499},[15,26473],{"className":26474,"style":940},[939],[15,26476,26478],{"className":26477},[944,945,946,947],[15,26479,26481],{"className":26480},[67,947],[15,26482,539],{"className":26483},[67,68,947],[15,26485,955],{"className":26486},[954],[15,26488,26490],{"className":26489},[927],[15,26491,26493],{"className":26492,"style":962},[931],[15,26494],{},[15,26496,13827],{"className":26497},[148],[15,26499],{"className":26500,"style":82},[77],[15,26502,14235],{"className":26503},[1648],[15,26505],{"className":26506,"style":82},[77],[15,26508,26510,26513,26516,26519,26591],{"className":26509},[58],[15,26511],{"className":26512,"style":124},[62],[15,26514,1348],{"className":26515},[67,26448],[15,26517,13818],{"className":26518},[132],[15,26520,26522,26525],{"className":26521},[67],[15,26523,45],{"className":26524,"style":82},[67,68],[15,26526,26528],{"className":26527},[918],[15,26529,26531,26583],{"className":26530},[922,923],[15,26532,26534,26580],{"className":26533},[927],[15,26535,26538],{"className":26536,"style":26537},[931],"height:0.2828em;",[15,26539,26540,26543],{"style":1499},[15,26541],{"className":26542,"style":940},[939],[15,26544,26546],{"className":26545},[944,945,946,947],[15,26547,26549],{"className":26548},[67,947],[15,26550,26552,26555],{"className":26551},[67,947],[15,26553,539],{"className":26554},[67,68,947],[15,26556,26558],{"className":26557},[918],[15,26559,26561],{"className":26560},[922],[15,26562,26564],{"className":26563},[927],[15,26565,26568],{"className":26566,"style":26567},[931],"height:0.6183em;",[15,26569,26571,26574],{"style":26570},"top:-2.786em;margin-right:0.0714em;",[15,26572],{"className":26573,"style":18417},[939],[15,26575,26577],{"className":26576},[944,18421,15089,947],[15,26578,26408],{"className":26579},[1648,947],[15,26581,955],{"className":26582},[954],[15,26584,26586],{"className":26585},[927],[15,26587,26589],{"className":26588,"style":962},[931],[15,26590],{},[15,26592,13827],{"className":26593},[148],[15,26595,26597,26610],{"className":26596,"translate":19},[18],[15,26598,26600],{"className":26599},[23],[25,26601,26602],{"xmlns":27},[29,26603,26604,26608],{},[32,26605,26606],{},[35,26607,37],{},[47,26609,37],{"encoding":49},[15,26611,26613],{"className":26612,"ariaHidden":41},[54],[15,26614,26616,26619],{"className":26615},[58],[15,26617],{"className":26618,"style":299},[62],[15,26620,37],{"className":26621,"style":69},[67,68]," 从参考水平 ",[15,26624,26626,26644],{"className":26625,"translate":19},[18],[15,26627,26629],{"className":26628},[23],[25,26630,26631],{"xmlns":27},[29,26632,26633,26641],{},[32,26634,26635],{},[872,26636,26637,26639],{},[35,26638,539],{},[39,26640,26408],{},[47,26642,26643],{"encoding":49},"x^*",[15,26645,26647],{"className":26646,"ariaHidden":41},[54],[15,26648,26650,26654],{"className":26649},[58],[15,26651],{"className":26652,"style":26653},[62],"height:0.6887em;",[15,26655,26657,26660],{"className":26656},[67],[15,26658,539],{"className":26659},[67,68],[15,26661,26663],{"className":26662},[918],[15,26664,26666],{"className":26665},[922],[15,26667,26669],{"className":26668},[927],[15,26670,26672],{"className":26671,"style":26653},[931],[15,26673,26674,26677],{"style":1002},[15,26675],{"className":26676,"style":940},[939],[15,26678,26680],{"className":26679},[944,945,946,947],[15,26681,26408],{"className":26682},[1648,947]," 改为 ",[15,26685,26687,26700],{"className":26686,"translate":19},[18],[15,26688,26690],{"className":26689},[23],[25,26691,26692],{"xmlns":27},[29,26693,26694,26698],{},[32,26695,26696],{},[35,26697,539],{},[47,26699,539],{"encoding":49},[15,26701,26703],{"className":26702,"ariaHidden":41},[54],[15,26704,26706,26709],{"className":26705},[58],[15,26707],{"className":26708,"style":635},[62],[15,26710,539],{"className":26711},[67,68]," 时结果期望的净变化。为区分上述两条通道各自的贡献，Pearl 引入两个第三层的量：",[1314,26714,26715],{},[11,26716,26717,26720,10600,27432,27589,27590,27618,27619,27647,27648,27676,27677,27796],{},[305,26718,26719],{},"定义 3.5（自然直接效应与自然间接效应）",[15,26721,26723,26873],{"className":26722,"translate":19},[18],[15,26724,26726],{"className":26725},[23],[25,26727,26728],{"xmlns":27},[29,26729,26730,26870],{},[32,26731,26732,26742,26744,26746,26748,26754,26756,26758,26760,26762,26782,26784,26786,26788,26790,26800,26802,26804,26806,26814,26816,26818,26820,26826,26828,26830,26832,26834,26840,26842,26844,26846,26848,26868],{},[32,26733,26734,26737,26740],{},[35,26735,26736],{"mathvariant":878},"N",[35,26738,26739],{"mathvariant":878},"D",[35,26741,1348],{"mathvariant":878},[39,26743,102],{"stretchy":101},[35,26745,539],{},[39,26747,42],{"separator":41},[872,26749,26750,26752],{},[35,26751,539],{},[39,26753,26408],{},[39,26755,111],{"stretchy":101},[39,26757,602],{},[35,26759,1348],{"mathvariant":13815},[39,26761,13818],{"stretchy":101},[863,26763,26764,26766],{},[35,26765,45],{},[32,26767,26768,26770,26772],{},[35,26769,539],{},[39,26771,42],{"separator":41},[863,26773,26774,26776],{},[35,26775,9469],{},[872,26777,26778,26780],{},[35,26779,539],{},[39,26781,26408],{},[39,26783,13827],{"stretchy":101},[39,26785,14235],{},[35,26787,1348],{"mathvariant":13815},[39,26789,13818],{"stretchy":101},[863,26791,26792,26794],{},[35,26793,45],{},[872,26795,26796,26798],{},[35,26797,539],{},[39,26799,26408],{},[39,26801,13827],{"stretchy":101},[39,26803,42],{"separator":41},[77,26805],{"width":10235},[32,26807,26808,26810,26812],{},[35,26809,26736],{"mathvariant":878},[35,26811,16674],{"mathvariant":878},[35,26813,1348],{"mathvariant":878},[39,26815,102],{"stretchy":101},[35,26817,539],{},[39,26819,42],{"separator":41},[872,26821,26822,26824],{},[35,26823,539],{},[39,26825,26408],{},[39,26827,111],{"stretchy":101},[39,26829,602],{},[35,26831,1348],{"mathvariant":13815},[39,26833,13818],{"stretchy":101},[863,26835,26836,26838],{},[35,26837,45],{},[35,26839,539],{},[39,26841,13827],{"stretchy":101},[39,26843,14235],{},[35,26845,1348],{"mathvariant":13815},[39,26847,13818],{"stretchy":101},[863,26849,26850,26852],{},[35,26851,45],{},[32,26853,26854,26856,26858],{},[35,26855,539],{},[39,26857,42],{"separator":41},[863,26859,26860,26862],{},[35,26861,9469],{},[872,26863,26864,26866],{},[35,26865,539],{},[39,26867,26408],{},[39,26869,13827],{"stretchy":101},[47,26871,26872],{"encoding":49},"\\mathrm{NDE}(x, x^*) = \\mathbb{E}[Y_{x, M_{x^*}}] - \\mathbb{E}[Y_{x^*}], \\qquad \\mathrm{NIE}(x, x^*) = \\mathbb{E}[Y_{x}] - \\mathbb{E}[Y_{x, M_{x^*}}]",[15,26874,26876,26942,27085,27238,27305],{"className":26875,"ariaHidden":41},[54],[15,26877,26879,26882,26889,26892,26895,26898,26901,26930,26933,26936,26939],{"className":26878},[58],[15,26880],{"className":26881,"style":124},[62],[15,26883,26885],{"className":26884},[67],[15,26886,26888],{"className":26887},[67,10382],"NDE",[15,26890,102],{"className":26891},[132],[15,26893,539],{"className":26894},[67,68],[15,26896,42],{"className":26897},[73],[15,26899],{"className":26900,"style":78},[77],[15,26902,26904,26907],{"className":26903},[67],[15,26905,539],{"className":26906},[67,68],[15,26908,26910],{"className":26909},[918],[15,26911,26913],{"className":26912},[922],[15,26914,26916],{"className":26915},[927],[15,26917,26919],{"className":26918,"style":26653},[931],[15,26920,26921,26924],{"style":1002},[15,26922],{"className":26923,"style":940},[939],[15,26925,26927],{"className":26926},[944,945,946,947],[15,26928,26408],{"className":26929},[1648,947],[15,26931,111],{"className":26932},[148],[15,26934],{"className":26935,"style":199},[77],[15,26937,602],{"className":26938},[203],[15,26940],{"className":26941,"style":199},[77],[15,26943,26945,26949,26952,26955,27073,27076,27079,27082],{"className":26944},[58],[15,26946],{"className":26947,"style":26948},[62],"height:1.0383em;vertical-align:-0.2883em;",[15,26950,1348],{"className":26951},[67,26448],[15,26953,13818],{"className":26954},[132],[15,26956,26958,26961],{"className":26957},[67],[15,26959,45],{"className":26960,"style":82},[67,68],[15,26962,26964],{"className":26963},[918],[15,26965,26967,27064],{"className":26966},[922,923],[15,26968,26970,27061],{"className":26969},[927],[15,26971,26973],{"className":26972,"style":7358},[931],[15,26974,26975,26978],{"style":1499},[15,26976],{"className":26977,"style":940},[939],[15,26979,26981],{"className":26980},[944,945,946,947],[15,26982,26984,26987,26990],{"className":26983},[67,947],[15,26985,539],{"className":26986},[67,68,947],[15,26988,42],{"className":26989},[73,947],[15,26991,26993,26996],{"className":26992},[67,947],[15,26994,9469],{"className":26995,"style":2570},[67,68,947],[15,26997,26999],{"className":26998},[918],[15,27000,27002,27052],{"className":27001},[922,923],[15,27003,27005,27049],{"className":27004},[927],[15,27006,27008],{"className":27007,"style":18677},[931],[15,27009,27011,27015],{"style":27010},"top:-2.3448em;margin-left:-0.109em;margin-right:0.0714em;",[15,27012],{"className":27013,"style":27014},[939],"height:2.5423em;",[15,27016,27018],{"className":27017},[944,18421,15089,947],[15,27019,27021],{"className":27020},[67,947],[15,27022,27024,27027],{"className":27023},[67,947],[15,27025,539],{"className":27026},[67,68,947],[15,27028,27030],{"className":27029},[918],[15,27031,27033],{"className":27032},[922],[15,27034,27036],{"className":27035},[927],[15,27037,27040],{"className":27038,"style":27039},[931],"height:0.7593em;",[15,27041,27043,27046],{"style":27042},"top:-2.794em;margin-right:0.1em;",[15,27044],{"className":27045,"style":18417},[939],[15,27047,26408],{"className":27048},[1648,947],[15,27050,955],{"className":27051},[954],[15,27053,27055],{"className":27054},[927],[15,27056,27059],{"className":27057,"style":27058},[931],"height:0.1975em;",[15,27060],{},[15,27062,955],{"className":27063},[954],[15,27065,27067],{"className":27066},[927],[15,27068,27071],{"className":27069,"style":27070},[931],"height:0.2883em;",[15,27072],{},[15,27074,13827],{"className":27075},[148],[15,27077],{"className":27078,"style":82},[77],[15,27080,14235],{"className":27081},[1648],[15,27083],{"className":27084,"style":82},[77],[15,27086,27088,27091,27094,27097,27166,27169,27172,27175,27178,27185,27188,27191,27194,27197,27226,27229,27232,27235],{"className":27087},[58],[15,27089],{"className":27090,"style":124},[62],[15,27092,1348],{"className":27093},[67,26448],[15,27095,13818],{"className":27096},[132],[15,27098,27100,27103],{"className":27099},[67],[15,27101,45],{"className":27102,"style":82},[67,68],[15,27104,27106],{"className":27105},[918],[15,27107,27109,27158],{"className":27108},[922,923],[15,27110,27112,27155],{"className":27111},[927],[15,27113,27115],{"className":27114,"style":26537},[931],[15,27116,27117,27120],{"style":1499},[15,27118],{"className":27119,"style":940},[939],[15,27121,27123],{"className":27122},[944,945,946,947],[15,27124,27126],{"className":27125},[67,947],[15,27127,27129,27132],{"className":27128},[67,947],[15,27130,539],{"className":27131},[67,68,947],[15,27133,27135],{"className":27134},[918],[15,27136,27138],{"className":27137},[922],[15,27139,27141],{"className":27140},[927],[15,27142,27144],{"className":27143,"style":26567},[931],[15,27145,27146,27149],{"style":26570},[15,27147],{"className":27148,"style":18417},[939],[15,27150,27152],{"className":27151},[944,18421,15089,947],[15,27153,26408],{"className":27154},[1648,947],[15,27156,955],{"className":27157},[954],[15,27159,27161],{"className":27160},[927],[15,27162,27164],{"className":27163,"style":962},[931],[15,27165],{},[15,27167,13827],{"className":27168},[148],[15,27170,42],{"className":27171},[73],[15,27173],{"className":27174,"style":10474},[77],[15,27176],{"className":27177,"style":78},[77],[15,27179,27181],{"className":27180},[67],[15,27182,27184],{"className":27183},[67,10382],"NIE",[15,27186,102],{"className":27187},[132],[15,27189,539],{"className":27190},[67,68],[15,27192,42],{"className":27193},[73],[15,27195],{"className":27196,"style":78},[77],[15,27198,27200,27203],{"className":27199},[67],[15,27201,539],{"className":27202},[67,68],[15,27204,27206],{"className":27205},[918],[15,27207,27209],{"className":27208},[922],[15,27210,27212],{"className":27211},[927],[15,27213,27215],{"className":27214,"style":26653},[931],[15,27216,27217,27220],{"style":1002},[15,27218],{"className":27219,"style":940},[939],[15,27221,27223],{"className":27222},[944,945,946,947],[15,27224,26408],{"className":27225},[1648,947],[15,27227,111],{"className":27228},[148],[15,27230],{"className":27231,"style":199},[77],[15,27233,602],{"className":27234},[203],[15,27236],{"className":27237,"style":199},[77],[15,27239,27241,27244,27247,27250,27293,27296,27299,27302],{"className":27240},[58],[15,27242],{"className":27243,"style":124},[62],[15,27245,1348],{"className":27246},[67,26448],[15,27248,13818],{"className":27249},[132],[15,27251,27253,27256],{"className":27252},[67],[15,27254,45],{"className":27255,"style":82},[67,68],[15,27257,27259],{"className":27258},[918],[15,27260,27262,27285],{"className":27261},[922,923],[15,27263,27265,27282],{"className":27264},[927],[15,27266,27268],{"className":27267,"style":932},[931],[15,27269,27270,27273],{"style":1499},[15,27271],{"className":27272,"style":940},[939],[15,27274,27276],{"className":27275},[944,945,946,947],[15,27277,27279],{"className":27278},[67,947],[15,27280,539],{"className":27281},[67,68,947],[15,27283,955],{"className":27284},[954],[15,27286,27288],{"className":27287},[927],[15,27289,27291],{"className":27290,"style":962},[931],[15,27292],{},[15,27294,13827],{"className":27295},[148],[15,27297],{"className":27298,"style":82},[77],[15,27300,14235],{"className":27301},[1648],[15,27303],{"className":27304,"style":82},[77],[15,27306,27308,27311,27314,27317,27429],{"className":27307},[58],[15,27309],{"className":27310,"style":26948},[62],[15,27312,1348],{"className":27313},[67,26448],[15,27315,13818],{"className":27316},[132],[15,27318,27320,27323],{"className":27319},[67],[15,27321,45],{"className":27322,"style":82},[67,68],[15,27324,27326],{"className":27325},[918],[15,27327,27329,27421],{"className":27328},[922,923],[15,27330,27332,27418],{"className":27331},[927],[15,27333,27335],{"className":27334,"style":7358},[931],[15,27336,27337,27340],{"style":1499},[15,27338],{"className":27339,"style":940},[939],[15,27341,27343],{"className":27342},[944,945,946,947],[15,27344,27346,27349,27352],{"className":27345},[67,947],[15,27347,539],{"className":27348},[67,68,947],[15,27350,42],{"className":27351},[73,947],[15,27353,27355,27358],{"className":27354},[67,947],[15,27356,9469],{"className":27357,"style":2570},[67,68,947],[15,27359,27361],{"className":27360},[918],[15,27362,27364,27410],{"className":27363},[922,923],[15,27365,27367,27407],{"className":27366},[927],[15,27368,27370],{"className":27369,"style":18677},[931],[15,27371,27372,27375],{"style":27010},[15,27373],{"className":27374,"style":27014},[939],[15,27376,27378],{"className":27377},[944,18421,15089,947],[15,27379,27381],{"className":27380},[67,947],[15,27382,27384,27387],{"className":27383},[67,947],[15,27385,539],{"className":27386},[67,68,947],[15,27388,27390],{"className":27389},[918],[15,27391,27393],{"className":27392},[922],[15,27394,27396],{"className":27395},[927],[15,27397,27399],{"className":27398,"style":27039},[931],[15,27400,27401,27404],{"style":27042},[15,27402],{"className":27403,"style":18417},[939],[15,27405,26408],{"className":27406},[1648,947],[15,27408,955],{"className":27409},[954],[15,27411,27413],{"className":27412},[927],[15,27414,27416],{"className":27415,"style":27058},[931],[15,27417],{},[15,27419,955],{"className":27420},[954],[15,27422,27424],{"className":27423},[927],[15,27425,27427],{"className":27426,"style":27070},[931],[15,27428],{},[15,27430,13827],{"className":27431},[148],[15,27433,27435,27467],{"className":27434,"translate":19},[18],[15,27436,27438],{"className":27437},[23],[25,27439,27440],{"xmlns":27},[29,27441,27442,27464],{},[32,27443,27444],{},[863,27445,27446,27448],{},[35,27447,45],{},[32,27449,27450,27452,27454],{},[35,27451,539],{},[39,27453,42],{"separator":41},[863,27455,27456,27458],{},[35,27457,9469],{},[872,27459,27460,27462],{},[35,27461,539],{},[39,27463,26408],{},[47,27465,27466],{"encoding":49},"Y_{x, M_{x^*}}",[15,27468,27470],{"className":27469,"ariaHidden":41},[54],[15,27471,27473,27477],{"className":27472},[58],[15,27474],{"className":27475,"style":27476},[62],"height:0.9716em;vertical-align:-0.2883em;",[15,27478,27480,27483],{"className":27479},[67],[15,27481,45],{"className":27482,"style":82},[67,68],[15,27484,27486],{"className":27485},[918],[15,27487,27489,27581],{"className":27488},[922,923],[15,27490,27492,27578],{"className":27491},[927],[15,27493,27495],{"className":27494,"style":7358},[931],[15,27496,27497,27500],{"style":1499},[15,27498],{"className":27499,"style":940},[939],[15,27501,27503],{"className":27502},[944,945,946,947],[15,27504,27506,27509,27512],{"className":27505},[67,947],[15,27507,539],{"className":27508},[67,68,947],[15,27510,42],{"className":27511},[73,947],[15,27513,27515,27518],{"className":27514},[67,947],[15,27516,9469],{"className":27517,"style":2570},[67,68,947],[15,27519,27521],{"className":27520},[918],[15,27522,27524,27570],{"className":27523},[922,923],[15,27525,27527,27567],{"className":27526},[927],[15,27528,27530],{"className":27529,"style":18677},[931],[15,27531,27532,27535],{"style":27010},[15,27533],{"className":27534,"style":27014},[939],[15,27536,27538],{"className":27537},[944,18421,15089,947],[15,27539,27541],{"className":27540},[67,947],[15,27542,27544,27547],{"className":27543},[67,947],[15,27545,539],{"className":27546},[67,68,947],[15,27548,27550],{"className":27549},[918],[15,27551,27553],{"className":27552},[922],[15,27554,27556],{"className":27555},[927],[15,27557,27559],{"className":27558,"style":27039},[931],[15,27560,27561,27564],{"style":27042},[15,27562],{"className":27563,"style":18417},[939],[15,27565,26408],{"className":27566},[1648,947],[15,27568,955],{"className":27569},[954],[15,27571,27573],{"className":27572},[927],[15,27574,27576],{"className":27575,"style":27058},[931],[15,27577],{},[15,27579,955],{"className":27580},[954],[15,27582,27584],{"className":27583},[927],[15,27585,27587],{"className":27586,"style":27070},[931],[15,27588],{}," 表示「把 ",[15,27591,27593,27606],{"className":27592,"translate":19},[18],[15,27594,27596],{"className":27595},[23],[25,27597,27598],{"xmlns":27},[29,27599,27600,27604],{},[32,27601,27602],{},[35,27603,37],{},[47,27605,37],{"encoding":49},[15,27607,27609],{"className":27608,"ariaHidden":41},[54],[15,27610,27612,27615],{"className":27611},[58],[15,27613],{"className":27614,"style":299},[62],[15,27616,37],{"className":27617,"style":69},[67,68]," 设为 ",[15,27620,27622,27635],{"className":27621,"translate":19},[18],[15,27623,27625],{"className":27624},[23],[25,27626,27627],{"xmlns":27},[29,27628,27629,27633],{},[32,27630,27631],{},[35,27632,539],{},[47,27634,539],{"encoding":49},[15,27636,27638],{"className":27637,"ariaHidden":41},[54],[15,27639,27641,27644],{"className":27640},[58],[15,27642],{"className":27643,"style":635},[62],[15,27645,539],{"className":27646},[67,68],"，同时把 ",[15,27649,27651,27664],{"className":27650,"translate":19},[18],[15,27652,27654],{"className":27653},[23],[25,27655,27656],{"xmlns":27},[29,27657,27658,27662],{},[32,27659,27660],{},[35,27661,9469],{},[47,27663,9469],{"encoding":49},[15,27665,27667],{"className":27666,"ariaHidden":41},[54],[15,27668,27670,27673],{"className":27669},[58],[15,27671],{"className":27672,"style":299},[62],[15,27674,9469],{"className":27675,"style":2570},[67,68]," 设为",[305,27678,27679,27680,27708,27709,7183,27767,27795],{},"若 ",[15,27681,27683,27696],{"className":27682,"translate":19},[18],[15,27684,27686],{"className":27685},[23],[25,27687,27688],{"xmlns":27},[29,27689,27690,27694],{},[32,27691,27692],{},[35,27693,37],{},[47,27695,37],{"encoding":49},[15,27697,27699],{"className":27698,"ariaHidden":41},[54],[15,27700,27702,27705],{"className":27701},[58],[15,27703],{"className":27704,"style":299},[62],[15,27706,37],{"className":27707,"style":69},[67,68]," 取 ",[15,27710,27712,27729],{"className":27711,"translate":19},[18],[15,27713,27715],{"className":27714},[23],[25,27716,27717],{"xmlns":27},[29,27718,27719,27727],{},[32,27720,27721],{},[872,27722,27723,27725],{},[35,27724,539],{},[39,27726,26408],{},[47,27728,26643],{"encoding":49},[15,27730,27732],{"className":27731,"ariaHidden":41},[54],[15,27733,27735,27738],{"className":27734},[58],[15,27736],{"className":27737,"style":26653},[62],[15,27739,27741,27744],{"className":27740},[67],[15,27742,539],{"className":27743},[67,68],[15,27745,27747],{"className":27746},[918],[15,27748,27750],{"className":27749},[922],[15,27751,27753],{"className":27752},[927],[15,27754,27756],{"className":27755,"style":26653},[931],[15,27757,27758,27761],{"style":1002},[15,27759],{"className":27760,"style":940},[939],[15,27762,27764],{"className":27763},[944,945,946,947],[15,27765,26408],{"className":27766},[1648,947],[15,27768,27770,27783],{"className":27769,"translate":19},[18],[15,27771,27773],{"className":27772},[23],[25,27774,27775],{"xmlns":27},[29,27776,27777,27781],{},[32,27778,27779],{},[35,27780,9469],{},[47,27782,9469],{"encoding":49},[15,27784,27786],{"className":27785,"ariaHidden":41},[54],[15,27787,27789,27792],{"className":27788},[58],[15,27790],{"className":27791,"style":299},[62],[15,27793,9469],{"className":27794,"style":2570},[67,68]," 本会取的值","」这一反事实量。",[11,27798,27799,27800,26358,27803],{},"由定义立即可得",[305,27801,27802],{},"总效应的精确分解",[15,27804,27806,27844],{"className":27805,"translate":19},[18],[15,27807,27809],{"className":27808},[23],[25,27810,27811],{"xmlns":27},[29,27812,27813,27841],{},[32,27814,27815,27821,27823,27831,27833],{},[32,27816,27817,27819],{},[35,27818,26375],{"mathvariant":878},[35,27820,1348],{"mathvariant":878},[39,27822,602],{},[32,27824,27825,27827,27829],{},[35,27826,26736],{"mathvariant":878},[35,27828,26739],{"mathvariant":878},[35,27830,1348],{"mathvariant":878},[39,27832,2894],{},[32,27834,27835,27837,27839],{},[35,27836,26736],{"mathvariant":878},[35,27838,16674],{"mathvariant":878},[35,27840,1348],{"mathvariant":878},[47,27842,27843],{"encoding":49},"\\mathrm{TE} = \\mathrm{NDE} + \\mathrm{NIE}",[15,27845,27847,27868,27889],{"className":27846,"ariaHidden":41},[54],[15,27848,27850,27853,27859,27862,27865],{"className":27849},[58],[15,27851],{"className":27852,"style":299},[62],[15,27854,27856],{"className":27855},[67],[15,27857,26429],{"className":27858},[67,10382],[15,27860],{"className":27861,"style":199},[77],[15,27863,602],{"className":27864},[203],[15,27866],{"className":27867,"style":199},[77],[15,27869,27871,27874,27880,27883,27886],{"className":27870},[58],[15,27872],{"className":27873,"style":1638},[62],[15,27875,27877],{"className":27876},[67],[15,27878,26888],{"className":27879},[67,10382],[15,27881],{"className":27882,"style":82},[77],[15,27884,2894],{"className":27885},[1648],[15,27887],{"className":27888,"style":82},[77],[15,27890,27892,27895],{"className":27891},[58],[15,27893],{"className":27894,"style":299},[62],[15,27896,27898],{"className":27897},[67],[15,27899,27184],{"className":27900},[67,10382],[11,27902,27903,27904,28007,28008,28077],{},"其含义可以这样读：NDE 让中介停留在「另一个世界」的取值上，因此度量的正是直接通道；NIE 则度量中介由 ",[15,27905,27907,27929],{"className":27906,"translate":19},[18],[15,27908,27910],{"className":27909},[23],[25,27911,27912],{"xmlns":27},[29,27913,27914,27926],{},[32,27915,27916],{},[863,27917,27918,27920],{},[35,27919,9469],{},[872,27921,27922,27924],{},[35,27923,539],{},[39,27925,26408],{},[47,27927,27928],{"encoding":49},"M_{x^*}",[15,27930,27932],{"className":27931,"ariaHidden":41},[54],[15,27933,27935,27938],{"className":27934},[58],[15,27936],{"className":27937,"style":1865},[62],[15,27939,27941,27944],{"className":27940},[67],[15,27942,9469],{"className":27943,"style":2570},[67,68],[15,27945,27947],{"className":27946},[918],[15,27948,27950,27999],{"className":27949},[922,923],[15,27951,27953,27996],{"className":27952},[927],[15,27954,27956],{"className":27955,"style":26537},[931],[15,27957,27958,27961],{"style":2585},[15,27959],{"className":27960,"style":940},[939],[15,27962,27964],{"className":27963},[944,945,946,947],[15,27965,27967],{"className":27966},[67,947],[15,27968,27970,27973],{"className":27969},[67,947],[15,27971,539],{"className":27972},[67,68,947],[15,27974,27976],{"className":27975},[918],[15,27977,27979],{"className":27978},[922],[15,27980,27982],{"className":27981},[927],[15,27983,27985],{"className":27984,"style":26567},[931],[15,27986,27987,27990],{"style":26570},[15,27988],{"className":27989,"style":18417},[939],[15,27991,27993],{"className":27992},[944,18421,15089,947],[15,27994,26408],{"className":27995},[1648,947],[15,27997,955],{"className":27998},[954],[15,28000,28002],{"className":28001},[927],[15,28003,28005],{"className":28004,"style":962},[931],[15,28006],{}," 变为 ",[15,28009,28011,28028],{"className":28010,"translate":19},[18],[15,28012,28014],{"className":28013},[23],[25,28015,28016],{"xmlns":27},[29,28017,28018,28026],{},[32,28019,28020],{},[863,28021,28022,28024],{},[35,28023,9469],{},[35,28025,539],{},[47,28027,18193],{"encoding":49},[15,28029,28031],{"className":28030,"ariaHidden":41},[54],[15,28032,28034,28037],{"className":28033},[58],[15,28035],{"className":28036,"style":1865},[62],[15,28038,28040,28043],{"className":28039},[67],[15,28041,9469],{"className":28042,"style":2570},[67,68],[15,28044,28046],{"className":28045},[918],[15,28047,28049,28069],{"className":28048},[922,923],[15,28050,28052,28066],{"className":28051},[927],[15,28053,28055],{"className":28054,"style":932},[931],[15,28056,28057,28060],{"style":2585},[15,28058],{"className":28059,"style":940},[939],[15,28061,28063],{"className":28062},[944,945,946,947],[15,28064,539],{"className":28065},[67,68,947],[15,28067,955],{"className":28068},[954],[15,28070,28072],{"className":28071},[927],[15,28073,28075],{"className":28074,"style":962},[931],[15,28076],{}," 所贡献的间接部分。",[11,28079,28080,28081,28239,28240,28268,28269,431,28319,28400],{},"需要特别注意，",[305,28082,28083,28238],{},[15,28084,28086,28117],{"className":28085,"translate":19},[18],[15,28087,28089],{"className":28088},[23],[25,28090,28091],{"xmlns":27},[29,28092,28093,28115],{},[32,28094,28095],{},[863,28096,28097,28099],{},[35,28098,45],{},[32,28100,28101,28103,28105],{},[35,28102,539],{},[39,28104,42],{"separator":41},[863,28106,28107,28109],{},[35,28108,9469],{},[872,28110,28111,28113],{},[35,28112,539],{},[39,28114,26408],{},[47,28116,27466],{"encoding":49},[15,28118,28120],{"className":28119,"ariaHidden":41},[54],[15,28121,28123,28126],{"className":28122},[58],[15,28124],{"className":28125,"style":27476},[62],[15,28127,28129,28132],{"className":28128},[67],[15,28130,45],{"className":28131,"style":82},[67,68],[15,28133,28135],{"className":28134},[918],[15,28136,28138,28230],{"className":28137},[922,923],[15,28139,28141,28227],{"className":28140},[927],[15,28142,28144],{"className":28143,"style":7358},[931],[15,28145,28146,28149],{"style":1499},[15,28147],{"className":28148,"style":940},[939],[15,28150,28152],{"className":28151},[944,945,946,947],[15,28153,28155,28158,28161],{"className":28154},[67,947],[15,28156,539],{"className":28157},[67,68,947],[15,28159,42],{"className":28160},[73,947],[15,28162,28164,28167],{"className":28163},[67,947],[15,28165,9469],{"className":28166,"style":2570},[67,68,947],[15,28168,28170],{"className":28169},[918],[15,28171,28173,28219],{"className":28172},[922,923],[15,28174,28176,28216],{"className":28175},[927],[15,28177,28179],{"className":28178,"style":18677},[931],[15,28180,28181,28184],{"style":27010},[15,28182],{"className":28183,"style":27014},[939],[15,28185,28187],{"className":28186},[944,18421,15089,947],[15,28188,28190],{"className":28189},[67,947],[15,28191,28193,28196],{"className":28192},[67,947],[15,28194,539],{"className":28195},[67,68,947],[15,28197,28199],{"className":28198},[918],[15,28200,28202],{"className":28201},[922],[15,28203,28205],{"className":28204},[927],[15,28206,28208],{"className":28207,"style":27039},[931],[15,28209,28210,28213],{"style":27042},[15,28211],{"className":28212,"style":18417},[939],[15,28214,26408],{"className":28215},[1648,947],[15,28217,955],{"className":28218},[954],[15,28220,28222],{"className":28221},[927],[15,28223,28225],{"className":28224,"style":27058},[931],[15,28226],{},[15,28228,955],{"className":28229},[954],[15,28231,28233],{"className":28232},[927],[15,28234,28236],{"className":28235,"style":27070},[931],[15,28237],{}," 是一个跨世界（cross-world）量","：它在同一个个体 ",[15,28241,28243,28256],{"className":28242,"translate":19},[18],[15,28244,28246],{"className":28245},[23],[25,28247,28248],{"xmlns":27},[29,28249,28250,28254],{},[32,28251,28252],{},[35,28253,13778],{},[47,28255,13778],{"encoding":49},[15,28257,28259],{"className":28258,"ariaHidden":41},[54],[15,28260,28262,28265],{"className":28261},[58],[15,28263],{"className":28264,"style":635},[62],[15,28266,13778],{"className":28267},[67,68]," 上同时引用了 ",[15,28270,28272,28289],{"className":28271,"translate":19},[18],[15,28273,28275],{"className":28274},[23],[25,28276,28277],{"xmlns":27},[29,28278,28279,28287],{},[32,28280,28281,28283,28285],{},[35,28282,37],{},[39,28284,602],{},[35,28286,539],{},[47,28288,607],{"encoding":49},[15,28290,28292,28310],{"className":28291,"ariaHidden":41},[54],[15,28293,28295,28298,28301,28304,28307],{"className":28294},[58],[15,28296],{"className":28297,"style":299},[62],[15,28299,37],{"className":28300,"style":69},[67,68],[15,28302],{"className":28303,"style":199},[77],[15,28305,602],{"className":28306},[203],[15,28308],{"className":28309,"style":199},[77],[15,28311,28313,28316],{"className":28312},[58],[15,28314],{"className":28315,"style":635},[62],[15,28317,539],{"className":28318},[67,68],[15,28320,28322,28344],{"className":28321,"translate":19},[18],[15,28323,28325],{"className":28324},[23],[25,28326,28327],{"xmlns":27},[29,28328,28329,28341],{},[32,28330,28331,28333,28335],{},[35,28332,37],{},[39,28334,602],{},[872,28336,28337,28339],{},[35,28338,539],{},[39,28340,26408],{},[47,28342,28343],{"encoding":49},"X=x^*",[15,28345,28347,28365],{"className":28346,"ariaHidden":41},[54],[15,28348,28350,28353,28356,28359,28362],{"className":28349},[58],[15,28351],{"className":28352,"style":299},[62],[15,28354,37],{"className":28355,"style":69},[67,68],[15,28357],{"className":28358,"style":199},[77],[15,28360,602],{"className":28361},[203],[15,28363],{"className":28364,"style":199},[77],[15,28366,28368,28371],{"className":28367},[58],[15,28369],{"className":28370,"style":26653},[62],[15,28372,28374,28377],{"className":28373},[67],[15,28375,539],{"className":28376},[67,68],[15,28378,28380],{"className":28379},[918],[15,28381,28383],{"className":28382},[922],[15,28384,28386],{"className":28385},[927],[15,28387,28389],{"className":28388,"style":26653},[931],[15,28390,28391,28394],{"style":1002},[15,28392],{"className":28393,"style":940},[939],[15,28395,28397],{"className":28396},[944,945,946,947],[15,28398,26408],{"className":28399},[1648,947]," 这两个互不相容的世界。因此中介分析在本质上属于第三层而非第二层——这也解释了为什么中介效应长期以来被认为是不可识别的。",[11,28402,28403,28406],{},[305,28404,28405],{},"可识别性条件（序贯可忽略性）","：要使 NDE 与 NIE 可由观测数据估计，需要同时满足",[7923,28408,28409,28496,28583,28669],{},[510,28410,28411,431,28439,28467,28468,6830],{},[15,28412,28414,28427],{"className":28413,"translate":19},[18],[15,28415,28417],{"className":28416},[23],[25,28418,28419],{"xmlns":27},[29,28420,28421,28425],{},[32,28422,28423],{},[35,28424,37],{},[47,28426,37],{"encoding":49},[15,28428,28430],{"className":28429,"ariaHidden":41},[54],[15,28431,28433,28436],{"className":28432},[58],[15,28434],{"className":28435,"style":299},[62],[15,28437,37],{"className":28438,"style":69},[67,68],[15,28440,28442,28455],{"className":28441,"translate":19},[18],[15,28443,28445],{"className":28444},[23],[25,28446,28447],{"xmlns":27},[29,28448,28449,28453],{},[32,28450,28451],{},[35,28452,45],{},[47,28454,45],{"encoding":49},[15,28456,28458],{"className":28457,"ariaHidden":41},[54],[15,28459,28461,28464],{"className":28460},[58],[15,28462],{"className":28463,"style":299},[62],[15,28465,45],{"className":28466,"style":82},[67,68]," 之间无未观测混杂（给定协变量 ",[15,28469,28471,28484],{"className":28470,"translate":19},[18],[15,28472,28474],{"className":28473},[23],[25,28475,28476],{"xmlns":27},[29,28477,28478,28482],{},[32,28479,28480],{},[35,28481,3795],{},[47,28483,3795],{"encoding":49},[15,28485,28487],{"className":28486,"ariaHidden":41},[54],[15,28488,28490,28493],{"className":28489},[58],[15,28491],{"className":28492,"style":299},[62],[15,28494,3795],{"className":28495,"style":128},[67,68],[510,28497,28498,431,28526,28554,28555,6830],{},[15,28499,28501,28514],{"className":28500,"translate":19},[18],[15,28502,28504],{"className":28503},[23],[25,28505,28506],{"xmlns":27},[29,28507,28508,28512],{},[32,28509,28510],{},[35,28511,9469],{},[47,28513,9469],{"encoding":49},[15,28515,28517],{"className":28516,"ariaHidden":41},[54],[15,28518,28520,28523],{"className":28519},[58],[15,28521],{"className":28522,"style":299},[62],[15,28524,9469],{"className":28525,"style":2570},[67,68],[15,28527,28529,28542],{"className":28528,"translate":19},[18],[15,28530,28532],{"className":28531},[23],[25,28533,28534],{"xmlns":27},[29,28535,28536,28540],{},[32,28537,28538],{},[35,28539,45],{},[47,28541,45],{"encoding":49},[15,28543,28545],{"className":28544,"ariaHidden":41},[54],[15,28546,28548,28551],{"className":28547},[58],[15,28549],{"className":28550,"style":299},[62],[15,28552,45],{"className":28553,"style":82},[67,68]," 之间无未观测混杂（给定 ",[15,28556,28558,28571],{"className":28557,"translate":19},[18],[15,28559,28561],{"className":28560},[23],[25,28562,28563],{"xmlns":27},[29,28564,28565,28569],{},[32,28566,28567],{},[35,28568,3795],{},[47,28570,3795],{"encoding":49},[15,28572,28574],{"className":28573,"ariaHidden":41},[54],[15,28575,28577,28580],{"className":28576},[58],[15,28578],{"className":28579,"style":299},[62],[15,28581,3795],{"className":28582,"style":128},[67,68],[510,28584,28585,431,28613,28554,28641,6830],{},[15,28586,28588,28601],{"className":28587,"translate":19},[18],[15,28589,28591],{"className":28590},[23],[25,28592,28593],{"xmlns":27},[29,28594,28595,28599],{},[32,28596,28597],{},[35,28598,37],{},[47,28600,37],{"encoding":49},[15,28602,28604],{"className":28603,"ariaHidden":41},[54],[15,28605,28607,28610],{"className":28606},[58],[15,28608],{"className":28609,"style":299},[62],[15,28611,37],{"className":28612,"style":69},[67,68],[15,28614,28616,28629],{"className":28615,"translate":19},[18],[15,28617,28619],{"className":28618},[23],[25,28620,28621],{"xmlns":27},[29,28622,28623,28627],{},[32,28624,28625],{},[35,28626,9469],{},[47,28628,9469],{"encoding":49},[15,28630,28632],{"className":28631,"ariaHidden":41},[54],[15,28633,28635,28638],{"className":28634},[58],[15,28636],{"className":28637,"style":299},[62],[15,28639,9469],{"className":28640,"style":2570},[67,68],[15,28642,28644,28657],{"className":28643,"translate":19},[18],[15,28645,28647],{"className":28646},[23],[25,28648,28649],{"xmlns":27},[29,28650,28651,28655],{},[32,28652,28653],{},[35,28654,3795],{},[47,28656,3795],{"encoding":49},[15,28658,28660],{"className":28659,"ariaHidden":41},[54],[15,28661,28663,28666],{"className":28662},[58],[15,28664],{"className":28665,"style":299},[62],[15,28667,3795],{"className":28668,"style":128},[67,68],[510,28670,28671,431,28699,28727,28728,28756],{},[15,28672,28674,28687],{"className":28673,"translate":19},[18],[15,28675,28677],{"className":28676},[23],[25,28678,28679],{"xmlns":27},[29,28680,28681,28685],{},[32,28682,28683],{},[35,28684,9469],{},[47,28686,9469],{"encoding":49},[15,28688,28690],{"className":28689,"ariaHidden":41},[54],[15,28691,28693,28696],{"className":28692},[58],[15,28694],{"className":28695,"style":299},[62],[15,28697,9469],{"className":28698,"style":2570},[67,68],[15,28700,28702,28715],{"className":28701,"translate":19},[18],[15,28703,28705],{"className":28704},[23],[25,28706,28707],{"xmlns":27},[29,28708,28709,28713],{},[32,28710,28711],{},[35,28712,45],{},[47,28714,45],{"encoding":49},[15,28716,28718],{"className":28717,"ariaHidden":41},[54],[15,28719,28721,28724],{"className":28720},[58],[15,28722],{"className":28723,"style":299},[62],[15,28725,45],{"className":28726,"style":82},[67,68]," 之间不存在受 ",[15,28729,28731,28744],{"className":28730,"translate":19},[18],[15,28732,28734],{"className":28733},[23],[25,28735,28736],{"xmlns":27},[29,28737,28738,28742],{},[32,28739,28740],{},[35,28741,37],{},[47,28743,37],{"encoding":49},[15,28745,28747],{"className":28746,"ariaHidden":41},[54],[15,28748,28750,28753],{"className":28749},[58],[15,28751],{"className":28752,"style":299},[62],[15,28754,37],{"className":28755,"style":69},[67,68]," 影响的混杂因子。",[11,28758,28759,28760,28763,28764,29192,29193,29291],{},"其中第 4 条最容易被忽略，也最强：它要求中介与结果之间不能存在被处理变量触及的共同原因。四条合称",[305,28761,28762],{},"序贯可忽略性（sequential ignorability）","。在此条件下，自然直接效应可由观测分布表达为\n",[15,28765,28767,28881],{"className":28766,"translate":19},[18],[15,28768,28770],{"className":28769},[23],[25,28771,28772],{"xmlns":27},[29,28773,28774,28878],{},[32,28775,28776,28784,28786,28799,28802,28804,28806,28808,28810,28812,28814,28816,28818,28820,28822,28824,28826,28828,28830,28832,28838,28840,28842,28844,28846,28848,28850,28852,28854,28856,28858,28864,28866,28868,28870,28872,28874,28876],{},[32,28777,28778,28780,28782],{},[35,28779,26736],{"mathvariant":878},[35,28781,26739],{"mathvariant":878},[35,28783,1348],{"mathvariant":878},[39,28785,602],{},[863,28787,28788,28790],{},[39,28789,20423],{},[32,28791,28792,28794,28796],{},[35,28793,9611],{},[39,28795,42],{"separator":41},[35,28797,28798],{},"w",[39,28800,13818],{"fence":101,"stretchy":41,"minsize":28801,"maxsize":28801},"1.8em",[35,28803,1348],{"mathvariant":13815},[39,28805,13818],{"stretchy":101},[35,28807,45],{},[39,28809,170],{},[35,28811,539],{},[39,28813,42],{"separator":41},[35,28815,9611],{},[39,28817,42],{"separator":41},[35,28819,28798],{},[39,28821,13827],{"stretchy":101},[39,28823,14235],{},[35,28825,1348],{"mathvariant":13815},[39,28827,13818],{"stretchy":101},[35,28829,45],{},[39,28831,170],{},[872,28833,28834,28836],{},[35,28835,539],{},[39,28837,26408],{},[39,28839,42],{"separator":41},[35,28841,9611],{},[39,28843,42],{"separator":41},[35,28845,28798],{},[39,28847,13827],{"stretchy":101},[39,28849,13827],{"fence":101,"stretchy":41,"minsize":28801,"maxsize":28801},[35,28851,98],{},[39,28853,102],{"stretchy":101},[35,28855,9611],{},[39,28857,170],{},[872,28859,28860,28862],{},[35,28861,539],{},[39,28863,26408],{},[39,28865,42],{"separator":41},[35,28867,28798],{},[39,28869,111],{"stretchy":101},[35,28871,98],{},[39,28873,102],{"stretchy":101},[35,28875,28798],{},[39,28877,111],{"stretchy":101},[47,28879,28880],{"encoding":49},"\\mathrm{NDE} = \\sum_{m, w}\\Big[\\mathbb{E}[Y \\mid x, m, w] - \\mathbb{E}[Y \\mid x^*, m, w]\\Big] P(m \\mid x^*, w) P(w)",[15,28882,28884,28905,28990,29029,29053,29133],{"className":28883,"ariaHidden":41},[54],[15,28885,28887,28890,28896,28899,28902],{"className":28886},[58],[15,28888],{"className":28889,"style":299},[62],[15,28891,28893],{"className":28892},[67],[15,28894,26888],{"className":28895},[67,10382],[15,28897],{"className":28898,"style":199},[77],[15,28900,602],{"className":28901},[203],[15,28903],{"className":28904,"style":199},[77],[15,28906,28908,28912,28962,28965,28972,28975,28978,28981,28984,28987],{"className":28907},[58],[15,28909],{"className":28910,"style":28911},[62],"height:1.8em;vertical-align:-0.65em;",[15,28913,28915,28918],{"className":28914},[12772],[15,28916,20423],{"className":28917,"style":12778},[12772,12776,12777],[15,28919,28921],{"className":28920},[918],[15,28922,28924,28954],{"className":28923},[922,923],[15,28925,28927,28951],{"className":28926},[927],[15,28928,28930],{"className":28929,"style":20620},[931],[15,28931,28932,28935],{"style":12794},[15,28933],{"className":28934,"style":940},[939],[15,28936,28938],{"className":28937},[944,945,946,947],[15,28939,28941,28944,28947],{"className":28940},[67,947],[15,28942,9611],{"className":28943},[67,68,947],[15,28945,42],{"className":28946},[73,947],[15,28948,28798],{"className":28949,"style":28950},[67,68,947],"margin-right:0.0269em;",[15,28952,955],{"className":28953},[954],[15,28955,28957],{"className":28956},[927],[15,28958,28960],{"className":28959,"style":19276},[931],[15,28961],{},[15,28963],{"className":28964,"style":78},[77],[15,28966,28968],{"className":28967},[67],[15,28969,13818],{"className":28970},[15088,28971],"size2",[15,28973,1348],{"className":28974},[67,26448],[15,28976,13818],{"className":28977},[132],[15,28979,45],{"className":28980,"style":82},[67,68],[15,28982],{"className":28983,"style":199},[77],[15,28985,170],{"className":28986},[203],[15,28988],{"className":28989,"style":199},[77],[15,28991,28993,28996,28999,29002,29005,29008,29011,29014,29017,29020,29023,29026],{"className":28992},[58],[15,28994],{"className":28995,"style":124},[62],[15,28997,539],{"className":28998},[67,68],[15,29000,42],{"className":29001},[73],[15,29003],{"className":29004,"style":78},[77],[15,29006,9611],{"className":29007},[67,68],[15,29009,42],{"className":29010},[73],[15,29012],{"className":29013,"style":78},[77],[15,29015,28798],{"className":29016,"style":28950},[67,68],[15,29018,13827],{"className":29019},[148],[15,29021],{"className":29022,"style":82},[77],[15,29024,14235],{"className":29025},[1648],[15,29027],{"className":29028,"style":82},[77],[15,29030,29032,29035,29038,29041,29044,29047,29050],{"className":29031},[58],[15,29033],{"className":29034,"style":124},[62],[15,29036,1348],{"className":29037},[67,26448],[15,29039,13818],{"className":29040},[132],[15,29042,45],{"className":29043,"style":82},[67,68],[15,29045],{"className":29046,"style":199},[77],[15,29048,170],{"className":29049},[203],[15,29051],{"className":29052,"style":199},[77],[15,29054,29056,29059,29088,29091,29094,29097,29100,29103,29106,29109,29115,29118,29121,29124,29127,29130],{"className":29055},[58],[15,29057],{"className":29058,"style":28911},[62],[15,29060,29062,29065],{"className":29061},[67],[15,29063,539],{"className":29064},[67,68],[15,29066,29068],{"className":29067},[918],[15,29069,29071],{"className":29070},[922],[15,29072,29074],{"className":29073},[927],[15,29075,29077],{"className":29076,"style":26653},[931],[15,29078,29079,29082],{"style":1002},[15,29080],{"className":29081,"style":940},[939],[15,29083,29085],{"className":29084},[944,945,946,947],[15,29086,26408],{"className":29087},[1648,947],[15,29089,42],{"className":29090},[73],[15,29092],{"className":29093,"style":78},[77],[15,29095,9611],{"className":29096},[67,68],[15,29098,42],{"className":29099},[73],[15,29101],{"className":29102,"style":78},[77],[15,29104,28798],{"className":29105,"style":28950},[67,68],[15,29107,13827],{"className":29108},[148],[15,29110,29112],{"className":29111},[67],[15,29113,13827],{"className":29114},[15088,28971],[15,29116,98],{"className":29117,"style":128},[67,68],[15,29119,102],{"className":29120},[132],[15,29122,9611],{"className":29123},[67,68],[15,29125],{"className":29126,"style":199},[77],[15,29128,170],{"className":29129},[203],[15,29131],{"className":29132,"style":199},[77],[15,29134,29136,29139,29168,29171,29174,29177,29180,29183,29186,29189],{"className":29135},[58],[15,29137],{"className":29138,"style":124},[62],[15,29140,29142,29145],{"className":29141},[67],[15,29143,539],{"className":29144},[67,68],[15,29146,29148],{"className":29147},[918],[15,29149,29151],{"className":29150},[922],[15,29152,29154],{"className":29153},[927],[15,29155,29157],{"className":29156,"style":26653},[931],[15,29158,29159,29162],{"style":1002},[15,29160],{"className":29161,"style":940},[939],[15,29163,29165],{"className":29164},[944,945,946,947],[15,29166,26408],{"className":29167},[1648,947],[15,29169,42],{"className":29170},[73],[15,29172],{"className":29173,"style":78},[77],[15,29175,28798],{"className":29176,"style":28950},[67,68],[15,29178,111],{"className":29179},[148],[15,29181,98],{"className":29182,"style":128},[67,68],[15,29184,102],{"className":29185},[132],[15,29187,28798],{"className":29188,"style":28950},[67,68],[15,29190,111],{"className":29191},[148],"\n自然间接效应则相应地由 ",[15,29194,29196,29234],{"className":29195,"translate":19},[18],[15,29197,29199],{"className":29198},[23],[25,29200,29201],{"xmlns":27},[29,29202,29203,29231],{},[32,29204,29205,29213,29215,29221,29223],{},[32,29206,29207,29209,29211],{},[35,29208,26736],{"mathvariant":878},[35,29210,16674],{"mathvariant":878},[35,29212,1348],{"mathvariant":878},[39,29214,602],{},[32,29216,29217,29219],{},[35,29218,26375],{"mathvariant":878},[35,29220,1348],{"mathvariant":878},[39,29222,14235],{},[32,29224,29225,29227,29229],{},[35,29226,26736],{"mathvariant":878},[35,29228,26739],{"mathvariant":878},[35,29230,1348],{"mathvariant":878},[47,29232,29233],{"encoding":49},"\\mathrm{NIE} = \\mathrm{TE} - \\mathrm{NDE}",[15,29235,29237,29258,29279],{"className":29236,"ariaHidden":41},[54],[15,29238,29240,29243,29249,29252,29255],{"className":29239},[58],[15,29241],{"className":29242,"style":299},[62],[15,29244,29246],{"className":29245},[67],[15,29247,27184],{"className":29248},[67,10382],[15,29250],{"className":29251,"style":199},[77],[15,29253,602],{"className":29254},[203],[15,29256],{"className":29257,"style":199},[77],[15,29259,29261,29264,29270,29273,29276],{"className":29260},[58],[15,29262],{"className":29263,"style":1638},[62],[15,29265,29267],{"className":29266},[67],[15,29268,26429],{"className":29269},[67,10382],[15,29271],{"className":29272,"style":82},[77],[15,29274,14235],{"className":29275},[1648],[15,29277],{"className":29278,"style":82},[77],[15,29280,29282,29285],{"className":29281},[58],[15,29283],{"className":29284,"style":299},[62],[15,29286,29288],{"className":29287},[67],[15,29289,26888],{"className":29290},[67,10382]," 给出。",[11,29293,29294,29297,29298,29371,29372,29400,29401,29429,29430,29433,29434,29437,29438,29466,29467,29495,29496,29524,29525,29597,29598,29626,29627,29678,29679,29707],{},[305,29295,29296],{},"回到例 1.2 的告诫","：实践中极易发生的一种错误，是把中介当作普通协变量放进回归模型 ",[15,29299,29301,29323],{"className":29300,"translate":19},[18],[15,29302,29304],{"className":29303},[23],[25,29305,29306],{"xmlns":27},[29,29307,29308,29320],{},[32,29309,29310,29312,29314,29316,29318],{},[35,29311,45],{},[39,29313,13760],{},[35,29315,37],{},[39,29317,2894],{},[35,29319,9469],{},[47,29321,29322],{"encoding":49},"Y \\sim X + M",[15,29324,29326,29344,29362],{"className":29325,"ariaHidden":41},[54],[15,29327,29329,29332,29335,29338,29341],{"className":29328},[58],[15,29330],{"className":29331,"style":299},[62],[15,29333,45],{"className":29334,"style":82},[67,68],[15,29336],{"className":29337,"style":199},[77],[15,29339,13760],{"className":29340},[203],[15,29342],{"className":29343,"style":199},[77],[15,29345,29347,29350,29353,29356,29359],{"className":29346},[58],[15,29348],{"className":29349,"style":1638},[62],[15,29351,37],{"className":29352,"style":69},[67,68],[15,29354],{"className":29355,"style":82},[77],[15,29357,2894],{"className":29358},[1648],[15,29360],{"className":29361,"style":82},[77],[15,29363,29365,29368],{"className":29364},[58],[15,29366],{"className":29367,"style":299},[62],[15,29369,9469],{"className":29370,"style":2570},[67,68],"，再把 ",[15,29373,29375,29388],{"className":29374,"translate":19},[18],[15,29376,29378],{"className":29377},[23],[25,29379,29380],{"xmlns":27},[29,29381,29382,29386],{},[32,29383,29384],{},[35,29385,37],{},[47,29387,37],{"encoding":49},[15,29389,29391],{"className":29390,"ariaHidden":41},[54],[15,29392,29394,29397],{"className":29393},[58],[15,29395],{"className":29396,"style":299},[62],[15,29398,37],{"className":29399,"style":69},[67,68]," 的系数解释为「",[15,29402,29404,29417],{"className":29403,"translate":19},[18],[15,29405,29407],{"className":29406},[23],[25,29408,29409],{"xmlns":27},[29,29410,29411,29415],{},[32,29412,29413],{},[35,29414,37],{},[47,29416,37],{"encoding":49},[15,29418,29420],{"className":29419,"ariaHidden":41},[54],[15,29421,29423,29426],{"className":29422},[58],[15,29424],{"className":29425,"style":299},[62],[15,29427,37],{"className":29428,"style":69},[67,68]," 的效应」。由上述分解立即可见，这样做得到的其实只是",[305,29431,29432],{},"直接效应"," NDE，它系统性地",[305,29435,29436],{},"遗漏","了经由 ",[15,29439,29441,29454],{"className":29440,"translate":19},[18],[15,29442,29444],{"className":29443},[23],[25,29445,29446],{"xmlns":27},[29,29447,29448,29452],{},[32,29449,29450],{},[35,29451,9469],{},[47,29453,9469],{"encoding":49},[15,29455,29457],{"className":29456,"ariaHidden":41},[54],[15,29458,29460,29463],{"className":29459},[58],[15,29461],{"className":29462,"style":299},[62],[15,29464,9469],{"className":29465,"style":2570},[67,68]," 传递的间接部分，因而会低估 ",[15,29468,29470,29483],{"className":29469,"translate":19},[18],[15,29471,29473],{"className":29472},[23],[25,29474,29475],{"xmlns":27},[29,29476,29477,29481],{},[32,29478,29479],{},[35,29480,37],{},[47,29482,37],{"encoding":49},[15,29484,29486],{"className":29485,"ariaHidden":41},[54],[15,29487,29489,29492],{"className":29488},[58],[15,29490],{"className":29491,"style":299},[62],[15,29493,37],{"className":29494,"style":69},[67,68]," 的总效应。而当「控制 ",[15,29497,29499,29512],{"className":29498,"translate":19},[18],[15,29500,29502],{"className":29501},[23],[25,29503,29504],{"xmlns":27},[29,29505,29506,29510],{},[32,29507,29508],{},[35,29509,9469],{},[47,29511,9469],{"encoding":49},[15,29513,29515],{"className":29514,"ariaHidden":41},[54],[15,29516,29518,29521],{"className":29517},[58],[15,29519],{"className":29520,"style":299},[62],[15,29522,9469],{"className":29523,"style":2570},[67,68],"」的动机恰恰是「我想排除混杂」时，这一操作等于是把待估计的那条因果通道本身切断了——这是链结构在实践中最重要的一个陷阱。即便只想得到 NDE，也仍然需要上述四条假设；只有在线性且无交互的特殊情形下，",[15,29526,29528,29549],{"className":29527,"translate":19},[18],[15,29529,29531],{"className":29530},[23],[25,29532,29533],{"xmlns":27},[29,29534,29535,29547],{},[32,29536,29537,29539,29541,29543,29545],{},[35,29538,45],{},[39,29540,13760],{},[35,29542,37],{},[39,29544,2894],{},[35,29546,9469],{},[47,29548,29322],{"encoding":49},[15,29550,29552,29570,29588],{"className":29551,"ariaHidden":41},[54],[15,29553,29555,29558,29561,29564,29567],{"className":29554},[58],[15,29556],{"className":29557,"style":299},[62],[15,29559,45],{"className":29560,"style":82},[67,68],[15,29562],{"className":29563,"style":199},[77],[15,29565,13760],{"className":29566},[203],[15,29568],{"className":29569,"style":199},[77],[15,29571,29573,29576,29579,29582,29585],{"className":29572},[58],[15,29574],{"className":29575,"style":1638},[62],[15,29577,37],{"className":29578,"style":69},[67,68],[15,29580],{"className":29581,"style":82},[77],[15,29583,2894],{"className":29584},[1648],[15,29586],{"className":29587,"style":82},[77],[15,29589,29591,29594],{"className":29590},[58],[15,29592],{"className":29593,"style":299},[62],[15,29595,9469],{"className":29596,"style":2570},[67,68]," 中 ",[15,29599,29601,29614],{"className":29600,"translate":19},[18],[15,29602,29604],{"className":29603},[23],[25,29605,29606],{"xmlns":27},[29,29607,29608,29612],{},[32,29609,29610],{},[35,29611,37],{},[47,29613,37],{"encoding":49},[15,29615,29617],{"className":29616,"ariaHidden":41},[54],[15,29618,29620,29623],{"className":29619},[58],[15,29621],{"className":29622,"style":299},[62],[15,29624,37],{"className":29625,"style":69},[67,68]," 的系数才恰好等于 NDE，一旦存在 ",[15,29628,29630,29648],{"className":29629,"translate":19},[18],[15,29631,29633],{"className":29632},[23],[25,29634,29635],{"xmlns":27},[29,29636,29637,29645],{},[32,29638,29639,29641,29643],{},[35,29640,37],{},[39,29642,1604],{},[35,29644,9469],{},[47,29646,29647],{"encoding":49},"X \\times M",[15,29649,29651,29669],{"className":29650,"ariaHidden":41},[54],[15,29652,29654,29657,29660,29663,29666],{"className":29653},[58],[15,29655],{"className":29656,"style":1638},[62],[15,29658,37],{"className":29659,"style":69},[67,68],[15,29661],{"className":29662,"style":82},[77],[15,29664,1604],{"className":29665},[1648],[15,29667],{"className":29668,"style":82},[77],[15,29670,29672,29675],{"className":29671},[58],[15,29673],{"className":29674,"style":299},[62],[15,29676,9469],{"className":29677,"style":2570},[67,68]," 交互或 ",[15,29680,29682,29695],{"className":29681,"translate":19},[18],[15,29683,29685],{"className":29684},[23],[25,29686,29687],{"xmlns":27},[29,29688,29689,29693],{},[32,29690,29691],{},[35,29692,9469],{},[47,29694,9469],{"encoding":49},[15,29696,29698],{"className":29697,"ariaHidden":41},[54],[15,29699,29701,29704],{"className":29700},[58],[15,29702],{"className":29703,"style":299},[62],[15,29705,9469],{"className":29706,"style":2570},[67,68]," 进入非线性的函数形式，该系数便失去直接效应的解释。",[1309,29709,29711],{"id":29710},"_35-可识别性do-演算后门准则与前门准则","3.5 可识别性：do-演算、后门准则与前门准则",[11,29713,29714,29715,29797,29798,2249],{},"在实践中，我们通常只有观测数据（第一层），希望知道某个干预量 ",[15,29716,29718,29749],{"className":29717,"translate":19},[18],[15,29719,29721],{"className":29720},[23],[25,29722,29723],{"xmlns":27},[29,29724,29725,29747],{},[32,29726,29727,29729,29731,29733,29735,29737,29739,29741,29743,29745],{},[35,29728,98],{},[39,29730,102],{"stretchy":101},[35,29732,534],{},[39,29734,170],{},[35,29736,696],{},[35,29738,699],{},[39,29740,102],{"stretchy":101},[35,29742,539],{},[39,29744,111],{"stretchy":101},[39,29746,111],{"stretchy":101},[47,29748,710],{"encoding":49},[15,29750,29752,29776],{"className":29751,"ariaHidden":41},[54],[15,29753,29755,29758,29761,29764,29767,29770,29773],{"className":29754},[58],[15,29756],{"className":29757,"style":124},[62],[15,29759,98],{"className":29760,"style":128},[67,68],[15,29762,102],{"className":29763},[132],[15,29765,534],{"className":29766,"style":563},[67,68],[15,29768],{"className":29769,"style":199},[77],[15,29771,170],{"className":29772},[203],[15,29774],{"className":29775,"style":199},[77],[15,29777,29779,29782,29785,29788,29791,29794],{"className":29778},[58],[15,29780],{"className":29781,"style":124},[62],[15,29783,696],{"className":29784},[67,68],[15,29786,699],{"className":29787},[67,68],[15,29789,102],{"className":29790},[132],[15,29792,539],{"className":29793},[67,68],[15,29795,759],{"className":29796},[148],"（第二层）能否用观测分布中的量表达出来，这一问题称为**可识别性（identifiability）**问题。Pearl 给出了一套完全在图的层面运作的工具：它只需要因果图本身，",[305,29799,29800,29801],{},"不需要知道任何结构方程的具体函数形式 ",[15,29802,29804,29821],{"className":29803,"translate":19},[18],[15,29805,29807],{"className":29806},[23],[25,29808,29809],{"xmlns":27},[29,29810,29811,29819],{},[32,29812,29813],{},[863,29814,29815,29817],{},[35,29816,5724],{},[35,29818,1682],{},[47,29820,10129],{"encoding":49},[15,29822,29824],{"className":29823,"ariaHidden":41},[54],[15,29825,29827,29830],{"className":29826},[58],[15,29828],{"className":29829,"style":4456},[62],[15,29831,29833,29836],{"className":29832},[67],[15,29834,5724],{"className":29835,"style":5772},[67,68],[15,29837,29839],{"className":29838},[918],[15,29840,29842,29862],{"className":29841},[922,923],[15,29843,29845,29859],{"className":29844},[927],[15,29846,29848],{"className":29847,"style":1733},[931],[15,29849,29850,29853],{"style":10023},[15,29851],{"className":29852,"style":940},[939],[15,29854,29856],{"className":29855},[944,945,946,947],[15,29857,1682],{"className":29858},[67,68,947],[15,29860,955],{"className":29861},[954],[15,29863,29865],{"className":29864},[927],[15,29866,29868],{"className":29867,"style":962},[931],[15,29869],{},[11,29871,29872,29873,29977,29978,30006,30007,30035,30036,30160,30161,30189,30190,2033,30234,30262,30263,30291],{},"记 ",[15,29874,29876,29897],{"className":29875,"translate":19},[18],[15,29877,29879],{"className":29878},[23],[25,29880,29881],{"xmlns":27},[29,29882,29883,29895],{},[32,29884,29885],{},[863,29886,29887,29889],{},[35,29888,1336],{},[18639,29890,29891,29893],{"accent":41},[35,29892,37],{},[39,29894,18645],{"stretchy":41},[47,29896,18648],{"encoding":49},[15,29898,29900],{"className":29899,"ariaHidden":41},[54],[15,29901,29903,29906],{"className":29902},[58],[15,29904],{"className":29905,"style":18658},[62],[15,29907,29909,29912],{"className":29908},[67],[15,29910,1336],{"className":29911},[67,68],[15,29913,29915],{"className":29914},[918],[15,29916,29918,29969],{"className":29917},[922,923],[15,29919,29921,29966],{"className":29920},[927],[15,29922,29924],{"className":29923,"style":18677},[931],[15,29925,29926,29929],{"style":18680},[15,29927],{"className":29928,"style":18684},[939],[15,29930,29932],{"className":29931},[944,945,946,947],[15,29933,29935],{"className":29934},[67,947],[15,29936,29938],{"className":29937},[67,18694,947],[15,29939,29941],{"className":29940},[922],[15,29942,29944],{"className":29943},[927],[15,29945,29947,29958],{"className":29946,"style":18704},[931],[15,29948,29949,29952],{"style":18707},[15,29950],{"className":29951,"style":18684},[939],[15,29953,29955],{"className":29954},[67,947],[15,29956,37],{"className":29957,"style":69},[67,68,947],[15,29959,29960,29963],{"style":18719},[15,29961],{"className":29962,"style":18684},[939],[15,29964],{"className":29965,"style":18727},[18726,947],[15,29967,955],{"className":29968},[954],[15,29970,29972],{"className":29971},[927],[15,29973,29975],{"className":29974,"style":18737},[931],[15,29976],{}," 为从 ",[15,29979,29981,29994],{"className":29980,"translate":19},[18],[15,29982,29984],{"className":29983},[23],[25,29985,29986],{"xmlns":27},[29,29987,29988,29992],{},[32,29989,29990],{},[35,29991,1336],{},[47,29993,1336],{"encoding":49},[15,29995,29997],{"className":29996,"ariaHidden":41},[54],[15,29998,30000,30003],{"className":29999},[58],[15,30001],{"className":30002,"style":299},[62],[15,30004,1336],{"className":30005},[67,68]," 中删去所有指向 ",[15,30008,30010,30023],{"className":30009,"translate":19},[18],[15,30011,30013],{"className":30012},[23],[25,30014,30015],{"xmlns":27},[29,30016,30017,30021],{},[32,30018,30019],{},[35,30020,37],{},[47,30022,37],{"encoding":49},[15,30024,30026],{"className":30025,"ariaHidden":41},[54],[15,30027,30029,30032],{"className":30028},[58],[15,30030],{"className":30031,"style":299},[62],[15,30033,37],{"className":30034,"style":69},[67,68]," 的边所得的图，",[15,30037,30039,30062],{"className":30038,"translate":19},[18],[15,30040,30042],{"className":30041},[23],[25,30043,30044],{"xmlns":27},[29,30045,30046,30059],{},[32,30047,30048],{},[863,30049,30050,30052],{},[35,30051,1336],{},[30053,30054,30055,30057],"munder",{"accentunder":41},[35,30056,37],{},[39,30058,18645],{"stretchy":41},[47,30060,30061],{"encoding":49},"G_{\\underline{X}}",[15,30063,30065],{"className":30064,"ariaHidden":41},[54],[15,30066,30068,30072],{"className":30067},[58],[15,30069],{"className":30070,"style":30071},[62],"height:1.0048em;vertical-align:-0.3215em;",[15,30073,30075,30078],{"className":30074},[67],[15,30076,1336],{"className":30077},[67,68],[15,30079,30081],{"className":30080},[918],[15,30082,30084,30151],{"className":30083},[922,923],[15,30085,30087,30148],{"className":30086},[927],[15,30088,30090],{"className":30089,"style":7358},[931],[15,30091,30093,30096],{"style":30092},"top:-2.85em;margin-left:0em;margin-right:0.05em;",[15,30094],{"className":30095,"style":18684},[939],[15,30097,30099],{"className":30098},[944,945,946,947],[15,30100,30102],{"className":30101},[67,947],[15,30103,30106],{"className":30104},[67,30105,947],"underline",[15,30107,30109,30139],{"className":30108},[922,923],[15,30110,30112,30136],{"className":30111},[927],[15,30113,30115,30125],{"className":30114,"style":299},[931],[15,30116,30118,30121],{"style":30117},"top:-2.804em;",[15,30119],{"className":30120,"style":18684},[939],[15,30122],{"className":30123,"style":18727},[30124,947],"underline-line",[15,30126,30127,30130],{"style":18707},[15,30128],{"className":30129,"style":18684},[939],[15,30131,30133],{"className":30132},[67,947],[15,30134,37],{"className":30135,"style":69},[67,68,947],[15,30137,955],{"className":30138},[954],[15,30140,30142],{"className":30141},[927],[15,30143,30146],{"className":30144,"style":30145},[931],"height:0.245em;",[15,30147],{},[15,30149,955],{"className":30150},[954],[15,30152,30154],{"className":30153},[927],[15,30155,30158],{"className":30156,"style":30157},[931],"height:0.3215em;",[15,30159],{}," 为删去所有从 ",[15,30162,30164,30177],{"className":30163,"translate":19},[18],[15,30165,30167],{"className":30166},[23],[25,30168,30169],{"xmlns":27},[29,30170,30171,30175],{},[32,30172,30173],{},[35,30174,37],{},[47,30176,37],{"encoding":49},[15,30178,30180],{"className":30179,"ariaHidden":41},[54],[15,30181,30183,30186],{"className":30182},[58],[15,30184],{"className":30185,"style":299},[62],[15,30187,37],{"className":30188,"style":69},[67,68]," 出发的边所得的图，并记 ",[15,30191,30193,30213],{"className":30192,"translate":19},[18],[15,30194,30196],{"className":30195},[23],[25,30197,30198],{"xmlns":27},[29,30199,30200,30210],{},[32,30201,30202,30204,30206,30208],{},[35,30203,4214],{},[39,30205,102],{"stretchy":101},[35,30207,3795],{},[39,30209,111],{"stretchy":101},[47,30211,30212],{"encoding":49},"Z(W)",[15,30214,30216],{"className":30215,"ariaHidden":41},[54],[15,30217,30219,30222,30225,30228,30231],{"className":30218},[58],[15,30220],{"className":30221,"style":124},[62],[15,30223,4214],{"className":30224,"style":4243},[67,68],[15,30226,102],{"className":30227},[132],[15,30229,3795],{"className":30230,"style":128},[67,68],[15,30232,111],{"className":30233},[148],[15,30235,30237,30250],{"className":30236,"translate":19},[18],[15,30238,30240],{"className":30239},[23],[25,30241,30242],{"xmlns":27},[29,30243,30244,30248],{},[32,30245,30246],{},[35,30247,4214],{},[47,30249,4214],{"encoding":49},[15,30251,30253],{"className":30252,"ariaHidden":41},[54],[15,30254,30256,30259],{"className":30255},[58],[15,30257],{"className":30258,"style":299},[62],[15,30260,4214],{"className":30261,"style":4243},[67,68]," 中不属于 ",[15,30264,30266,30279],{"className":30265,"translate":19},[18],[15,30267,30269],{"className":30268},[23],[25,30270,30271],{"xmlns":27},[29,30272,30273,30277],{},[32,30274,30275],{},[35,30276,3795],{},[47,30278,3795],{"encoding":49},[15,30280,30282],{"className":30281,"ariaHidden":41},[54],[15,30283,30285,30288],{"className":30284},[58],[15,30286],{"className":30287,"style":299},[62],[15,30289,3795],{"className":30290,"style":128},[67,68]," 的后代的节点子集，则：",[1314,30293,30294,30368],{},[11,30295,30296,30299,30300,505],{},[305,30297,30298],{},"定理 3.2（do-演算三规则）"," 对任意互不相交的变量集合 ",[15,30301,30303,30329],{"className":30302,"translate":19},[18],[15,30304,30306],{"className":30305},[23],[25,30307,30308],{"xmlns":27},[29,30309,30310,30326],{},[32,30311,30312,30314,30316,30318,30320,30322,30324],{},[35,30313,37],{},[39,30315,42],{"separator":41},[35,30317,45],{},[39,30319,42],{"separator":41},[35,30321,4214],{},[39,30323,42],{"separator":41},[35,30325,3795],{},[47,30327,30328],{"encoding":49},"X, Y, Z, W",[15,30330,30332],{"className":30331,"ariaHidden":41},[54],[15,30333,30335,30338,30341,30344,30347,30350,30353,30356,30359,30362,30365],{"className":30334},[58],[15,30336],{"className":30337,"style":63},[62],[15,30339,37],{"className":30340,"style":69},[67,68],[15,30342,42],{"className":30343},[73],[15,30345],{"className":30346,"style":78},[77],[15,30348,45],{"className":30349,"style":82},[67,68],[15,30351,42],{"className":30352},[73],[15,30354],{"className":30355,"style":78},[77],[15,30357,4214],{"className":30358,"style":4243},[67,68],[15,30360,42],{"className":30361},[73],[15,30363],{"className":30364,"style":78},[77],[15,30366,3795],{"className":30367,"style":128},[67,68],[507,30369,30370,30826,31363],{},[510,30371,30372,7936,30375,30621,30622],{},[305,30373,30374],{},"规则 1（插入 \u002F 删除观测）",[15,30376,30378,30428],{"className":30377,"translate":19},[18],[15,30379,30381],{"className":30380},[23],[25,30382,30383],{"xmlns":27},[29,30384,30385,30425],{},[32,30386,30387,30389,30391,30393,30395,30397,30399,30401,30403,30405,30407,30409,30411],{},[39,30388,102],{"stretchy":101},[35,30390,45],{},[39,30392,236],{},[238,30394,240],{},[238,30396,240],{},[238,30398,240],{},[39,30400,236],{},[35,30402,4214],{},[39,30404,170],{},[35,30406,37],{},[39,30408,42],{"separator":41},[35,30410,3795],{},[863,30412,30413,30415],{},[39,30414,111],{"stretchy":101},[863,30416,30417,30419],{},[35,30418,1336],{},[18639,30420,30421,30423],{"accent":41},[35,30422,37],{},[39,30424,18645],{"stretchy":41},[47,30426,30427],{"encoding":49},"(Y \\perp\\!\\!\\!\\perp Z \\mid X, W)_{G_{\\overline{X}}}",[15,30429,30431,30458,30470,30488],{"className":30430,"ariaHidden":41},[54],[15,30432,30434,30437,30440,30443,30446,30449,30452,30455],{"className":30433},[58],[15,30435],{"className":30436,"style":124},[62],[15,30438,102],{"className":30439},[132],[15,30441,45],{"className":30442,"style":82},[67,68],[15,30444],{"className":30445,"style":199},[77],[15,30447,236],{"className":30448},[203],[15,30450],{"className":30451,"style":274},[77],[15,30453],{"className":30454,"style":274},[77],[15,30456],{"className":30457,"style":274},[77],[15,30459,30461,30464,30467],{"className":30460},[58],[15,30462],{"className":30463,"style":261},[62],[15,30465,236],{"className":30466},[203],[15,30468],{"className":30469,"style":199},[77],[15,30471,30473,30476,30479,30482,30485],{"className":30472},[58],[15,30474],{"className":30475,"style":124},[62],[15,30477,4214],{"className":30478,"style":4243},[67,68],[15,30480],{"className":30481,"style":199},[77],[15,30483,170],{"className":30484},[203],[15,30486],{"className":30487,"style":199},[77],[15,30489,30491,30495,30498,30501,30504,30507],{"className":30490},[58],[15,30492],{"className":30493,"style":30494},[62],"height:1.1228em;vertical-align:-0.3728em;",[15,30496,37],{"className":30497,"style":69},[67,68],[15,30499,42],{"className":30500},[73],[15,30502],{"className":30503,"style":78},[77],[15,30505,3795],{"className":30506,"style":128},[67,68],[15,30508,30510,30513],{"className":30509},[148],[15,30511,111],{"className":30512},[148],[15,30514,30516],{"className":30515},[918],[15,30517,30519,30612],{"className":30518},[922,923],[15,30520,30522,30609],{"className":30521},[927],[15,30523,30525],{"className":30524,"style":7358},[931],[15,30526,30527,30530],{"style":30092},[15,30528],{"className":30529,"style":18684},[939],[15,30531,30533],{"className":30532},[944,945,946,947],[15,30534,30536],{"className":30535},[67,947],[15,30537,30539,30542],{"className":30538},[67,947],[15,30540,1336],{"className":30541},[67,68,947],[15,30543,30545],{"className":30544},[918],[15,30546,30548,30600],{"className":30547},[922,923],[15,30549,30551,30597],{"className":30550},[927],[15,30552,30554],{"className":30553,"style":18677},[931],[15,30555,30557,30560],{"style":30556},"top:-2.6817em;margin-left:0em;margin-right:0.0714em;",[15,30558],{"className":30559,"style":18684},[939],[15,30561,30563],{"className":30562},[944,18421,15089,947],[15,30564,30566],{"className":30565},[67,947],[15,30567,30569],{"className":30568},[67,18694,947],[15,30570,30572],{"className":30571},[922],[15,30573,30575],{"className":30574},[927],[15,30576,30578,30589],{"className":30577,"style":18704},[931],[15,30579,30580,30583],{"style":18707},[15,30581],{"className":30582,"style":18684},[939],[15,30584,30586],{"className":30585},[67,947],[15,30587,37],{"className":30588,"style":69},[67,68,947],[15,30590,30591,30594],{"style":18719},[15,30592],{"className":30593,"style":18684},[939],[15,30595],{"className":30596,"style":18727},[18726,947],[15,30598,955],{"className":30599},[954],[15,30601,30603],{"className":30602},[927],[15,30604,30607],{"className":30605,"style":30606},[931],"height:0.3183em;",[15,30608],{},[15,30610,955],{"className":30611},[954],[15,30613,30615],{"className":30614},[927],[15,30616,30619],{"className":30617,"style":30618},[931],"height:0.3728em;",[15,30620],{},"，则\n",[15,30623,30625,30691],{"className":30624,"translate":19},[18],[15,30626,30628],{"className":30627},[23],[25,30629,30630],{"xmlns":27},[29,30631,30632,30688],{},[32,30633,30634,30636,30638,30640,30642,30644,30646,30648,30650,30652,30654,30656,30658,30660,30662,30664,30666,30668,30670,30672,30674,30676,30678,30680,30682,30684,30686],{},[35,30635,98],{},[39,30637,102],{"stretchy":101},[35,30639,534],{},[39,30641,170],{},[35,30643,696],{},[35,30645,699],{},[39,30647,102],{"stretchy":101},[35,30649,539],{},[39,30651,111],{"stretchy":101},[39,30653,42],{"separator":41},[35,30655,5819],{},[39,30657,42],{"separator":41},[35,30659,28798],{},[39,30661,111],{"stretchy":101},[39,30663,602],{},[35,30665,98],{},[39,30667,102],{"stretchy":101},[35,30669,534],{},[39,30671,170],{},[35,30673,696],{},[35,30675,699],{},[39,30677,102],{"stretchy":101},[35,30679,539],{},[39,30681,111],{"stretchy":101},[39,30683,42],{"separator":41},[35,30685,28798],{},[39,30687,111],{"stretchy":101},[47,30689,30690],{"encoding":49},"P(y 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2（干预与观测的互换）",[15,30832,30834,30892],{"className":30833,"translate":19},[18],[15,30835,30837],{"className":30836},[23],[25,30838,30839],{"xmlns":27},[29,30840,30841,30889],{},[32,30842,30843,30845,30847,30849,30851,30853,30855,30857,30859,30861,30863,30865,30867],{},[39,30844,102],{"stretchy":101},[35,30846,45],{},[39,30848,236],{},[238,30850,240],{},[238,30852,240],{},[238,30854,240],{},[39,30856,236],{},[35,30858,4214],{},[39,30860,170],{},[35,30862,37],{},[39,30864,42],{"separator":41},[35,30866,3795],{},[863,30868,30869,30871],{},[39,30870,111],{"stretchy":101},[863,30872,30873,30875],{},[35,30874,1336],{},[32,30876,30877,30883],{},[18639,30878,30879,30881],{"accent":41},[35,30880,37],{},[39,30882,18645],{"stretchy":41},[30053,30884,30885,30887],{"accentunder":41},[35,30886,4214],{},[39,30888,18645],{"stretchy":41},[47,30890,30891],{"encoding":49},"(Y \\perp\\!\\!\\!\\perp Z \\mid X, W)_{G_{\\overline{X}\\underline{Z}}}",[15,30893,30895,30922,30934,30952],{"className":30894,"ariaHidden":41},[54],[15,30896,30898,30901,30904,30907,30910,30913,30916,30919],{"className":30897},[58],[15,30899],{"className":30900,"style":124},[62],[15,30902,102],{"className":30903},[132],[15,30905,45],{"className":30906,"style":82},[67,68],[15,30908],{"className":30909,"style":199},[77],[15,30911,236],{"className":30912},[203],[15,30914],{"className":30915,"style":274},[77],[15,30917],{"className":30918,"style":274},[77],[15,30920],{"className":30921,"style":274},[77],[15,30923,30925,30928,30931],{"className":30924},[58],[15,30926],{"className":30927,"style":261},[62],[15,30929,236],{"className":30930},[203],[15,30932],{"className":30933,"style":199},[77],[15,30935,30937,30940,30943,30946,30949],{"className":30936},[58],[15,30938],{"className":30939,"style":124},[62],[15,30941,4214],{"className":30942,"style":4243},[67,68],[15,30944],{"className":30945,"style":199},[77],[15,30947,170],{"className":30948},[203],[15,30950],{"className":30951,"style":199},[77],[15,30953,30955,30959,30962,30965,30968,30971],{"className":30954},[58],[15,30956],{"className":30957,"style":30958},[62],"height:1.2453em;vertical-align:-0.4953em;",[15,30960,37],{"className":30961,"style":69},[67,68],[15,30963,42],{"className":30964},[73],[15,30966],{"className":30967,"style":78},[77],[15,30969,3795],{"className":30970,"style":128},[67,68],[15,30972,30974,30977],{"className":30973},[148],[15,30975,111],{"className":30976},[148],[15,30978,30980],{"className":30979},[918],[15,30981,30983,31117],{"className":30982},[922,923],[15,30984,30986,31114],{"className":30985},[927],[15,30987,30989],{"className":30988,"style":7358},[931],[15,30990,30991,30994],{"style":30092},[15,30992],{"className":30993,"style":18684},[939],[15,30995,30997],{"className":30996},[944,945,946,947],[15,30998,31000],{"className":30999},[67,947],[15,31001,31003,31006],{"className":31002},[67,947],[15,31004,1336],{"className":31005},[67,68,947],[15,31007,31009],{"className":31008},[918],[15,31010,31012,31105],{"className":31011},[922,923],[15,31013,31015,31102],{"className":31014},[927],[15,31016,31018],{"className":31017,"style":18677},[931],[15,31019,31020,31023],{"style":30556},[15,31021],{"className":31022,"style":18684},[939],[15,31024,31026],{"className":31025},[944,18421,15089,947],[15,31027,31029,31060],{"className":31028},[67,947],[15,31030,31032],{"className":31031},[67,18694,947],[15,31033,31035],{"className":31034},[922],[15,31036,31038],{"className":31037},[927],[15,31039,31041,31052],{"className":31040,"style":18704},[931],[15,31042,31043,31046],{"style":18707},[15,31044],{"className":31045,"style":18684},[939],[15,31047,31049],{"className":31048},[67,947],[15,31050,37],{"className":31051,"style":69},[67,68,947],[15,31053,31054,31057],{"style":18719},[15,31055],{"className":31056,"style":18684},[939],[15,31058],{"className":31059,"style":18727},[18726,947],[15,31061,31063],{"className":31062},[67,30105,947],[15,31064,31066,31094],{"className":31065},[922,923],[15,31067,31069,31091],{"className":31068},[927],[15,31070,31072,31080],{"className":31071,"style":299},[931],[15,31073,31074,31077],{"style":30117},[15,31075],{"className":31076,"style":18684},[939],[15,31078],{"className":31079,"style":18727},[30124,947],[15,31081,31082,31085],{"style":18707},[15,31083],{"className":31084,"style":18684},[939],[15,31086,31088],{"className":31087},[67,947],[15,31089,4214],{"className":31090,"style":4243},[67,68,947],[15,31092,955],{"className":31093},[954],[15,31095,31097],{"className":31096},[927],[15,31098,31100],{"className":31099,"style":30145},[931],[15,31101],{},[15,31103,955],{"className":31104},[954],[15,31106,31108],{"className":31107},[927],[15,31109,31112],{"className":31110,"style":31111},[931],"height:0.4933em;",[15,31113],{},[15,31115,955],{"className":31116},[954],[15,31118,31120],{"className":31119},[927],[15,31121,31124],{"className":31122,"style":31123},[931],"height:0.4953em;",[15,31125],{},[15,31127,31129,31207],{"className":31128,"translate":19},[18],[15,31130,31132],{"className":31131},[23],[25,31133,31134],{"xmlns":27},[29,31135,31136,31204],{},[32,31137,31138,31140,31142,31144,31146,31148,31150,31152,31154,31156,31158,31160,31162,31164,31166,31168,31170,31172,31174,31176,31178,31180,31182,31184,31186,31188,31190,31192,31194,31196,31198,31200,31202],{},[35,31139,98],{},[39,31141,102],{"stretchy":101},[35,31143,534],{},[39,31145,170],{},[35,31147,696],{},[35,31149,699],{},[39,31151,102],{"stretchy":101},[35,31153,539],{},[39,31155,111],{"stretchy":101},[39,31157,42],{"separator":41},[35,31159,696],{},[35,31161,699],{},[39,31163,102],{"stretchy":101},[35,31165,5819],{},[39,31167,111],{"stretchy":101},[39,31169,42],{"separator":41},[35,31171,28798],{},[39,31173,111],{"stretchy":101},[39,31175,602],{},[35,31177,98],{},[39,31179,102],{"stretchy":101},[35,31181,534],{},[39,31183,170],{},[35,31185,696],{},[35,31187,699],{},[39,31189,102],{"stretchy":101}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\\mid do(x), do(z), w) = P(y \\mid do(x), z, 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3（插入 \u002F 删除干预）",[15,31369,31371,31437],{"className":31370,"translate":19},[18],[15,31372,31374],{"className":31373},[23],[25,31375,31376],{"xmlns":27},[29,31377,31378,31434],{},[32,31379,31380,31382,31384,31386,31388,31390,31392,31394,31396,31398,31400,31402,31404],{},[39,31381,102],{"stretchy":101},[35,31383,45],{},[39,31385,236],{},[238,31387,240],{},[238,31389,240],{},[238,31391,240],{},[39,31393,236],{},[35,31395,4214],{},[39,31397,170],{},[35,31399,37],{},[39,31401,42],{"separator":41},[35,31403,3795],{},[863,31405,31406,31408],{},[39,31407,111],{"stretchy":101},[863,31409,31410,31412],{},[35,31411,1336],{},[32,31413,31414,31420],{},[18639,31415,31416,31418],{"accent":41},[35,31417,37],{},[39,31419,18645],{"stretchy":41},[18639,31421,31422,31432],{"accent":41},[32,31423,31424,31426,31428,31430],{},[35,31425,4214],{},[39,31427,102],{"stretchy":101},[35,31429,3795],{},[39,31431,111],{"stretchy":101},[39,31433,18645],{"stretchy":41},[47,31435,31436],{"encoding":49},"(Y \\perp\\!\\!\\!\\perp Z \\mid X, W)_{G_{\\overline{X}\\overline{Z(W)}}}",[15,31438,31440,31467,31479,31497],{"className":31439,"ariaHidden":41},[54],[15,31441,31443,31446,31449,31452,31455,31458,31461,31464],{"className":31442},[58],[15,31444],{"className":31445,"style":124},[62],[15,31447,102],{"className":31448},[132],[15,31450,45],{"className":31451,"style":82},[67,68],[15,31453],{"className":31454,"style":199},[77],[15,31456,236],{"className":31457},[203],[15,31459],{"className":31460,"style":274},[77],[15,31462],{"className":31463,"style":274},[77],[15,31465],{"className":31466,"style":274},[77],[15,31468,31470,31473,31476],{"className":31469},[58],[15,31471],{"className":31472,"style":261},[62],[15,31474,236],{"className":31475},[203],[15,31477],{"className":31478,"style":199},[77],[15,31480,31482,31485,31488,31491,31494],{"className":31481},[58],[15,31483],{"className":31484,"style":124},[62],[15,31486,4214],{"className":31487,"style":4243},[67,68],[15,31489],{"className":31490,"style":199},[77],[15,31492,170],{"className":31493},[203],[15,31495],{"className":31496,"style":199},[77],[15,31498,31500,31504,31507,31510,31513,31516],{"className":31499},[58],[15,31501],{"className":31502,"style":31503},[62],"height:1.2811em;vertical-align:-0.5311em;",[15,31505,37],{"className":31506,"style":69},[67,68],[15,31508,42],{"className":31509},[73],[15,31511],{"className":31512,"style":78},[77],[15,31514,3795],{"className":31515,"style":128},[67,68],[15,31517,31519,31522],{"className":31518},[148],[15,31520,111],{"className":31521},[148],[15,31523,31525],{"className":31524},[918],[15,31526,31528,31675],{"className":31527},[922,923],[15,31529,31531,31672],{"className":31530},[927],[15,31532,31534],{"className":31533,"style":7358},[931],[15,31535,31536,31539],{"style":30092},[15,31537],{"className":31538,"style":18684},[939],[15,31540,31542],{"className":31541},[944,945,946,947],[15,31543,31545],{"className":31544},[67,947],[15,31546,31548,31551],{"className":31547},[67,947],[15,31549,1336],{"className":31550},[67,68,947],[15,31552,31554],{"className":31553},[918],[15,31555,31557,31663],{"className":31556},[922,923],[15,31558,31560,31660],{"className":31559},[927],[15,31561,31563],{"className":31562,"style":18677},[931],[15,31564,31566,31569],{"style":31565},"top:-2.6341em;margin-left:0em;margin-right:0.0714em;",[15,31567],{"className":31568,"style":18684},[939],[15,31570,31572],{"className":31571},[944,18421,15089,947],[15,31573,31575,31606],{"className":31574},[67,947],[15,31576,31578],{"className":31577},[67,18694,947],[15,31579,31581],{"className":31580},[922],[15,31582,31584],{"className":31583},[927],[15,31585,31587,31598],{"className":31586,"style":18704},[931],[15,31588,31589,31592],{"style":18707},[15,31590],{"className":31591,"style":18684},[939],[15,31593,31595],{"className":31594},[67,947],[15,31596,37],{"className":31597,"style":69},[67,68,947],[15,31599,31600,31603],{"style":18719},[15,31601],{"className":31602,"style":18684},[939],[15,31604],{"className":31605,"style":18727},[18726,947],[15,31607,31609],{"className":31608},[67,18694,947],[15,31610,31612,31651],{"className":31611},[922,923],[15,31613,31615,31648],{"className":31614},[927],[15,31616,31619,31639],{"className":31617,"style":31618},[931],"height:0.995em;",[15,31620,31621,31624],{"style":18707},[15,31622],{"className":31623,"style":18684},[939],[15,31625,31627,31630,31633,31636],{"className":31626},[67,947],[15,31628,4214],{"className":31629,"style":4243},[67,68,947],[15,31631,102],{"className":31632},[132,947],[15,31634,3795],{"className":31635,"style":128},[67,68,947],[15,31637,111],{"className":31638},[148,947],[15,31640,31642,31645],{"style":31641},"top:-3.897em;",[15,31643],{"className":31644,"style":18684},[939],[15,31646],{"className":31647,"style":18727},[18726,947],[15,31649,955],{"className":31650},[954],[15,31652,31654],{"className":31653},[927],[15,31655,31658],{"className":31656,"style":31657},[931],"height:0.25em;",[15,31659],{},[15,31661,955],{"className":31662},[954],[15,31664,31666],{"className":31665},[927],[15,31667,31670],{"className":31668,"style":31669},[931],"height:0.5445em;",[15,31671],{},[15,31673,955],{"className":31674},[954],[15,31676,31678],{"className":31677},[927],[15,31679,31682],{"className":31680,"style":31681},[931],"height:0.5311em;",[15,31683],{},[15,31685,31687,31761],{"className":31686,"translate":19},[18],[15,31688,31690],{"className":31689},[23],[25,31691,31692],{"xmlns":27},[29,31693,31694,31758],{},[32,31695,31696,31698,31700,31702,31704,31706,31708,31710,31712,31714,31716,31718,31720,31722,31724,31726,31728,31730,31732,31734,31736,31738,31740,31742,31744,31746,31748,31750,31752,31754,31756],{},[35,31697,98],{},[39,31699,102],{"stretchy":101},[35,31701,534],{},[39,31703,170],{},[35,31705,696],{},[35,31707,699],{},[39,31709,102],{"stretchy":101},[35,31711,539],{},[39,31713,111],{"stretchy":101},[39,31715,42],{"separator":41},[35,31717,696],{},[35,31719,699],{},[39,31721,102],{"stretchy":101},[35,31723,5819],{},[39,31725,111],{"stretchy":101},[39,31727,42],{"separator":41},[35,31729,28798],{},[39,31731,111],{"stretchy":101},[39,31733,602],{},[35,31735,98],{},[39,31737,102],{"stretchy":101},[35,31739,534],{},[39,31741,170],{},[35,31743,696],{},[35,31745,699],{},[39,31747,102],{"stretchy":101},[35,31749,539],{},[39,31751,111],{"stretchy":101},[39,31753,42],{"separator":41},[35,31755,28798],{},[39,31757,111],{"stretchy":101},[47,31759,31760],{"encoding":49},"P(y \\mid do(x), do(z), w) = P(y \\mid do(x), w)",[15,31762,31764,31788,31851,31875],{"className":31763,"ariaHidden":41},[54],[15,31765,31767,31770,31773,31776,31779,31782,31785],{"className":31766},[58],[15,31768],{"className":31769,"style":124},[62],[15,31771,98],{"className":31772,"style":128},[67,68],[15,31774,102],{"className":31775},[132],[15,31777,534],{"className":31778,"style":563},[67,68],[15,31780],{"className":31781,"style":199},[77],[15,31783,170],{"className":31784},[203],[15,31786],{"className":31787,"style":199},[77],[15,31789,31791,31794,31797,31800,31803,31806,31809,31812,31815,31818,31821,31824,31827,31830,31833,31836,31839,31842,31845,31848],{"className":31790},[58],[15,31792],{"className":31793,"style":124},[62],[15,31795,696],{"className":31796},[67,68],[15,31798,699],{"className":31799},[67,68],[15,31801,102],{"className":31802},[132],[15,31804,539],{"className":31805},[67,68],[15,31807,111],{"className":31808},[148],[15,31810,42],{"className":31811},[73],[15,31813],{"className":31814,"style":78},[77],[15,31816,696],{"className":31817},[67,68],[15,31819,699],{"className":31820},[67,68],[15,31822,102],{"className":31823},[132],[15,31825,5819],{"className":31826,"style":5853},[67,68],[15,31828,111],{"className":31829},[148],[15,31831,42],{"className":31832},[73],[15,31834],{"className":31835,"style":78},[77],[15,31837,28798],{"className":31838,"style":28950},[67,68],[15,31840,111],{"className":31841},[148],[15,31843],{"className":31844,"style":199},[77],[15,31846,602],{"className":31847},[203],[15,31849],{"className":31850,"style":199},[77],[15,31852,31854,31857,31860,31863,31866,31869,31872],{"className":31853},[58],[15,31855],{"className":31856,"style":124},[62],[15,31858,98],{"className":31859,"style":128},[67,68],[15,31861,102],{"className":31862},[132],[15,31864,534],{"className":31865,"style":563},[67,68],[15,31867],{"className":31868,"style":199},[77],[15,31870,170],{"className":31871},[203],[15,31873],{"className":31874,"style":199},[77],[15,31876,31878,31881,31884,31887,31890,31893,31896,31899,31902,31905],{"className":31877},[58],[15,31879],{"className":31880,"style":124},[62],[15,31882,696],{"className":31883},[67,68],[15,31885,699],{"className":31886},[67,68],[15,31888,102],{"className":31889},[132],[15,31891,539],{"className":31892},[67,68],[15,31894,111],{"className":31895},[148],[15,31897,42],{"className":31898},[73],[15,31900],{"className":31901,"style":78},[77],[15,31903,28798],{"className":31904,"style":28950},[67,68],[15,31906,111],{"className":31907},[148],[11,31909,31910,31911,31945,31946,31979,31980,32013,32014,32096,32097,32134,32135,32138,32139,32172,32173,32176],{},"三条规则的形态高度一致：每一条都在某个 d-分离判据成立时，把一个含 ",[15,31912,31914,31930],{"className":31913,"translate":19},[18],[15,31915,31917],{"className":31916},[23],[25,31918,31919],{"xmlns":27},[29,31920,31921,31927],{},[32,31922,31923,31925],{},[35,31924,696],{},[35,31926,699],{},[47,31928,31929],{"encoding":49},"do",[15,31931,31933],{"className":31932,"ariaHidden":41},[54],[15,31934,31936,31939,31942],{"className":31935},[58],[15,31937],{"className":31938,"style":261},[62],[15,31940,696],{"className":31941},[67,68],[15,31943,699],{"className":31944},[67,68]," 算子的表达式改写为 ",[15,31947,31949,31964],{"className":31948,"translate":19},[18],[15,31950,31952],{"className":31951},[23],[25,31953,31954],{"xmlns":27},[29,31955,31956,31962],{},[32,31957,31958,31960],{},[35,31959,696],{},[35,31961,699],{},[47,31963,31929],{"encoding":49},[15,31965,31967],{"className":31966,"ariaHidden":41},[54],[15,31968,31970,31973,31976],{"className":31969},[58],[15,31971],{"className":31972,"style":261},[62],[15,31974,696],{"className":31975},[67,68],[15,31977,699],{"className":31978},[67,68]," 算子更少（或不含 ",[15,31981,31983,31998],{"className":31982,"translate":19},[18],[15,31984,31986],{"className":31985},[23],[25,31987,31988],{"xmlns":27},[29,31989,31990,31996],{},[32,31991,31992,31994],{},[35,31993,696],{},[35,31995,699],{},[47,31997,31929],{"encoding":49},[15,31999,32001],{"className":32000,"ariaHidden":41},[54],[15,32002,32004,32007,32010],{"className":32003},[58],[15,32005],{"className":32006,"style":261},[62],[15,32008,696],{"className":32009},[67,68],[15,32011,699],{"className":32012},[67,68],"）的表达式。因此判断 ",[15,32015,32017,32048],{"className":32016,"translate":19},[18],[15,32018,32020],{"className":32019},[23],[25,32021,32022],{"xmlns":27},[29,32023,32024,32046],{},[32,32025,32026,32028,32030,32032,32034,32036,32038,32040,32042,32044],{},[35,32027,98],{},[39,32029,102],{"stretchy":101},[35,32031,534],{},[39,32033,170],{},[35,32035,696],{},[35,32037,699],{},[39,32039,102],{"stretchy":101},[35,32041,539],{},[39,32043,111],{"stretchy":101},[39,32045,111],{"stretchy":101},[47,32047,710],{"encoding":49},[15,32049,32051,32075],{"className":32050,"ariaHidden":41},[54],[15,32052,32054,32057,32060,32063,32066,32069,32072],{"className":32053},[58],[15,32055],{"className":32056,"style":124},[62],[15,32058,98],{"className":32059,"style":128},[67,68],[15,32061,102],{"className":32062},[132],[15,32064,534],{"className":32065,"style":563},[67,68],[15,32067],{"className":32068,"style":199},[77],[15,32070,170],{"className":32071},[203],[15,32073],{"className":32074,"style":199},[77],[15,32076,32078,32081,32084,32087,32090,32093],{"className":32077},[58],[15,32079],{"className":32080,"style":124},[62],[15,32082,696],{"className":32083},[67,68],[15,32085,699],{"className":32086},[67,68],[15,32088,102],{"className":32089},[132],[15,32091,539],{"className":32092},[67,68],[15,32094,759],{"className":32095},[148]," 是否可识别的过程，就是反复应用三条规则、尝试",[305,32098,32099,32100,32133],{},"消去全部 ",[15,32101,32103,32118],{"className":32102,"translate":19},[18],[15,32104,32106],{"className":32105},[23],[25,32107,32108],{"xmlns":27},[29,32109,32110,32116],{},[32,32111,32112,32114],{},[35,32113,696],{},[35,32115,699],{},[47,32117,31929],{"encoding":49},[15,32119,32121],{"className":32120,"ariaHidden":41},[54],[15,32122,32124,32127,32130],{"className":32123},[58],[15,32125],{"className":32126,"style":261},[62],[15,32128,696],{"className":32129},[67,68],[15,32131,699],{"className":32132},[67,68]," 算子","的过程。Shpitser 与 Pearl（2006）进一步证明了这套规则对可识别性是",[305,32136,32137],{},"完备的","：若不存在任何有限次的规则应用序列能把目标量化为不含 ",[15,32140,32142,32157],{"className":32141,"translate":19},[18],[15,32143,32145],{"className":32144},[23],[25,32146,32147],{"xmlns":27},[29,32148,32149,32155],{},[32,32150,32151,32153],{},[35,32152,696],{},[35,32154,699],{},[47,32156,31929],{"encoding":49},[15,32158,32160],{"className":32159,"ariaHidden":41},[54],[15,32161,32163,32166,32169],{"className":32162},[58],[15,32164],{"className":32165,"style":261},[62],[15,32167,696],{"className":32168},[67,68],[15,32170,699],{"className":32171},[67,68]," 的形式，则该量确实不可由观测分布识别。这一点很重要——它为「不可识别」这一否定性结论提供了",[305,32174,32175],{},"证明手段","，而不只是「暂时没想到办法」。",[11,32178,32179],{},"若不想每次都从三条规则出发作推导，可以使用若干直接给出识别公式的充分性准则。其中最重要的一条是后门准则：",[1314,32181,32182],{},[11,32183,32184,32187,32188,32216,32217,32245,32246,32274,32275,32303,32304,32345,32346,32374,32375,32605,32606,32634,32635,32638],{},[305,32185,32186],{},"定理 3.3（后门准则，Back-door Criterion）"," 若变量集合 ",[15,32189,32191,32204],{"className":32190,"translate":19},[18],[15,32192,32194],{"className":32193},[23],[25,32195,32196],{"xmlns":27},[29,32197,32198,32202],{},[32,32199,32200],{},[35,32201,3779],{},[47,32203,3779],{"encoding":49},[15,32205,32207],{"className":32206,"ariaHidden":41},[54],[15,32208,32210,32213],{"className":32209},[58],[15,32211],{"className":32212,"style":299},[62],[15,32214,3779],{"className":32215,"style":1396},[67,68]," 满足：(i) ",[15,32218,32220,32233],{"className":32219,"translate":19},[18],[15,32221,32223],{"className":32222},[23],[25,32224,32225],{"xmlns":27},[29,32226,32227,32231],{},[32,32228,32229],{},[35,32230,3779],{},[47,32232,3779],{"encoding":49},[15,32234,32236],{"className":32235,"ariaHidden":41},[54],[15,32237,32239,32242],{"className":32238},[58],[15,32240],{"className":32241,"style":299},[62],[15,32243,3779],{"className":32244,"style":1396},[67,68]," 中不包含 ",[15,32247,32249,32262],{"className":32248,"translate":19},[18],[15,32250,32252],{"className":32251},[23],[25,32253,32254],{"xmlns":27},[29,32255,32256,32260],{},[32,32257,32258],{},[35,32259,37],{},[47,32261,37],{"encoding":49},[15,32263,32265],{"className":32264,"ariaHidden":41},[54],[15,32266,32268,32271],{"className":32267},[58],[15,32269],{"className":32270,"style":299},[62],[15,32272,37],{"className":32273,"style":69},[67,68]," 的任何后代；(ii) ",[15,32276,32278,32291],{"className":32277,"translate":19},[18],[15,32279,32281],{"className":32280},[23],[25,32282,32283],{"xmlns":27},[29,32284,32285,32289],{},[32,32286,32287],{},[35,32288,3779],{},[47,32290,3779],{"encoding":49},[15,32292,32294],{"className":32293,"ariaHidden":41},[54],[15,32295,32297,32300],{"className":32296},[58],[15,32298],{"className":32299,"style":299},[62],[15,32301,3779],{"className":32302,"style":1396},[67,68]," 阻断了 ",[15,32305,32307,32324],{"className":32306,"translate":19},[18],[15,32308,32310],{"className":32309},[23],[25,32311,32312],{"xmlns":27},[29,32313,32314,32322],{},[32,32315,32316,32318,32320],{},[35,32317,37],{},[39,32319,42],{"separator":41},[35,32321,45],{},[47,32323,50],{"encoding":49},[15,32325,32327],{"className":32326,"ariaHidden":41},[54],[15,32328,32330,32333,32336,32339,32342],{"className":32329},[58],[15,32331],{"className":32332,"style":63},[62],[15,32334,37],{"className":32335,"style":69},[67,68],[15,32337,42],{"className":32338},[73],[15,32340],{"className":32341,"style":78},[77],[15,32343,45],{"className":32344,"style":82},[67,68]," 之间所有以指向 ",[15,32347,32349,32362],{"className":32348,"translate":19},[18],[15,32350,32352],{"className":32351},[23],[25,32353,32354],{"xmlns":27},[29,32355,32356,32360],{},[32,32357,32358],{},[35,32359,37],{},[47,32361,37],{"encoding":49},[15,32363,32365],{"className":32364,"ariaHidden":41},[54],[15,32366,32368,32371],{"className":32367},[58],[15,32369],{"className":32370,"style":299},[62],[15,32372,37],{"className":32373,"style":69},[67,68]," 的边起始的路径（「后门路径」），则\n",[15,32376,32378,32445],{"className":32377,"translate":19},[18],[15,32379,32381],{"className":32380},[23],[25,32382,32383],{"xmlns":27},[29,32384,32385,32442],{},[32,32386,32387,32389,32391,32393,32395,32397,32399,32401,32403,32405,32407,32409,32415,32417,32419,32421,32423,32425,32427,32429,32431,32434,32436,32438,32440],{},[35,32388,98],{},[39,32390,102],{"stretchy":101},[35,32392,534],{},[39,32394,170],{},[35,32396,696],{},[35,32398,699],{},[39,32400,102],{"stretchy":101},[35,32402,539],{},[39,32404,111],{"stretchy":101},[39,32406,111],{"stretchy":101},[39,32408,602],{},[863,32410,32411,32413],{},[39,32412,20423],{},[35,32414,20426],{},[35,32416,98],{},[39,32418,102],{"stretchy":101},[35,32420,534],{},[39,32422,170],{},[35,32424,539],{},[39,32426,42],{"separator":41},[35,32428,20426],{},[39,32430,111],{"stretchy":101},[238,32432,32433],{}," ",[35,32435,98],{},[39,32437,102],{"stretchy":101},[35,32439,20426],{},[39,32441,111],{"stretchy":101},[47,32443,32444],{"encoding":49},"P(y \\mid do(x)) = \\sum_s P(y \\mid x, s) \\, P(s)",[15,32446,32448,32472,32502,32569],{"className":32447,"ariaHidden":41},[54],[15,32449,32451,32454,32457,32460,32463,32466,32469],{"className":32450},[58],[15,32452],{"className":32453,"style":124},[62],[15,32455,98],{"className":32456,"style":128},[67,68],[15,32458,102],{"className":32459},[132],[15,32461,534],{"className":32462,"style":563},[67,68],[15,32464],{"className":32465,"style":199},[77],[15,32467,170],{"className":32468},[203],[15,32470],{"className":32471,"style":199},[77],[15,32473,32475,32478,32481,32484,32487,32490,32493,32496,32499],{"className":32474},[58],[15,32476],{"className":32477,"style":124},[62],[15,32479,696],{"className":32480},[67,68],[15,32482,699],{"className":32483},[67,68],[15,32485,102],{"className":32486},[132],[15,32488,539],{"className":32489},[67,68],[15,32491,759],{"className":32492},[148],[15,32494],{"className":32495,"style":199},[77],[15,32497,602],{"className":32498},[203],[15,32500],{"className":32501,"style":199},[77],[15,32503,32505,32508,32548,32551,32554,32557,32560,32563,32566],{"className":32504},[58],[15,32506],{"className":32507,"style":20601},[62],[15,32509,32511,32514],{"className":32510},[12772],[15,32512,20423],{"className":32513,"style":12778},[12772,12776,12777],[15,32515,32517],{"className":32516},[918],[15,32518,32520,32540],{"className":32519},[922,923],[15,32521,32523,32537],{"className":32522},[927],[15,32524,32526],{"className":32525,"style":20620},[931],[15,32527,32528,32531],{"style":12794},[15,32529],{"className":32530,"style":940},[939],[15,32532,32534],{"className":32533},[944,945,946,947],[15,32535,20426],{"className":32536},[67,68,947],[15,32538,955],{"className":32539},[954],[15,32541,32543],{"className":32542},[927],[15,32544,32546],{"className":32545,"style":12834},[931],[15,32547],{},[15,32549],{"className":32550,"style":78},[77],[15,32552,98],{"className":32553,"style":128},[67,68],[15,32555,102],{"className":32556},[132],[15,32558,534],{"className":32559,"style":563},[67,68],[15,32561],{"className":32562,"style":199},[77],[15,32564,170],{"className":32565},[203],[15,32567],{"className":32568,"style":199},[77],[15,32570,32572,32575,32578,32581,32584,32587,32590,32593,32596,32599,32602],{"className":32571},[58],[15,32573],{"className":32574,"style":124},[62],[15,32576,539],{"className":32577},[67,68],[15,32579,42],{"className":32580},[73],[15,32582],{"className":32583,"style":78},[77],[15,32585,20426],{"className":32586},[67,68],[15,32588,111],{"className":32589},[148],[15,32591],{"className":32592,"style":78},[77],[15,32594,98],{"className":32595,"style":128},[67,68],[15,32597,102],{"className":32598},[132],[15,32600,20426],{"className":32601},[67,68],[15,32603,111],{"className":32604},[148],"\n即干预效果可以通过对满足后门准则的变量集合 ",[15,32607,32609,32622],{"className":32608,"translate":19},[18],[15,32610,32612],{"className":32611},[23],[25,32613,32614],{"xmlns":27},[29,32615,32616,32620],{},[32,32617,32618],{},[35,32619,3779],{},[47,32621,3779],{"encoding":49},[15,32623,32625],{"className":32624,"ariaHidden":41},[54],[15,32626,32628,32631],{"className":32627},[58],[15,32629],{"className":32630,"style":299},[62],[15,32632,3779],{"className":32633,"style":1396},[67,68]," 做",[305,32636,32637],{},"分层加权平均（standardization）","，完全由观测数据估计得出，而无需真正实施干预、进行随机对照实验。",[11,32640,32641,32642,32670,32671,32699,32700,431,32728,32756],{},"条件 (i) 的必要性，正是第一部分对撞结构那一结论的直接后果：一旦把 ",[15,32643,32645,32658],{"className":32644,"translate":19},[18],[15,32646,32648],{"className":32647},[23],[25,32649,32650],{"xmlns":27},[29,32651,32652,32656],{},[32,32653,32654],{},[35,32655,37],{},[47,32657,37],{"encoding":49},[15,32659,32661],{"className":32660,"ariaHidden":41},[54],[15,32662,32664,32667],{"className":32663},[58],[15,32665],{"className":32666,"style":299},[62],[15,32668,37],{"className":32669,"style":69},[67,68]," 的后代放进 ",[15,32672,32674,32687],{"className":32673,"translate":19},[18],[15,32675,32677],{"className":32676},[23],[25,32678,32679],{"xmlns":27},[29,32680,32681,32685],{},[32,32682,32683],{},[35,32684,3779],{},[47,32686,3779],{"encoding":49},[15,32688,32690],{"className":32689,"ariaHidden":41},[54],[15,32691,32693,32696],{"className":32692},[58],[15,32694],{"className":32695,"style":299},[62],[15,32697,3779],{"className":32698,"style":1396},[67,68],"，就可能在 ",[15,32701,32703,32716],{"className":32702,"translate":19},[18],[15,32704,32706],{"className":32705},[23],[25,32707,32708],{"xmlns":27},[29,32709,32710,32714],{},[32,32711,32712],{},[35,32713,37],{},[47,32715,37],{"encoding":49},[15,32717,32719],{"className":32718,"ariaHidden":41},[54],[15,32720,32722,32725],{"className":32721},[58],[15,32723],{"className":32724,"style":299},[62],[15,32726,37],{"className":32727,"style":69},[67,68],[15,32729,32731,32744],{"className":32730,"translate":19},[18],[15,32732,32734],{"className":32733},[23],[25,32735,32736],{"xmlns":27},[29,32737,32738,32742],{},[32,32739,32740],{},[35,32741,45],{},[47,32743,45],{"encoding":49},[15,32745,32747],{"className":32746,"ariaHidden":41},[54],[15,32748,32750,32753],{"className":32749},[58],[15,32751],{"className":32752,"style":299},[62],[15,32754,45],{"className":32755,"style":82},[67,68]," 之间人为打开一条对撞路径，制造出并不存在的关联。",[11,32758,32759,32760,32763,32764,32767],{},"不过后门准则有一个明显的局限：它要求所有混杂变量",[305,32761,32762],{},"都被观测到、且可以被条件化","。而在现实中，这一要求经常落空。以下这条准则则可以在",[305,32765,32766],{},"存在未观测混杂","的情形下绕过这一困难：",[1314,32769,32770],{},[11,32771,32772,3758,32775,32216,32803,32831,32832,32860,32861,2104,32889,32891,32892,4697,32920,32948,32949,32977,32978,2356,33006,33034,33035,33063,33064],{},[305,32773,32774],{},"定理 3.4（前门准则，Front-door Criterion）",[15,32776,32778,32791],{"className":32777,"translate":19},[18],[15,32779,32781],{"className":32780},[23],[25,32782,32783],{"xmlns":27},[29,32784,32785,32789],{},[32,32786,32787],{},[35,32788,9469],{},[47,32790,9469],{"encoding":49},[15,32792,32794],{"className":32793,"ariaHidden":41},[54],[15,32795,32797,32800],{"className":32796},[58],[15,32798],{"className":32799,"style":299},[62],[15,32801,9469],{"className":32802,"style":2570},[67,68],[15,32804,32806,32819],{"className":32805,"translate":19},[18],[15,32807,32809],{"className":32808},[23],[25,32810,32811],{"xmlns":27},[29,32812,32813,32817],{},[32,32814,32815],{},[35,32816,9469],{},[47,32818,9469],{"encoding":49},[15,32820,32822],{"className":32821,"ariaHidden":41},[54],[15,32823,32825,32828],{"className":32824},[58],[15,32826],{"className":32827,"style":299},[62],[15,32829,9469],{"className":32830,"style":2570},[67,68]," 阻断了所有从 ",[15,32833,32835,32848],{"className":32834,"translate":19},[18],[15,32836,32838],{"className":32837},[23],[25,32839,32840],{"xmlns":27},[29,32841,32842,32846],{},[32,32843,32844],{},[35,32845,37],{},[47,32847,37],{"encoding":49},[15,32849,32851],{"className":32850,"ariaHidden":41},[54],[15,32852,32854,32857],{"className":32853},[58],[15,32855],{"className":32856,"style":299},[62],[15,32858,37],{"className":32859,"style":69},[67,68]," 指向 ",[15,32862,32864,32877],{"className":32863,"translate":19},[18],[15,32865,32867],{"className":32866},[23],[25,32868,32869],{"xmlns":27},[29,32870,32871,32875],{},[32,32872,32873],{},[35,32874,45],{},[47,32876,45],{"encoding":49},[15,32878,32880],{"className":32879,"ariaHidden":41},[54],[15,32881,32883,32886],{"className":32882},[58],[15,32884],{"className":32885,"style":299},[62],[15,32887,45],{"className":32888,"style":82},[67,68],[305,32890,2963],{},"（即 ",[15,32893,32895,32908],{"className":32894,"translate":19},[18],[15,32896,32898],{"className":32897},[23],[25,32899,32900],{"xmlns":27},[29,32901,32902,32906],{},[32,32903,32904],{},[35,32905,37],{},[47,32907,37],{"encoding":49},[15,32909,32911],{"className":32910,"ariaHidden":41},[54],[15,32912,32914,32917],{"className":32913},[58],[15,32915],{"className":32916,"style":299},[62],[15,32918,37],{"className":32919,"style":69},[67,68],[15,32921,32923,32936],{"className":32922,"translate":19},[18],[15,32924,32926],{"className":32925},[23],[25,32927,32928],{"xmlns":27},[29,32929,32930,32934],{},[32,32931,32932],{},[35,32933,45],{},[47,32935,45],{"encoding":49},[15,32937,32939],{"className":32938,"ariaHidden":41},[54],[15,32940,32942,32945],{"className":32941},[58],[15,32943],{"className":32944,"style":299},[62],[15,32946,45],{"className":32947,"style":82},[67,68]," 的全部因果影响都经过 ",[15,32950,32952,32965],{"className":32951,"translate":19},[18],[15,32953,32955],{"className":32954},[23],[25,32956,32957],{"xmlns":27},[29,32958,32959,32963],{},[32,32960,32961],{},[35,32962,9469],{},[47,32964,9469],{"encoding":49},[15,32966,32968],{"className":32967,"ariaHidden":41},[54],[15,32969,32971,32974],{"className":32970},[58],[15,32972],{"className":32973,"style":299},[62],[15,32975,9469],{"className":32976,"style":2570},[67,68]," 传送）；(ii) 不存在从 ",[15,32979,32981,32994],{"className":32980,"translate":19},[18],[15,32982,32984],{"className":32983},[23],[25,32985,32986],{"xmlns":27},[29,32987,32988,32992],{},[32,32989,32990],{},[35,32991,9469],{},[47,32993,9469],{"encoding":49},[15,32995,32997],{"className":32996,"ariaHidden":41},[54],[15,32998,33000,33003],{"className":32999},[58],[15,33001],{"className":33002,"style":299},[62],[15,33004,9469],{"className":33005,"style":2570},[67,68],[15,33007,33009,33022],{"className":33008,"translate":19},[18],[15,33010,33012],{"className":33011},[23],[25,33013,33014],{"xmlns":27},[29,33015,33016,33020],{},[32,33017,33018],{},[35,33019,45],{},[47,33021,45],{"encoding":49},[15,33023,33025],{"className":33024,"ariaHidden":41},[54],[15,33026,33028,33031],{"className":33027},[58],[15,33029],{"className":33030,"style":299},[62],[15,33032,45],{"className":33033,"style":82},[67,68]," 的、未被 ",[15,33036,33038,33051],{"className":33037,"translate":19},[18],[15,33039,33041],{"className":33040},[23],[25,33042,33043],{"xmlns":27},[29,33044,33045,33049],{},[32,33046,33047],{},[35,33048,37],{},[47,33050,37],{"encoding":49},[15,33052,33054],{"className":33053,"ariaHidden":41},[54],[15,33055,33057,33060],{"className":33056},[58],[15,33058],{"className":33059,"style":299},[62],[15,33061,37],{"className":33062,"style":69},[67,68]," 阻断的后门路径。则\n",[15,33065,33067,33161],{"className":33066,"translate":19},[18],[15,33068,33070],{"className":33069},[23],[25,33071,33072],{"xmlns":27},[29,33073,33074,33158],{},[32,33075,33076,33078,33080,33082,33084,33086,33088,33090,33092,33094,33096,33098,33104,33106,33108,33110,33112,33114,33116,33126,33128,33130,33132,33134,33136,33138,33144,33146,33148,33150,33156],{},[35,33077,98],{},[39,33079,102],{"stretchy":101},[35,33081,534],{},[39,33083,170],{},[35,33085,696],{},[35,33087,699],{},[39,33089,102],{"stretchy":101},[35,33091,539],{},[39,33093,111],{"stretchy":101},[39,33095,111],{"stretchy":101},[39,33097,602],{},[863,33099,33100,33102],{},[39,33101,20423],{},[35,33103,9611],{},[35,33105,98],{},[39,33107,102],{"stretchy":101},[35,33109,9611],{},[39,33111,170],{},[35,33113,539],{},[39,33115,111],{"stretchy":101},[863,33117,33118,33120],{},[39,33119,20423],{},[872,33121,33122,33124],{},[35,33123,539],{},[39,33125,880],{"mathvariant":878,"lspace":879,"rspace":879},[35,33127,98],{},[39,33129,102],{"stretchy":101},[35,33131,534],{},[39,33133,170],{},[35,33135,9611],{},[39,33137,42],{"separator":41},[872,33139,33140,33142],{},[35,33141,539],{},[39,33143,880],{"mathvariant":878,"lspace":879,"rspace":879},[39,33145,111],{"stretchy":101},[35,33147,98],{},[39,33149,102],{"stretchy":101},[872,33151,33152,33154],{},[35,33153,539],{},[39,33155,880],{"mathvariant":878,"lspace":879,"rspace":879},[39,33157,111],{"stretchy":101},[47,33159,33160],{"encoding":49},"P(y \\mid do(x)) = \\sum_m P(m \\mid x) \\sum_{x'} P(y \\mid m, x') P(x')",[15,33162,33164,33188,33218,33285,33395],{"className":33163,"ariaHidden":41},[54],[15,33165,33167,33170,33173,33176,33179,33182,33185],{"className":33166},[58],[15,33168],{"className":33169,"style":124},[62],[15,33171,98],{"className":33172,"style":128},[67,68],[15,33174,102],{"className":33175},[132],[15,33177,534],{"className":33178,"style":563},[67,68],[15,33180],{"className":33181,"style":199},[77],[15,33183,170],{"className":33184},[203],[15,33186],{"className":33187,"style":199},[77],[15,33189,33191,33194,33197,33200,33203,33206,33209,33212,33215],{"className":33190},[58],[15,33192],{"className":33193,"style":124},[62],[15,33195,696],{"className":33196},[67,68],[15,33198,699],{"className":33199},[67,68],[15,33201,102],{"className":33202},[132],[15,33204,539],{"className":33205},[67,68],[15,33207,759],{"className":33208},[148],[15,33210],{"className":33211,"style":199},[77],[15,33213,602],{"className":33214},[203],[15,33216],{"className":33217,"style":199},[77],[15,33219,33221,33224,33264,33267,33270,33273,33276,33279,33282],{"className":33220},[58],[15,33222],{"className":33223,"style":20601},[62],[15,33225,33227,33230],{"className":33226},[12772],[15,33228,20423],{"className":33229,"style":12778},[12772,12776,12777],[15,33231,33233],{"className":33232},[918],[15,33234,33236,33256],{"className":33235},[922,923],[15,33237,33239,33253],{"className":33238},[927],[15,33240,33242],{"className":33241,"style":20620},[931],[15,33243,33244,33247],{"style":12794},[15,33245],{"className":33246,"style":940},[939],[15,33248,33250],{"className":33249},[944,945,946,947],[15,33251,9611],{"className":33252},[67,68,947],[15,33254,955],{"className":33255},[954],[15,33257,33259],{"className":33258},[927],[15,33260,33262],{"className":33261,"style":12834},[931],[15,33263],{},[15,33265],{"className":33266,"style":78},[77],[15,33268,98],{"className":33269,"style":128},[67,68],[15,33271,102],{"className":33272},[132],[15,33274,9611],{"className":33275},[67,68],[15,33277],{"className":33278,"style":199},[77],[15,33280,170],{"className":33281},[203],[15,33283],{"className":33284,"style":199},[77],[15,33286,33288,33291,33294,33297,33300,33374,33377,33380,33383,33386,33389,33392],{"className":33287},[58],[15,33289],{"className":33290,"style":20601},[62],[15,33292,539],{"className":33293},[67,68],[15,33295,111],{"className":33296},[148],[15,33298],{"className":33299,"style":78},[77],[15,33301,33303,33306],{"className":33302},[12772],[15,33304,20423],{"className":33305,"style":12778},[12772,12776,12777],[15,33307,33309],{"className":33308},[918],[15,33310,33312,33366],{"className":33311},[922,923],[15,33313,33315,33363],{"className":33314},[927],[15,33316,33319],{"className":33317,"style":33318},[931],"height:0.1783em;",[15,33320,33321,33324],{"style":12794},[15,33322],{"className":33323,"style":940},[939],[15,33325,33327],{"className":33326},[944,945,946,947],[15,33328,33330],{"className":33329},[67,947],[15,33331,33333,33336],{"className":33332},[67,947],[15,33334,539],{"className":33335},[67,68,947],[15,33337,33339],{"className":33338},[918],[15,33340,33342],{"className":33341},[922],[15,33343,33345],{"className":33344},[927],[15,33346,33349],{"className":33347,"style":33348},[931],"height:0.6828em;",[15,33350,33351,33354],{"style":26570},[15,33352],{"className":33353,"style":18417},[939],[15,33355,33357],{"className":33356},[944,18421,15089,947],[15,33358,33360],{"className":33359},[67,947],[15,33361,880],{"className":33362},[67,947],[15,33364,955],{"className":33365},[954],[15,33367,33369],{"className":33368},[927],[15,33370,33372],{"className":33371,"style":12834},[931],[15,33373],{},[15,33375],{"className":33376,"style":78},[77],[15,33378,98],{"className":33379,"style":128},[67,68],[15,33381,102],{"className":33382},[132],[15,33384,534],{"className":33385,"style":563},[67,68],[15,33387],{"className":33388,"style":199},[77],[15,33390,170],{"className":33391},[203],[15,33393],{"className":33394,"style":199},[77],[15,33396,33398,33401,33404,33407,33410,33442,33445,33448,33451,33483],{"className":33397},[58],[15,33399],{"className":33400,"style":980},[62],[15,33402,9611],{"className":33403},[67,68],[15,33405,42],{"className":33406},[73],[15,33408],{"className":33409,"style":78},[77],[15,33411,33413,33416],{"className":33412},[67],[15,33414,539],{"className":33415},[67,68],[15,33417,33419],{"className":33418},[918],[15,33420,33422],{"className":33421},[922],[15,33423,33425],{"className":33424},[927],[15,33426,33428],{"className":33427,"style":999},[931],[15,33429,33430,33433],{"style":1002},[15,33431],{"className":33432,"style":940},[939],[15,33434,33436],{"className":33435},[944,945,946,947],[15,33437,33439],{"className":33438},[67,947],[15,33440,880],{"className":33441},[67,947],[15,33443,111],{"className":33444},[148],[15,33446,98],{"className":33447,"style":128},[67,68],[15,33449,102],{"className":33450},[132],[15,33452,33454,33457],{"className":33453},[67],[15,33455,539],{"className":33456},[67,68],[15,33458,33460],{"className":33459},[918],[15,33461,33463],{"className":33462},[922],[15,33464,33466],{"className":33465},[927],[15,33467,33469],{"className":33468,"style":999},[931],[15,33470,33471,33474],{"style":1002},[15,33472],{"className":33473,"style":940},[939],[15,33475,33477],{"className":33476},[944,945,946,947],[15,33478,33480],{"className":33479},[67,947],[15,33481,880],{"className":33482},[67,947],[15,33484,111],{"className":33485},[148],[1314,33487,33488,33728,33734],{},[11,33489,33490,33493,33494,33522,33523,33574,33575,33626,33627,1400,33699,33727],{},[305,33491,33492],{},"例 3.4"," 回到例 1.2 的吸烟模型，但这次显式承认存在未观测的混杂：设 ",[15,33495,33497,33510],{"className":33496,"translate":19},[18],[15,33498,33500],{"className":33499},[23],[25,33501,33502],{"xmlns":27},[29,33503,33504,33508],{},[32,33505,33506],{},[35,33507,2458],{},[47,33509,2458],{"encoding":49},[15,33511,33513],{"className":33512,"ariaHidden":41},[54],[15,33514,33516,33519],{"className":33515},[58],[15,33517],{"className":33518,"style":299},[62],[15,33520,2458],{"className":33521,"style":2570},[67,68]," 为不可观测的遗传因素，",[15,33524,33526,33544],{"className":33525,"translate":19},[18],[15,33527,33529],{"className":33528},[23],[25,33530,33531],{"xmlns":27},[29,33532,33533,33541],{},[32,33534,33535,33537,33539],{},[35,33536,2458],{},[39,33538,1846],{},[35,33540,37],{},[47,33542,33543],{"encoding":49},"U \\to X",[15,33545,33547,33565],{"className":33546,"ariaHidden":41},[54],[15,33548,33550,33553,33556,33559,33562],{"className":33549},[58],[15,33551],{"className":33552,"style":299},[62],[15,33554,2458],{"className":33555,"style":2570},[67,68],[15,33557],{"className":33558,"style":199},[77],[15,33560,1846],{"className":33561},[203],[15,33563],{"className":33564,"style":199},[77],[15,33566,33568,33571],{"className":33567},[58],[15,33569],{"className":33570,"style":299},[62],[15,33572,37],{"className":33573,"style":69},[67,68],"（吸烟）且 ",[15,33576,33578,33596],{"className":33577,"translate":19},[18],[15,33579,33581],{"className":33580},[23],[25,33582,33583],{"xmlns":27},[29,33584,33585,33593],{},[32,33586,33587,33589,33591],{},[35,33588,2458],{},[39,33590,1846],{},[35,33592,45],{},[47,33594,33595],{"encoding":49},"U \\to Y",[15,33597,33599,33617],{"className":33598,"ariaHidden":41},[54],[15,33600,33602,33605,33608,33611,33614],{"className":33601},[58],[15,33603],{"className":33604,"style":299},[62],[15,33606,2458],{"className":33607,"style":2570},[67,68],[15,33609],{"className":33610,"style":199},[77],[15,33612,1846],{"className":33613},[203],[15,33615],{"className":33616,"style":199},[77],[15,33618,33620,33623],{"className":33619},[58],[15,33621],{"className":33622,"style":299},[62],[15,33624,45],{"className":33625,"style":82},[67,68],"（肺癌）；已知的结构为 ",[15,33628,33630,33651],{"className":33629,"translate":19},[18],[15,33631,33633],{"className":33632},[23],[25,33634,33635],{"xmlns":27},[29,33636,33637,33649],{},[32,33638,33639,33641,33643,33645,33647],{},[35,33640,37],{},[39,33642,1846],{},[35,33644,9469],{},[39,33646,1846],{},[35,33648,45],{},[47,33650,26246],{"encoding":49},[15,33652,33654,33672,33690],{"className":33653,"ariaHidden":41},[54],[15,33655,33657,33660,33663,33666,33669],{"className":33656},[58],[15,33658],{"className":33659,"style":299},[62],[15,33661,37],{"className":33662,"style":69},[67,68],[15,33664],{"className":33665,"style":199},[77],[15,33667,1846],{"className":33668},[203],[15,33670],{"className":33671,"style":199},[77],[15,33673,33675,33678,33681,33684,33687],{"className":33674},[58],[15,33676],{"className":33677,"style":299},[62],[15,33679,9469],{"className":33680,"style":2570},[67,68],[15,33682],{"className":33683,"style":199},[77],[15,33685,1846],{"className":33686},[203],[15,33688],{"className":33689,"style":199},[77],[15,33691,33693,33696],{"className":33692},[58],[15,33694],{"className":33695,"style":299},[62],[15,33697,45],{"className":33698,"style":82},[67,68],[15,33700,33702,33715],{"className":33701,"translate":19},[18],[15,33703,33705],{"className":33704},[23],[25,33706,33707],{"xmlns":27},[29,33708,33709,33713],{},[32,33710,33711],{},[35,33712,9469],{},[47,33714,9469],{"encoding":49},[15,33716,33718],{"className":33717,"ariaHidden":41},[54],[15,33719,33721,33724],{"className":33720},[58],[15,33722],{"className":33723,"style":299},[62],[15,33725,9469],{"className":33726,"style":2570},[67,68]," 为焦油沉积。",[4118,33729,33732],{"className":33730,"code":33731,"language":4123},[4121],"            U        （不可观测）\n       ╱         ╲\n      ↓           ↓\n      X ──→ M ──→ Y\n",[4125,33733,33731],{"__ignoreMap":4127},[11,33735,33736,33737,431,33765,33793,33794,33867,33868,33896,33897,33925,33926,6667,33998,2356,34026,34054,34055,34083,34084,34503,34504,34507],{},"此时 ",[15,33738,33740,33753],{"className":33739,"translate":19},[18],[15,33741,33743],{"className":33742},[23],[25,33744,33745],{"xmlns":27},[29,33746,33747,33751],{},[32,33748,33749],{},[35,33750,37],{},[47,33752,37],{"encoding":49},[15,33754,33756],{"className":33755,"ariaHidden":41},[54],[15,33757,33759,33762],{"className":33758},[58],[15,33760],{"className":33761,"style":299},[62],[15,33763,37],{"className":33764,"style":69},[67,68],[15,33766,33768,33781],{"className":33767,"translate":19},[18],[15,33769,33771],{"className":33770},[23],[25,33772,33773],{"xmlns":27},[29,33774,33775,33779],{},[32,33776,33777],{},[35,33778,45],{},[47,33780,45],{"encoding":49},[15,33782,33784],{"className":33783,"ariaHidden":41},[54],[15,33785,33787,33790],{"className":33786},[58],[15,33788],{"className":33789,"style":299},[62],[15,33791,45],{"className":33792,"style":82},[67,68]," 之间的后门路径 ",[15,33795,33797,33819],{"className":33796,"translate":19},[18],[15,33798,33800],{"className":33799},[23],[25,33801,33802],{"xmlns":27},[29,33803,33804,33816],{},[32,33805,33806,33808,33810,33812,33814],{},[35,33807,37],{},[39,33809,4882],{},[35,33811,2458],{},[39,33813,1846],{},[35,33815,45],{},[47,33817,33818],{"encoding":49},"X \\leftarrow U \\to Y",[15,33820,33822,33840,33858],{"className":33821,"ariaHidden":41},[54],[15,33823,33825,33828,33831,33834,33837],{"className":33824},[58],[15,33826],{"className":33827,"style":299},[62],[15,33829,37],{"className":33830,"style":69},[67,68],[15,33832],{"className":33833,"style":199},[77],[15,33835,4882],{"className":33836},[203],[15,33838],{"className":33839,"style":199},[77],[15,33841,33843,33846,33849,33852,33855],{"className":33842},[58],[15,33844],{"className":33845,"style":299},[62],[15,33847,2458],{"className":33848,"style":2570},[67,68],[15,33850],{"className":33851,"style":199},[77],[15,33853,1846],{"className":33854},[203],[15,33856],{"className":33857,"style":199},[77],[15,33859,33861,33864],{"className":33860},[58],[15,33862],{"className":33863,"style":299},[62],[15,33865,45],{"className":33866,"style":82},[67,68]," 无法被阻断（",[15,33869,33871,33884],{"className":33870,"translate":19},[18],[15,33872,33874],{"className":33873},[23],[25,33875,33876],{"xmlns":27},[29,33877,33878,33882],{},[32,33879,33880],{},[35,33881,2458],{},[47,33883,2458],{"encoding":49},[15,33885,33887],{"className":33886,"ariaHidden":41},[54],[15,33888,33890,33893],{"className":33889},[58],[15,33891],{"className":33892,"style":299},[62],[15,33894,2458],{"className":33895,"style":2570},[67,68]," 不可观测），后门准则失效。但 ",[15,33898,33900,33913],{"className":33899,"translate":19},[18],[15,33901,33903],{"className":33902},[23],[25,33904,33905],{"xmlns":27},[29,33906,33907,33911],{},[32,33908,33909],{},[35,33910,9469],{},[47,33912,9469],{"encoding":49},[15,33914,33916],{"className":33915,"ariaHidden":41},[54],[15,33917,33919,33922],{"className":33918},[58],[15,33920],{"className":33921,"style":299},[62],[15,33923,9469],{"className":33924,"style":2570},[67,68]," 阻断了唯一的因果路径 ",[15,33927,33929,33950],{"className":33928,"translate":19},[18],[15,33930,33932],{"className":33931},[23],[25,33933,33934],{"xmlns":27},[29,33935,33936,33948],{},[32,33937,33938,33940,33942,33944,33946],{},[35,33939,37],{},[39,33941,1846],{},[35,33943,9469],{},[39,33945,1846],{},[35,33947,45],{},[47,33949,26246],{"encoding":49},[15,33951,33953,33971,33989],{"className":33952,"ariaHidden":41},[54],[15,33954,33956,33959,33962,33965,33968],{"className":33955},[58],[15,33957],{"className":33958,"style":299},[62],[15,33960,37],{"className":33961,"style":69},[67,68],[15,33963],{"className":33964,"style":199},[77],[15,33966,1846],{"className":33967},[203],[15,33969],{"className":33970,"style":199},[77],[15,33972,33974,33977,33980,33983,33986],{"className":33973},[58],[15,33975],{"className":33976,"style":299},[62],[15,33978,9469],{"className":33979,"style":2570},[67,68],[15,33981],{"className":33982,"style":199},[77],[15,33984,1846],{"className":33985},[203],[15,33987],{"className":33988,"style":199},[77],[15,33990,33992,33995],{"className":33991},[58],[15,33993],{"className":33994,"style":299},[62],[15,33996,45],{"className":33997,"style":82},[67,68],[15,33999,34001,34014],{"className":34000,"translate":19},[18],[15,34002,34004],{"className":34003},[23],[25,34005,34006],{"xmlns":27},[29,34007,34008,34012],{},[32,34009,34010],{},[35,34011,9469],{},[47,34013,9469],{"encoding":49},[15,34015,34017],{"className":34016,"ariaHidden":41},[54],[15,34018,34020,34023],{"className":34019},[58],[15,34021],{"className":34022,"style":299},[62],[15,34024,9469],{"className":34025,"style":2570},[67,68],[15,34027,34029,34042],{"className":34028,"translate":19},[18],[15,34030,34032],{"className":34031},[23],[25,34033,34034],{"xmlns":27},[29,34035,34036,34040],{},[32,34037,34038],{},[35,34039,45],{},[47,34041,45],{"encoding":49},[15,34043,34045],{"className":34044,"ariaHidden":41},[54],[15,34046,34048,34051],{"className":34047},[58],[15,34049],{"className":34050,"style":299},[62],[15,34052,45],{"className":34053,"style":82},[67,68]," 不存在除经由 ",[15,34056,34058,34071],{"className":34057,"translate":19},[18],[15,34059,34061],{"className":34060},[23],[25,34062,34063],{"xmlns":27},[29,34064,34065,34069],{},[32,34066,34067],{},[35,34068,37],{},[47,34070,37],{"encoding":49},[15,34072,34074],{"className":34073,"ariaHidden":41},[54],[15,34075,34077,34080],{"className":34076},[58],[15,34078],{"className":34079,"style":299},[62],[15,34081,37],{"className":34082,"style":69},[67,68]," 之外的后门路径，因此前门准则给出\n",[15,34085,34087,34180],{"className":34086,"translate":19},[18],[15,34088,34090],{"className":34089},[23],[25,34091,34092],{"xmlns":27},[29,34093,34094,34178],{},[32,34095,34096,34098,34100,34102,34104,34106,34108,34110,34112,34114,34116,34118,34124,34126,34128,34130,34132,34134,34136,34146,34148,34150,34152,34154,34156,34158,34164,34166,34168,34170,34176],{},[35,34097,98],{},[39,34099,102],{"stretchy":101},[35,34101,534],{},[39,34103,170],{},[35,34105,696],{},[35,34107,699],{},[39,34109,102],{"stretchy":101},[35,34111,539],{},[39,34113,111],{"stretchy":101},[39,34115,111],{"stretchy":101},[39,34117,602],{},[863,34119,34120,34122],{},[39,34121,20423],{},[35,34123,9611],{},[35,34125,98],{},[39,34127,102],{"stretchy":101},[35,34129,9611],{},[39,34131,170],{},[35,34133,539],{},[39,34135,111],{"stretchy":101},[863,34137,34138,34140],{},[39,34139,20423],{},[872,34141,34142,34144],{},[35,34143,539],{},[39,34145,880],{"mathvariant":878,"lspace":879,"rspace":879},[35,34147,98],{},[39,34149,102],{"stretchy":101},[35,34151,534],{},[39,34153,170],{},[35,34155,9611],{},[39,34157,42],{"separator":41},[872,34159,34160,34162],{},[35,34161,539],{},[39,34163,880],{"mathvariant":878,"lspace":879,"rspace":879},[39,34165,111],{"stretchy":101},[35,34167,98],{},[39,34169,102],{"stretchy":101},[872,34171,34172,34174],{},[35,34173,539],{},[39,34175,880],{"mathvariant":878,"lspace":879,"rspace":879},[39,34177,111],{"stretchy":101},[47,34179,33160],{"encoding":49},[15,34181,34183,34207,34237,34304,34412],{"className":34182,"ariaHidden":41},[54],[15,34184,34186,34189,34192,34195,34198,34201,34204],{"className":34185},[58],[15,34187],{"className":34188,"style":124},[62],[15,34190,98],{"className":34191,"style":128},[67,68],[15,34193,102],{"className":34194},[132],[15,34196,534],{"className":34197,"style":563},[67,68],[15,34199],{"className":34200,"style":199},[77],[15,34202,170],{"className":34203},[203],[15,34205],{"className":34206,"style":199},[77],[15,34208,34210,34213,34216,34219,34222,34225,34228,34231,34234],{"className":34209},[58],[15,34211],{"className":34212,"style":124},[62],[15,34214,696],{"className":34215},[67,68],[15,34217,699],{"className":34218},[67,68],[15,34220,102],{"className":34221},[132],[15,34223,539],{"className":34224},[67,68],[15,34226,759],{"className":34227},[148],[15,34229],{"className":34230,"style":199},[77],[15,34232,602],{"className":34233},[203],[15,34235],{"className":34236,"style":199},[77],[15,34238,34240,34243,34283,34286,34289,34292,34295,34298,34301],{"className":34239},[58],[15,34241],{"className":34242,"style":20601},[62],[15,34244,34246,34249],{"className":34245},[12772],[15,34247,20423],{"className":34248,"style":12778},[12772,12776,12777],[15,34250,34252],{"className":34251},[918],[15,34253,34255,34275],{"className":34254},[922,923],[15,34256,34258,34272],{"className":34257},[927],[15,34259,34261],{"className":34260,"style":20620},[931],[15,34262,34263,34266],{"style":12794},[15,34264],{"className":34265,"style":940},[939],[15,34267,34269],{"className":34268},[944,945,946,947],[15,34270,9611],{"className":34271},[67,68,947],[15,34273,955],{"className":34274},[954],[15,34276,34278],{"className":34277},[927],[15,34279,34281],{"className":34280,"style":12834},[931],[15,34282],{},[15,34284],{"className":34285,"style":78},[77],[15,34287,98],{"className":34288,"style":128},[67,68],[15,34290,102],{"className":34291},[132],[15,34293,9611],{"className":34294},[67,68],[15,34296],{"className":34297,"style":199},[77],[15,34299,170],{"className":34300},[203],[15,34302],{"className":34303,"style":199},[77],[15,34305,34307,34310,34313,34316,34319,34391,34394,34397,34400,34403,34406,34409],{"className":34306},[58],[15,34308],{"className":34309,"style":20601},[62],[15,34311,539],{"className":34312},[67,68],[15,34314,111],{"className":34315},[148],[15,34317],{"className":34318,"style":78},[77],[15,34320,34322,34325],{"className":34321},[12772],[15,34323,20423],{"className":34324,"style":12778},[12772,12776,12777],[15,34326,34328],{"className":34327},[918],[15,34329,34331,34383],{"className":34330},[922,923],[15,34332,34334,34380],{"className":34333},[927],[15,34335,34337],{"className":34336,"style":33318},[931],[15,34338,34339,34342],{"style":12794},[15,34340],{"className":34341,"style":940},[939],[15,34343,34345],{"className":34344},[944,945,946,947],[15,34346,34348],{"className":34347},[67,947],[15,34349,34351,34354],{"className":34350},[67,947],[15,34352,539],{"className":34353},[67,68,947],[15,34355,34357],{"className":34356},[918],[15,34358,34360],{"className":34359},[922],[15,34361,34363],{"className":34362},[927],[15,34364,34366],{"className":34365,"style":33348},[931],[15,34367,34368,34371],{"style":26570},[15,34369],{"className":34370,"style":18417},[939],[15,34372,34374],{"className":34373},[944,18421,15089,947],[15,34375,34377],{"className":34376},[67,947],[15,34378,880],{"className":34379},[67,947],[15,34381,955],{"className":34382},[954],[15,34384,34386],{"className":34385},[927],[15,34387,34389],{"className":34388,"style":12834},[931],[15,34390],{},[15,34392],{"className":34393,"style":78},[77],[15,34395,98],{"className":34396,"style":128},[67,68],[15,34398,102],{"className":34399},[132],[15,34401,534],{"className":34402,"style":563},[67,68],[15,34404],{"className":34405,"style":199},[77],[15,34407,170],{"className":34408},[203],[15,34410],{"className":34411,"style":199},[77],[15,34413,34415,34418,34421,34424,34427,34459,34462,34465,34468,34500],{"className":34414},[58],[15,34416],{"className":34417,"style":980},[62],[15,34419,9611],{"className":34420},[67,68],[15,34422,42],{"className":34423},[73],[15,34425],{"className":34426,"style":78},[77],[15,34428,34430,34433],{"className":34429},[67],[15,34431,539],{"className":34432},[67,68],[15,34434,34436],{"className":34435},[918],[15,34437,34439],{"className":34438},[922],[15,34440,34442],{"className":34441},[927],[15,34443,34445],{"className":34444,"style":999},[931],[15,34446,34447,34450],{"style":1002},[15,34448],{"className":34449,"style":940},[939],[15,34451,34453],{"className":34452},[944,945,946,947],[15,34454,34456],{"className":34455},[67,947],[15,34457,880],{"className":34458},[67,947],[15,34460,111],{"className":34461},[148],[15,34463,98],{"className":34464,"style":128},[67,68],[15,34466,102],{"className":34467},[132],[15,34469,34471,34474],{"className":34470},[67],[15,34472,539],{"className":34473},[67,68],[15,34475,34477],{"className":34476},[918],[15,34478,34480],{"className":34479},[922],[15,34481,34483],{"className":34482},[927],[15,34484,34486],{"className":34485,"style":999},[931],[15,34487,34488,34491],{"style":1002},[15,34489],{"className":34490,"style":940},[939],[15,34492,34494],{"className":34493},[944,945,946,947],[15,34495,34497],{"className":34496},[67,947],[15,34498,880],{"className":34499},[67,947],[15,34501,111],{"className":34502},[148],"\n即：",[305,34505,34506],{},"即便存在不可观测的混杂，只要有一个满足前门条件的中介变量，吸烟对肺癌的因果效应仍然可以从纯观测数据中识别出来。"," 这是因果图相对于纯统计框架的一个相当反直觉的力量所在——它把「哪些数据是可用的」与「哪些机制是可靠的」分开处理，从而在因果推断看似无从下手之处找回了一条通路。",[11,34509,34510],{},"前门准则同时也是 2.1 节中「半马尔可夫型 SCM」这一概念唯一的实际用武之地：当外生变量之间存在相关的隐藏噪声时，正是这类准则在继续保证可识别性。但必须强调，前门准则的适用面很窄——它要求恰好存在一个阻断全部因果路径的中介变量，并且该中介与结果之间不存在未观测的混杂。对一般结构的半马尔可夫型 SCM，可识别性并不自动成立。",[11,34512,34513,34514,34542,34543,34546],{},"这一准则将第一部分中「该控制哪些变量」的图论直觉，与第三部分的干预定义精确对接：叉结构中的混杂因子正是典型的满足后门准则的调整集合，而对撞结构中的变量则应被排除在 ",[15,34515,34517,34530],{"className":34516,"translate":19},[18],[15,34518,34520],{"className":34519},[23],[25,34521,34522],{"xmlns":27},[29,34523,34524,34528],{},[32,34525,34526],{},[35,34527,3779],{},[47,34529,3779],{"encoding":49},[15,34531,34533],{"className":34532,"ariaHidden":41},[54],[15,34534,34536,34539],{"className":34535},[58],[15,34537],{"className":34538,"style":299},[62],[15,34540,3779],{"className":34541,"style":1396},[67,68]," 之外。这一对应关系并非巧合：",[305,34544,34545],{},"满足后门准则的调整集合，正是一个能够阻断全部非因果路径的 d-分离集合","，第一部分与第三部分在此处精确接榫。至此，本文从因果图出发、经由结构因果模型、最终落脚于结构方程与 do-演算的逻辑链条已经闭合。剩下要问的是：这一体系与统计学、计量经济学中既有的因果推断工具相比处于什么位置，以及它的成立依赖哪些假设。",[1305,34548,34549],{"id":34549},"相邻框架与适用边界",[11,34551,34552],{},"本文至此勾勒的是一套自洽的形式化体系。但因果推断在统计学、计量经济学与机器学习中并非只有这一种语言。本部分把它与两个最重要的相邻传统作对照，说明各自的着眼点与互补之处，最后梳理该体系成立所依赖的假设与边界。",[1309,34554,34556],{"id":34555},"_41-潜在结果框架一种等价的语言","4.1 潜在结果框架：一种等价的语言",[11,34558,34559,34560,34563],{},"与结构因果模型并行发展的，是由 Rubin 等人推动的",[305,34561,34562],{},"潜在结果框架（Potential Outcome Framework，亦称 Rubin 因果模型）","。它不诉诸图，而是从个体层面的潜在结果出发：",[1314,34565,34566],{},[11,34567,34568,6354,34571,34645,34646,34674,34675,34760,34761,34846,34847,35010,35011,2249],{},[305,34569,34570],{},"定义 4.1（潜在结果与因果效应）",[15,34572,34574,34600],{"className":34573,"translate":19},[18],[15,34575,34577],{"className":34576},[23],[25,34578,34579],{"xmlns":27},[29,34580,34581,34597],{},[32,34582,34583,34585,34587,34589,34591,34593,34595],{},[35,34584,37],{},[39,34586,1696],{},[39,34588,1419],{"stretchy":101},[1425,34590,2461],{},[39,34592,42],{"separator":41},[1425,34594,1427],{},[39,34596,1444],{"stretchy":101},[47,34598,34599],{"encoding":49},"X \\in \\{0,1\\}",[15,34601,34603,34621],{"className":34602,"ariaHidden":41},[54],[15,34604,34606,34609,34612,34615,34618],{"className":34605},[58],[15,34607],{"className":34608,"style":6645},[62],[15,34610,37],{"className":34611,"style":69},[67,68],[15,34613],{"className":34614,"style":199},[77],[15,34616,1696],{"className":34617},[203],[15,34619],{"className":34620,"style":199},[77],[15,34622,34624,34627,34630,34633,34636,34639,34642],{"className":34623},[58],[15,34625],{"className":34626,"style":124},[62],[15,34628,1419],{"className":34629},[132],[15,34631,2461],{"className":34632},[67],[15,34634,42],{"className":34635},[73],[15,34637],{"className":34638,"style":78},[77],[15,34640,1427],{"className":34641},[67],[15,34643,1444],{"className":34644},[148]," 为处理指示变量。对每个个体 ",[15,34647,34649,34662],{"className":34648,"translate":19},[18],[15,34650,34652],{"className":34651},[23],[25,34653,34654],{"xmlns":27},[29,34655,34656,34660],{},[32,34657,34658],{},[35,34659,1682],{},[47,34661,1682],{"encoding":49},[15,34663,34665],{"className":34664,"ariaHidden":41},[54],[15,34666,34668,34671],{"className":34667},[58],[15,34669],{"className":34670,"style":11284},[62],[15,34672,1682],{"className":34673},[67,68],"，定义两个潜在结果 ",[15,34676,34678,34702],{"className":34677,"translate":19},[18],[15,34679,34681],{"className":34680},[23],[25,34682,34683],{"xmlns":27},[29,34684,34685,34699],{},[32,34686,34687,34693,34695,34697],{},[863,34688,34689,34691],{},[35,34690,45],{},[35,34692,1682],{},[39,34694,102],{"stretchy":101},[1425,34696,1427],{},[39,34698,111],{"stretchy":101},[47,34700,34701],{"encoding":49},"Y_i(1)",[15,34703,34705],{"className":34704,"ariaHidden":41},[54],[15,34706,34708,34711,34751,34754,34757],{"className":34707},[58],[15,34709],{"className":34710,"style":124},[62],[15,34712,34714,34717],{"className":34713},[67],[15,34715,45],{"className":34716,"style":82},[67,68],[15,34718,34720],{"className":34719},[918],[15,34721,34723,34743],{"className":34722},[922,923],[15,34724,34726,34740],{"className":34725},[927],[15,34727,34729],{"className":34728,"style":1733},[931],[15,34730,34731,34734],{"style":1499},[15,34732],{"className":34733,"style":940},[939],[15,34735,34737],{"className":34736},[944,945,946,947],[15,34738,1682],{"className":34739},[67,68,947],[15,34741,955],{"className":34742},[954],[15,34744,34746],{"className":34745},[927],[15,34747,34749],{"className":34748,"style":962},[931],[15,34750],{},[15,34752,102],{"className":34753},[132],[15,34755,1427],{"className":34756},[67],[15,34758,111],{"className":34759},[148],"（接受处理时的结果）与 ",[15,34762,34764,34788],{"className":34763,"translate":19},[18],[15,34765,34767],{"className":34766},[23],[25,34768,34769],{"xmlns":27},[29,34770,34771,34785],{},[32,34772,34773,34779,34781,34783],{},[863,34774,34775,34777],{},[35,34776,45],{},[35,34778,1682],{},[39,34780,102],{"stretchy":101},[1425,34782,2461],{},[39,34784,111],{"stretchy":101},[47,34786,34787],{"encoding":49},"Y_i(0)",[15,34789,34791],{"className":34790,"ariaHidden":41},[54],[15,34792,34794,34797,34837,34840,34843],{"className":34793},[58],[15,34795],{"className":34796,"style":124},[62],[15,34798,34800,34803],{"className":34799},[67],[15,34801,45],{"className":34802,"style":82},[67,68],[15,34804,34806],{"className":34805},[918],[15,34807,34809,34829],{"className":34808},[922,923],[15,34810,34812,34826],{"className":34811},[927],[15,34813,34815],{"className":34814,"style":1733},[931],[15,34816,34817,34820],{"style":1499},[15,34818],{"className":34819,"style":940},[939],[15,34821,34823],{"className":34822},[944,945,946,947],[15,34824,1682],{"className":34825},[67,68,947],[15,34827,955],{"className":34828},[954],[15,34830,34832],{"className":34831},[927],[15,34833,34835],{"className":34834,"style":962},[931],[15,34836],{},[15,34838,102],{"className":34839},[132],[15,34841,2461],{"className":34842},[67],[15,34844,111],{"className":34845},[148],"（未接受处理时的结果）。个体因果效应定义为 ",[15,34848,34850,34888],{"className":34849,"translate":19},[18],[15,34851,34853],{"className":34852},[23],[25,34854,34855],{"xmlns":27},[29,34856,34857,34885],{},[32,34858,34859,34865,34867,34869,34871,34873,34879,34881,34883],{},[863,34860,34861,34863],{},[35,34862,45],{},[35,34864,1682],{},[39,34866,102],{"stretchy":101},[1425,34868,1427],{},[39,34870,111],{"stretchy":101},[39,34872,14235],{},[863,34874,34875,34877],{},[35,34876,45],{},[35,34878,1682],{},[39,34880,102],{"stretchy":101},[1425,34882,2461],{},[39,34884,111],{"stretchy":101},[47,34886,34887],{"encoding":49},"Y_i(1) - Y_i(0)",[15,34889,34891,34955],{"className":34890,"ariaHidden":41},[54],[15,34892,34894,34897,34937,34940,34943,34946,34949,34952],{"className":34893},[58],[15,34895],{"className":34896,"style":124},[62],[15,34898,34900,34903],{"className":34899},[67],[15,34901,45],{"className":34902,"style":82},[67,68],[15,34904,34906],{"className":34905},[918],[15,34907,34909,34929],{"className":34908},[922,923],[15,34910,34912,34926],{"className":34911},[927],[15,34913,34915],{"className":34914,"style":1733},[931],[15,34916,34917,34920],{"style":1499},[15,34918],{"className":34919,"style":940},[939],[15,34921,34923],{"className":34922},[944,945,946,947],[15,34924,1682],{"className":34925},[67,68,947],[15,34927,955],{"className":34928},[954],[15,34930,34932],{"className":34931},[927],[15,34933,34935],{"className":34934,"style":962},[931],[15,34936],{},[15,34938,102],{"className":34939},[132],[15,34941,1427],{"className":34942},[67],[15,34944,111],{"className":34945},[148],[15,34947],{"className":34948,"style":82},[77],[15,34950,14235],{"className":34951},[1648],[15,34953],{"className":34954,"style":82},[77],[15,34956,34958,34961,35001,35004,35007],{"className":34957},[58],[15,34959],{"className":34960,"style":124},[62],[15,34962,34964,34967],{"className":34963},[67],[15,34965,45],{"className":34966,"style":82},[67,68],[15,34968,34970],{"className":34969},[918],[15,34971,34973,34993],{"className":34972},[922,923],[15,34974,34976,34990],{"className":34975},[927],[15,34977,34979],{"className":34978,"style":1733},[931],[15,34980,34981,34984],{"style":1499},[15,34982],{"className":34983,"style":940},[939],[15,34985,34987],{"className":34986},[944,945,946,947],[15,34988,1682],{"className":34989},[67,68,947],[15,34991,955],{"className":34992},[954],[15,34994,34996],{"className":34995},[927],[15,34997,34999],{"className":34998,"style":962},[931],[15,35000],{},[15,35002,102],{"className":35003},[132],[15,35005,2461],{"className":35006},[67],[15,35008,111],{"className":35009},[148],"，平均处理效应定义为 ",[15,35012,35014,35061],{"className":35013,"translate":19},[18],[15,35015,35017],{"className":35016},[23],[25,35018,35019],{"xmlns":27},[29,35020,35021,35058],{},[32,35022,35023,35032,35034,35036,35038,35040,35042,35044,35046,35048,35050,35052,35054,35056],{},[32,35024,35025,35028,35030],{},[35,35026,35027],{"mathvariant":878},"A",[35,35029,26375],{"mathvariant":878},[35,35031,1348],{"mathvariant":878},[39,35033,602],{},[35,35035,1348],{"mathvariant":13815},[39,35037,13818],{"stretchy":101},[35,35039,45],{},[39,35041,102],{"stretchy":101},[1425,35043,1427],{},[39,35045,111],{"stretchy":101},[39,35047,14235],{},[35,35049,45],{},[39,35051,102],{"stretchy":101},[1425,35053,2461],{},[39,35055,111],{"stretchy":101},[39,35057,13827],{"stretchy":101},[47,35059,35060],{"encoding":49},"\\mathrm{ATE} = \\mathbb{E}[Y(1) - Y(0)]",[15,35062,35064,35086,35119],{"className":35063,"ariaHidden":41},[54],[15,35065,35067,35070,35077,35080,35083],{"className":35066},[58],[15,35068],{"className":35069,"style":299},[62],[15,35071,35073],{"className":35072},[67],[15,35074,35076],{"className":35075},[67,10382],"ATE",[15,35078],{"className":35079,"style":199},[77],[15,35081,602],{"className":35082},[203],[15,35084],{"className":35085,"style":199},[77],[15,35087,35089,35092,35095,35098,35101,35104,35107,35110,35113,35116],{"className":35088},[58],[15,35090],{"className":35091,"style":124},[62],[15,35093,1348],{"className":35094},[67,26448],[15,35096,13818],{"className":35097},[132],[15,35099,45],{"className":35100,"style":82},[67,68],[15,35102,102],{"className":35103},[132],[15,35105,1427],{"className":35106},[67],[15,35108,111],{"className":35109},[148],[15,35111],{"className":35112,"style":82},[77],[15,35114,14235],{"className":35115},[1648],[15,35117],{"className":35118,"style":82},[77],[15,35120,35122,35125,35128,35131,35134],{"className":35121},[58],[15,35123],{"className":35124,"style":124},[62],[15,35126,45],{"className":35127,"style":82},[67,68],[15,35129,102],{"className":35130},[132],[15,35132,2461],{"className":35133},[67],[15,35135,35137],{"className":35136},[148],")]",[11,35139,35140,35141,35144,35145,35272],{},"这一框架的核心困难称作",[305,35142,35143],{},"因果推断的根本问题（Fundamental Problem of Causal Inference）","：对任何个体，我们只能观测到 ",[15,35146,35148,35176],{"className":35147,"translate":19},[18],[15,35149,35151],{"className":35150},[23],[25,35152,35153],{"xmlns":27},[29,35154,35155,35173],{},[32,35156,35157,35163,35165,35171],{},[863,35158,35159,35161],{},[35,35160,45],{},[35,35162,1682],{},[39,35164,102],{"stretchy":101},[863,35166,35167,35169],{},[35,35168,37],{},[35,35170,1682],{},[39,35172,111],{"stretchy":101},[47,35174,35175],{"encoding":49},"Y_i(X_i)",[15,35177,35179],{"className":35178,"ariaHidden":41},[54],[15,35180,35182,35185,35225,35228,35269],{"className":35181},[58],[15,35183],{"className":35184,"style":124},[62],[15,35186,35188,35191],{"className":35187},[67],[15,35189,45],{"className":35190,"style":82},[67,68],[15,35192,35194],{"className":35193},[918],[15,35195,35197,35217],{"className":35196},[922,923],[15,35198,35200,35214],{"className":35199},[927],[15,35201,35203],{"className":35202,"style":1733},[931],[15,35204,35205,35208],{"style":1499},[15,35206],{"className":35207,"style":940},[939],[15,35209,35211],{"className":35210},[944,945,946,947],[15,35212,1682],{"className":35213},[67,68,947],[15,35215,955],{"className":35216},[954],[15,35218,35220],{"className":35219},[927],[15,35221,35223],{"className":35222,"style":962},[931],[15,35224],{},[15,35226,102],{"className":35227},[132],[15,35229,35231,35234],{"className":35230},[67],[15,35232,37],{"className":35233,"style":69},[67,68],[15,35235,35237],{"className":35236},[918],[15,35238,35240,35261],{"className":35239},[922,923],[15,35241,35243,35258],{"className":35242},[927],[15,35244,35246],{"className":35245,"style":1733},[931],[15,35247,35249,35252],{"style":35248},"top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;",[15,35250],{"className":35251,"style":940},[939],[15,35253,35255],{"className":35254},[944,945,946,947],[15,35256,1682],{"className":35257},[67,68,947],[15,35259,955],{"className":35260},[954],[15,35262,35264],{"className":35263},[927],[15,35265,35267],{"className":35266,"style":962},[931],[15,35268],{},[15,35270,111],{"className":35271},[148],"，另一个潜在结果永远缺失。因此个体因果效应原则上不可观测，只能转而估计总体层面的量。",[11,35274,35275,35276,35361,35362,35532,35533,35561,35562,35655,35656,35659],{},"这与本文 3.3 节的三步算法形成直接对照：潜在结果框架中的 ",[15,35277,35279,35303],{"className":35278,"translate":19},[18],[15,35280,35282],{"className":35281},[23],[25,35283,35284],{"xmlns":27},[29,35285,35286,35300],{},[32,35287,35288,35294,35296,35298],{},[863,35289,35290,35292],{},[35,35291,45],{},[35,35293,1682],{},[39,35295,102],{"stretchy":101},[35,35297,539],{},[39,35299,111],{"stretchy":101},[47,35301,35302],{"encoding":49},"Y_i(x)",[15,35304,35306],{"className":35305,"ariaHidden":41},[54],[15,35307,35309,35312,35352,35355,35358],{"className":35308},[58],[15,35310],{"className":35311,"style":124},[62],[15,35313,35315,35318],{"className":35314},[67],[15,35316,45],{"className":35317,"style":82},[67,68],[15,35319,35321],{"className":35320},[918],[15,35322,35324,35344],{"className":35323},[922,923],[15,35325,35327,35341],{"className":35326},[927],[15,35328,35330],{"className":35329,"style":1733},[931],[15,35331,35332,35335],{"style":1499},[15,35333],{"className":35334,"style":940},[939],[15,35336,35338],{"className":35337},[944,945,946,947],[15,35339,1682],{"className":35340},[67,68,947],[15,35342,955],{"className":35343},[954],[15,35345,35347],{"className":35346},[927],[15,35348,35350],{"className":35349,"style":962},[931],[15,35351],{},[15,35353,102],{"className":35354},[132],[15,35356,539],{"className":35357},[67,68],[15,35359,111],{"className":35360},[148]," 正是 SCM 中的 ",[15,35363,35365,35397],{"className":35364,"translate":19},[18],[15,35366,35368],{"className":35367},[23],[25,35369,35370],{"xmlns":27},[29,35371,35372,35394],{},[32,35373,35374,35384,35386,35392],{},[863,35375,35376,35378],{},[35,35377,45],{},[863,35379,35380,35382],{},[35,35381,9469],{},[35,35383,539],{},[39,35385,102],{"stretchy":101},[863,35387,35388,35390],{},[35,35389,13778],{},[35,35391,1682],{},[39,35393,111],{"stretchy":101},[47,35395,35396],{"encoding":49},"Y_{M_x}(u_i)",[15,35398,35400],{"className":35399,"ariaHidden":41},[54],[15,35401,35403,35406,35486,35489,35529],{"className":35402},[58],[15,35404],{"className":35405,"style":18362},[62],[15,35407,35409,35412],{"className":35408},[67],[15,35410,45],{"className":35411,"style":82},[67,68],[15,35413,35415],{"className":35414},[918],[15,35416,35418,35478],{"className":35417},[922,923],[15,35419,35421,35475],{"className":35420},[927],[15,35422,35424],{"className":35423,"style":7358},[931],[15,35425,35426,35429],{"style":1499},[15,35427],{"className":35428,"style":940},[939],[15,35430,35432],{"className":35431},[944,945,946,947],[15,35433,35435],{"className":35434},[67,947],[15,35436,35438,35441],{"className":35437},[67,947],[15,35439,9469],{"className":35440,"style":2570},[67,68,947],[15,35442,35444],{"className":35443},[918],[15,35445,35447,35467],{"className":35446},[922,923],[15,35448,35450,35464],{"className":35449},[927],[15,35451,35453],{"className":35452,"style":18410},[931],[15,35454,35455,35458],{"style":18413},[15,35456],{"className":35457,"style":18417},[939],[15,35459,35461],{"className":35460},[944,18421,15089,947],[15,35462,539],{"className":35463},[67,68,947],[15,35465,955],{"className":35466},[954],[15,35468,35470],{"className":35469},[927],[15,35471,35473],{"className":35472,"style":18434},[931],[15,35474],{},[15,35476,955],{"className":35477},[954],[15,35479,35481],{"className":35480},[927],[15,35482,35484],{"className":35483,"style":18446},[931],[15,35485],{},[15,35487,102],{"className":35488},[132],[15,35490,35492,35495],{"className":35491},[67],[15,35493,13778],{"className":35494},[67,68],[15,35496,35498],{"className":35497},[918],[15,35499,35501,35521],{"className":35500},[922,923],[15,35502,35504,35518],{"className":35503},[927],[15,35505,35507],{"className":35506,"style":1733},[931],[15,35508,35509,35512],{"style":7289},[15,35510],{"className":35511,"style":940},[939],[15,35513,35515],{"className":35514},[944,945,946,947],[15,35516,1682],{"className":35517},[67,68,947],[15,35519,955],{"className":35520},[954],[15,35522,35524],{"className":35523},[927],[15,35525,35527],{"className":35526,"style":962},[931],[15,35528],{},[15,35530,111],{"className":35531},[148],"，个体 ",[15,35534,35536,35549],{"className":35535,"translate":19},[18],[15,35537,35539],{"className":35538},[23],[25,35540,35541],{"xmlns":27},[29,35542,35543,35547],{},[32,35544,35545],{},[35,35546,1682],{},[47,35548,1682],{"encoding":49},[15,35550,35552],{"className":35551,"ariaHidden":41},[54],[15,35553,35555,35558],{"className":35554},[58],[15,35556],{"className":35557,"style":11284},[62],[15,35559,1682],{"className":35560},[67,68]," 即外生变量的一次实现 ",[15,35563,35565,35587],{"className":35564,"translate":19},[18],[15,35566,35568],{"className":35567},[23],[25,35569,35570],{"xmlns":27},[29,35571,35572,35584],{},[32,35573,35574,35576,35578],{},[35,35575,2458],{},[39,35577,602],{},[863,35579,35580,35582],{},[35,35581,13778],{},[35,35583,1682],{},[47,35585,35586],{"encoding":49},"U = u_i",[15,35588,35590,35608],{"className":35589,"ariaHidden":41},[54],[15,35591,35593,35596,35599,35602,35605],{"className":35592},[58],[15,35594],{"className":35595,"style":299},[62],[15,35597,2458],{"className":35598,"style":2570},[67,68],[15,35600],{"className":35601,"style":199},[77],[15,35603,602],{"className":35604},[203],[15,35606],{"className":35607,"style":199},[77],[15,35609,35611,35615],{"className":35610},[58],[15,35612],{"className":35613,"style":35614},[62],"height:0.5806em;vertical-align:-0.15em;",[15,35616,35618,35621],{"className":35617},[67],[15,35619,13778],{"className":35620},[67,68],[15,35622,35624],{"className":35623},[918],[15,35625,35627,35647],{"className":35626},[922,923],[15,35628,35630,35644],{"className":35629},[927],[15,35631,35633],{"className":35632,"style":1733},[931],[15,35634,35635,35638],{"style":7289},[15,35636],{"className":35637,"style":940},[939],[15,35639,35641],{"className":35640},[944,945,946,947],[15,35642,1682],{"className":35643},[67,68,947],[15,35645,955],{"className":35646},[954],[15,35648,35650],{"className":35649},[927],[15,35651,35653],{"className":35652,"style":962},[931],[15,35654],{},"。事实上，在只涉及可操纵变量、且不引用跨世界量的范围内，两套形式化被证明是",[305,35657,35658],{},"等价的","；SCM 的表达力略宽一些，例如它可以容纳不可操纵的变量（如年龄、性别），而这在严格的潜在结果表述中会造成困难。二者共享同一组识别性条件，只是表述方式不同：",[507,35661,35662,35669],{},[510,35663,35664,35665,35668],{},"SCM 用 ",[305,35666,35667],{},"d-分离与后门准则","回答「应当控制哪些变量」，把这一判断变成图上的机械判定；",[510,35670,35671,35672,4335,35675,35834,35835,35960],{},"潜在结果框架用",[305,35673,35674],{},"可忽略性假设（ignorability）",[15,35676,35678,35728],{"className":35677,"translate":19},[18],[15,35679,35681],{"className":35680},[23],[25,35682,35683],{"xmlns":27},[29,35684,35685,35725],{},[32,35686,35687,35689,35691,35693,35695,35697,35699,35701,35703,35705,35707,35709,35711,35713,35715,35717,35719,35721,35723],{},[39,35688,102],{"fence":101,"stretchy":41,"minsize":14230,"maxsize":14230},[35,35690,45],{},[39,35692,102],{"stretchy":101},[1425,35694,1427],{},[39,35696,111],{"stretchy":101},[39,35698,42],{"separator":41},[35,35700,45],{},[39,35702,102],{"stretchy":101},[1425,35704,2461],{},[39,35706,111],{"stretchy":101},[39,35708,111],{"fence":101,"stretchy":41,"minsize":14230,"maxsize":14230},[39,35710,236],{},[238,35712,240],{},[238,35714,240],{},[238,35716,240],{},[39,35718,236],{},[35,35720,37],{},[39,35722,170],{},[35,35724,3795],{},[47,35726,35727],{"encoding":49},"\\big(Y(1), Y(0)\\big) \\perp\\!\\!\\!\\perp X \\mid W",[15,35729,35731,35795,35807,35825],{"className":35730,"ariaHidden":41},[54],[15,35732,35734,35738,35744,35747,35750,35753,35756,35759,35762,35765,35768,35771,35774,35780,35783,35786,35789,35792],{"className":35733},[58],[15,35735],{"className":35736,"style":35737},[62],"height:1.2em;vertical-align:-0.35em;",[15,35739,35741],{"className":35740},[67],[15,35742,102],{"className":35743},[15088,15089],[15,35745,45],{"className":35746,"style":82},[67,68],[15,35748,102],{"className":35749},[132],[15,35751,1427],{"className":35752},[67],[15,35754,111],{"className":35755},[148],[15,35757,42],{"className":35758},[73],[15,35760],{"className":35761,"style":78},[77],[15,35763,45],{"className":35764,"style":82},[67,68],[15,35766,102],{"className":35767},[132],[15,35769,2461],{"className":35770},[67],[15,35772,111],{"className":35773},[148],[15,35775,35777],{"className":35776},[67],[15,35778,111],{"className":35779},[15088,15089],[15,35781],{"className":35782,"style":199},[77],[15,35784,236],{"className":35785},[203],[15,35787],{"className":35788,"style":274},[77],[15,35790],{"className":35791,"style":274},[77],[15,35793],{"className":35794,"style":274},[77],[15,35796,35798,35801,35804],{"className":35797},[58],[15,35799],{"className":35800,"style":261},[62],[15,35802,236],{"className":35803},[203],[15,35805],{"className":35806,"style":199},[77],[15,35808,35810,35813,35816,35819,35822],{"className":35809},[58],[15,35811],{"className":35812,"style":124},[62],[15,35814,37],{"className":35815,"style":69},[67,68],[15,35817],{"className":35818,"style":199},[77],[15,35820,170],{"className":35821},[203],[15,35823],{"className":35824,"style":199},[77],[15,35826,35828,35831],{"className":35827},[58],[15,35829],{"className":35830,"style":299},[62],[15,35832,3795],{"className":35833,"style":128},[67,68]," 表达同一件事，并由此导出倾向得分 ",[15,35836,35838,35876],{"className":35837,"translate":19},[18],[15,35839,35841],{"className":35840},[23],[25,35842,35843],{"xmlns":27},[29,35844,35845,35873],{},[32,35846,35847,35849,35851,35853,35855,35857,35859,35861,35863,35865,35867,35869,35871],{},[35,35848,13768],{},[39,35850,102],{"stretchy":101},[35,35852,3795],{},[39,35854,111],{"stretchy":101},[39,35856,602],{},[35,35858,98],{},[39,35860,102],{"stretchy":101},[35,35862,37],{},[39,35864,602],{},[1425,35866,1427],{},[39,35868,170],{},[35,35870,3795],{},[39,35872,111],{"stretchy":101},[47,35874,35875],{"encoding":49},"e(W) = P(X = 1 \\mid W)",[15,35877,35879,35906,35930,35948],{"className":35878,"ariaHidden":41},[54],[15,35880,35882,35885,35888,35891,35894,35897,35900,35903],{"className":35881},[58],[15,35883],{"className":35884,"style":124},[62],[15,35886,13768],{"className":35887},[67,68],[15,35889,102],{"className":35890},[132],[15,35892,3795],{"className":35893,"style":128},[67,68],[15,35895,111],{"className":35896},[148],[15,35898],{"className":35899,"style":199},[77],[15,35901,602],{"className":35902},[203],[15,35904],{"className":35905,"style":199},[77],[15,35907,35909,35912,35915,35918,35921,35924,35927],{"className":35908},[58],[15,35910],{"className":35911,"style":124},[62],[15,35913,98],{"className":35914,"style":128},[67,68],[15,35916,102],{"className":35917},[132],[15,35919,37],{"className":35920,"style":69},[67,68],[15,35922],{"className":35923,"style":199},[77],[15,35925,602],{"className":35926},[203],[15,35928],{"className":35929,"style":199},[77],[15,35931,35933,35936,35939,35942,35945],{"className":35932},[58],[15,35934],{"className":35935,"style":124},[62],[15,35937,1427],{"className":35938},[67],[15,35940],{"className":35941,"style":199},[77],[15,35943,170],{"className":35944},[203],[15,35946],{"className":35947,"style":199},[77],[15,35949,35951,35954,35957],{"className":35950},[58],[15,35952],{"className":35953,"style":124},[62],[15,35955,3795],{"className":35956,"style":128},[67,68],[15,35958,111],{"className":35959},[148],"，以及逆概率加权（IPW）、双重稳健估计等成熟的估计工具。",[11,35962,35963,35964,36106,36107,36135,36136,36164,36165,36168,36169,10678,36172,36304],{},"值得注意的是，",[15,35965,35967,36013],{"className":35966,"translate":19},[18],[15,35968,35970],{"className":35969},[23],[25,35971,35972],{"xmlns":27},[29,35973,35974,36010],{},[32,35975,35976,35978,35980,35982,35984,35986,35988,35990,35992,35994,35996,35998,36000,36002,36004,36006,36008],{},[35,35977,45],{},[39,35979,102],{"stretchy":101},[1425,35981,1427],{},[39,35983,111],{"stretchy":101},[39,35985,42],{"separator":41},[35,35987,45],{},[39,35989,102],{"stretchy":101},[1425,35991,2461],{},[39,35993,111],{"stretchy":101},[39,35995,236],{},[238,35997,240],{},[238,35999,240],{},[238,36001,240],{},[39,36003,236],{},[35,36005,37],{},[39,36007,170],{},[35,36009,3795],{},[47,36011,36012],{"encoding":49},"Y(1), Y(0) \\perp\\!\\!\\!\\perp X \\mid W",[15,36014,36016,36067,36079,36097],{"className":36015,"ariaHidden":41},[54],[15,36017,36019,36022,36025,36028,36031,36034,36037,36040,36043,36046,36049,36052,36055,36058,36061,36064],{"className":36018},[58],[15,36020],{"className":36021,"style":124},[62],[15,36023,45],{"className":36024,"style":82},[67,68],[15,36026,102],{"className":36027},[132],[15,36029,1427],{"className":36030},[67],[15,36032,111],{"className":36033},[148],[15,36035,42],{"className":36036},[73],[15,36038],{"className":36039,"style":78},[77],[15,36041,45],{"className":36042,"style":82},[67,68],[15,36044,102],{"className":36045},[132],[15,36047,2461],{"className":36048},[67],[15,36050,111],{"className":36051},[148],[15,36053],{"className":36054,"style":199},[77],[15,36056,236],{"className":36057},[203],[15,36059],{"className":36060,"style":274},[77],[15,36062],{"className":36063,"style":274},[77],[15,36065],{"className":36066,"style":274},[77],[15,36068,36070,36073,36076],{"className":36069},[58],[15,36071],{"className":36072,"style":261},[62],[15,36074,236],{"className":36075},[203],[15,36077],{"className":36078,"style":199},[77],[15,36080,36082,36085,36088,36091,36094],{"className":36081},[58],[15,36083],{"className":36084,"style":124},[62],[15,36086,37],{"className":36087,"style":69},[67,68],[15,36089],{"className":36090,"style":199},[77],[15,36092,170],{"className":36093},[203],[15,36095],{"className":36096,"style":199},[77],[15,36098,36100,36103],{"className":36099},[58],[15,36101],{"className":36102,"style":299},[62],[15,36104,3795],{"className":36105,"style":128},[67,68]," 与「",[15,36108,36110,36123],{"className":36109,"translate":19},[18],[15,36111,36113],{"className":36112},[23],[25,36114,36115],{"xmlns":27},[29,36116,36117,36121],{},[32,36118,36119],{},[35,36120,3795],{},[47,36122,3795],{"encoding":49},[15,36124,36126],{"className":36125,"ariaHidden":41},[54],[15,36127,36129,36132],{"className":36128},[58],[15,36130],{"className":36131,"style":299},[62],[15,36133,3795],{"className":36134,"style":128},[67,68]," 满足后门准则」所刻画的正是同一组条件：随机化（或条件随机化）在图上做的事情，恰恰就是删除指向 ",[15,36137,36139,36152],{"className":36138,"translate":19},[18],[15,36140,36142],{"className":36141},[23],[25,36143,36144],{"xmlns":27},[29,36145,36146,36150],{},[32,36147,36148],{},[35,36149,37],{},[47,36151,37],{"encoding":49},[15,36153,36155],{"className":36154,"ariaHidden":41},[54],[15,36156,36158,36161],{"className":36157},[58],[15,36159],{"className":36160,"style":299},[62],[15,36162,37],{"className":36163,"style":69},[67,68]," 的全部入边。此外，潜在结果框架还引入了 SCM 表述中不显式出现的两条假设——",[305,36166,36167],{},"SUTVA","（个体的结果不受他人处理状态的影响，且处理版本唯一）与",[305,36170,36171],{},"重叠性",[15,36173,36175,36211],{"className":36174,"translate":19},[18],[15,36176,36178],{"className":36177},[23],[25,36179,36180],{"xmlns":27},[29,36181,36182,36208],{},[32,36183,36184,36186,36188,36190,36192,36194,36196,36198,36200,36202,36204,36206],{},[1425,36185,2461],{},[39,36187,21780],{},[35,36189,98],{},[39,36191,102],{"stretchy":101},[35,36193,37],{},[39,36195,602],{},[1425,36197,1427],{},[39,36199,170],{},[35,36201,3795],{},[39,36203,111],{"stretchy":101},[39,36205,21780],{},[1425,36207,1427],{},[47,36209,36210],{"encoding":49},"0 \u003C P(X=1\\mid W) \u003C 1",[15,36212,36214,36232,36256,36274,36295],{"className":36213,"ariaHidden":41},[54],[15,36215,36217,36220,36223,36226,36229],{"className":36216},[58],[15,36218],{"className":36219,"style":21795},[62],[15,36221,2461],{"className":36222},[67],[15,36224],{"className":36225,"style":199},[77],[15,36227,21780],{"className":36228},[203],[15,36230],{"className":36231,"style":199},[77],[15,36233,36235,36238,36241,36244,36247,36250,36253],{"className":36234},[58],[15,36236],{"className":36237,"style":124},[62],[15,36239,98],{"className":36240,"style":128},[67,68],[15,36242,102],{"className":36243},[132],[15,36245,37],{"className":36246,"style":69},[67,68],[15,36248],{"className":36249,"style":199},[77],[15,36251,602],{"className":36252},[203],[15,36254],{"className":36255,"style":199},[77],[15,36257,36259,36262,36265,36268,36271],{"className":36258},[58],[15,36260],{"className":36261,"style":124},[62],[15,36263,1427],{"className":36264},[67],[15,36266],{"className":36267,"style":199},[77],[15,36269,170],{"className":36270},[203],[15,36272],{"className":36273,"style":199},[77],[15,36275,36277,36280,36283,36286,36289,36292],{"className":36276},[58],[15,36278],{"className":36279,"style":124},[62],[15,36281,3795],{"className":36282,"style":128},[67,68],[15,36284,111],{"className":36285},[148],[15,36287],{"className":36288,"style":199},[77],[15,36290,21780],{"className":36291},[203],[15,36293],{"className":36294,"style":199},[77],[15,36296,36298,36301],{"className":36297},[58],[15,36299],{"className":36300,"style":3149},[62],[15,36302,1427],{"className":36303},[67],"）。前者在存在干扰或溢出效应（如疫苗接种、社交网络中的实验）时会被违反，而这类情形在图上需要特殊的结构才能建模。这是两个框架互补而非竞争的一个典型例子。",[1309,36306,36308],{"id":36307},"_42-传统结构方程模型同一名称下的另一条传统","4.2 传统结构方程模型：同一名称下的另一条传统",[11,36310,36311],{},"「结构方程模型」这一术语在统计学、心理测量学与社会科学中已有数十年的历史，其含义与本文所述并不相同。为避免混淆，此处有必要作一辨析。",[11,36313,36314,36315,36318,36319,36322,36323,36326,36327,36389],{},"经典意义上的 SEM 由两部分组成：",[305,36316,36317],{},"测量模型","（潜变量与观测指标之间的因子结构，即验证性因子分析）与",[305,36320,36321],{},"结构模型","（潜变量之间的路径系数）。它以观测变量的",[305,36324,36325],{},"协方差矩阵","为拟合对象，通过极大似然等方法估计参数，并以 ",[15,36328,36330,36350],{"className":36329,"translate":19},[18],[15,36331,36333],{"className":36332},[23],[25,36334,36335],{"xmlns":27},[29,36336,36337,36347],{},[32,36338,36339],{},[872,36340,36341,36344],{},[35,36342,36343],{},"χ",[1425,36345,36346],{},"2",[47,36348,36349],{"encoding":49},"\\chi^2",[15,36351,36353],{"className":36352,"ariaHidden":41},[54],[15,36354,36356,36360],{"className":36355},[58],[15,36357],{"className":36358,"style":36359},[62],"height:1.0085em;vertical-align:-0.1944em;",[15,36361,36363,36366],{"className":36362},[67],[15,36364,36343],{"className":36365},[67,68],[15,36367,36369],{"className":36368},[918],[15,36370,36372],{"className":36371},[922],[15,36373,36375],{"className":36374},[927],[15,36376,36378],{"className":36377,"style":16420},[931],[15,36379,36380,36383],{"style":1002},[15,36381],{"className":36382,"style":940},[939],[15,36384,36386],{"className":36385},[944,945,946,947],[15,36387,36346],{"className":36388},[67,947],"、CFI、RMSEA 等指标评价模型与数据的整体拟合优度，典型应用是心理量表与社会科学的潜变量建模。",[11,36391,36392],{},"与本文的因果结构模型相比，二者的差别可以归纳为三点：",[7923,36394,36395,36405,36415],{},[510,36396,36397,36400,36401,36404],{},[305,36398,36399],{},"边的语义不同","。经典 SEM 的路径图本质上是对协方差结构分解的图解，方向由理论约定，模型检验关心的是「这个协方差模式能否被这个路径图解释」；而本文的 SCM 把每条边当作「直接原因」这一",[305,36402,36403],{},"不可从数据验证的结构性假设","（见 1.1 节），并强调它必须来自数据之外。",[510,36406,36407,36410,36411,36414],{},[305,36408,36409],{},"是否具备 do-算子","。经典 SEM 没有干预的语义，其路径系数",[305,36412,36413],{},"不能被直接解释为干预效应","，只有在额外假设（通常等同于后门准则）下，这些参数才恰好与因果效应一致。这也正是同一份协方差矩阵可以同时被多个方向不同的路径图拟合的原因。",[510,36416,36417,36420,36421,36449,36450,36478],{},[305,36418,36419],{},"反事实的可识别性来自假设而非数据","。经典 SEM 通常假设线性、可加且噪声服从高斯分布，而正如 3.3 节所指出的，在这一特殊设定下 ",[15,36422,36424,36437],{"className":36423,"translate":19},[18],[15,36425,36427],{"className":36426},[23],[25,36428,36429],{"xmlns":27},[29,36430,36431,36435],{},[32,36432,36433],{},[35,36434,2458],{},[47,36436,2458],{"encoding":49},[15,36438,36440],{"className":36439,"ariaHidden":41},[54],[15,36441,36443,36446],{"className":36442},[58],[15,36444],{"className":36445,"style":299},[62],[15,36447,2458],{"className":36448,"style":2570},[67,68]," 可由 ",[15,36451,36453,36466],{"className":36452,"translate":19},[18],[15,36454,36456],{"className":36455},[23],[25,36457,36458],{"xmlns":27},[29,36459,36460,36464],{},[32,36461,36462],{},[35,36463,1343],{},[47,36465,1343],{"encoding":49},[15,36467,36469],{"className":36468,"ariaHidden":41},[54],[15,36470,36472,36475],{"className":36471},[58],[15,36473],{"className":36474,"style":299},[62],[15,36476,1343],{"className":36477,"style":82},[67,68]," 唯一反解，反事实量因此「自动可识别」。这既是它能够讨论个体效应的原因，也是它最脆弱的地方：结论的强度完全由函数形式的假设承担。",[11,36480,36481],{},"一句话概括：经典 SEM 关心的是「协方差结构能否被一个路径图解释」，而结构因果模型关心的是「若外部改变某个变量，其余变量将如何变化」。",[1309,36483,36485],{"id":36484},"_43-随机对照试验的因果语义","4.3 随机对照试验的因果语义",[11,36487,36488],{},"本文的形式化工具同时给出了随机对照试验（RCT）为何享有「黄金标准」地位的一个精确解释。",[11,36490,36491,36492,36520,36521,36549,36550,36553,36554,36608,36609,36751,36752,36755,36756,36759,36760,36788],{},"在因果图中，随机分配意味着 ",[15,36493,36495,36508],{"className":36494,"translate":19},[18],[15,36496,36498],{"className":36497},[23],[25,36499,36500],{"xmlns":27},[29,36501,36502,36506],{},[32,36503,36504],{},[35,36505,37],{},[47,36507,37],{"encoding":49},[15,36509,36511],{"className":36510,"ariaHidden":41},[54],[15,36512,36514,36517],{"className":36513},[58],[15,36515],{"className":36516,"style":299},[62],[15,36518,37],{"className":36519,"style":69},[67,68]," 的取值由模型之外的机制（随机数生成器）决定，因此 ",[15,36522,36524,36537],{"className":36523,"translate":19},[18],[15,36525,36527],{"className":36526},[23],[25,36528,36529],{"xmlns":27},[29,36530,36531,36535],{},[32,36532,36533],{},[35,36534,37],{},[47,36536,37],{"encoding":49},[15,36538,36540],{"className":36539,"ariaHidden":41},[54],[15,36541,36543,36546],{"className":36542},[58],[15,36544],{"className":36545,"style":299},[62],[15,36547,37],{"className":36548,"style":69},[67,68]," 在图中",[305,36551,36552],{},"没有任何父节点","，也就不存在任何后门路径。由后门准则（取 ",[15,36555,36557,36576],{"className":36556,"translate":19},[18],[15,36558,36560],{"className":36559},[23],[25,36561,36562],{"xmlns":27},[29,36563,36564,36573],{},[32,36565,36566,36568,36570],{},[35,36567,3779],{},[39,36569,602],{},[35,36571,36572],{"mathvariant":878},"∅",[47,36574,36575],{"encoding":49},"S = \\varnothing",[15,36577,36579,36597],{"className":36578,"ariaHidden":41},[54],[15,36580,36582,36585,36588,36591,36594],{"className":36581},[58],[15,36583],{"className":36584,"style":299},[62],[15,36586,3779],{"className":36587,"style":1396},[67,68],[15,36589],{"className":36590,"style":199},[77],[15,36592,602],{"className":36593},[203],[15,36595],{"className":36596,"style":199},[77],[15,36598,36600,36604],{"className":36599},[58],[15,36601],{"className":36602,"style":36603},[62],"height:0.6633em;vertical-align:-0.0817em;",[15,36605,36572],{"className":36606},[67,36607],"amsrm","）立即得到\n",[15,36610,36612,36658],{"className":36611,"translate":19},[18],[15,36613,36615],{"className":36614},[23],[25,36616,36617],{"xmlns":27},[29,36618,36619,36655],{},[32,36620,36621,36623,36625,36627,36629,36631,36633,36635,36637,36639,36641,36643,36645,36647,36649,36651,36653],{},[35,36622,98],{},[39,36624,102],{"stretchy":101},[35,36626,534],{},[39,36628,170],{},[35,36630,696],{},[35,36632,699],{},[39,36634,102],{"stretchy":101},[35,36636,539],{},[39,36638,111],{"stretchy":101},[39,36640,111],{"stretchy":101},[39,36642,602],{},[35,36644,98],{},[39,36646,102],{"stretchy":101},[35,36648,534],{},[39,36650,170],{},[35,36652,539],{},[39,36654,111],{"stretchy":101},[47,36656,36657],{"encoding":49},"P(y \\mid do(x)) = P(y \\mid x)",[15,36659,36661,36685,36715,36739],{"className":36660,"ariaHidden":41},[54],[15,36662,36664,36667,36670,36673,36676,36679,36682],{"className":36663},[58],[15,36665],{"className":36666,"style":124},[62],[15,36668,98],{"className":36669,"style":128},[67,68],[15,36671,102],{"className":36672},[132],[15,36674,534],{"className":36675,"style":563},[67,68],[15,36677],{"className":36678,"style":199},[77],[15,36680,170],{"className":36681},[203],[15,36683],{"className":36684,"style":199},[77],[15,36686,36688,36691,36694,36697,36700,36703,36706,36709,36712],{"className":36687},[58],[15,36689],{"className":36690,"style":124},[62],[15,36692,696],{"className":36693},[67,68],[15,36695,699],{"className":36696},[67,68],[15,36698,102],{"className":36699},[132],[15,36701,539],{"className":36702},[67,68],[15,36704,759],{"className":36705},[148],[15,36707],{"className":36708,"style":199},[77],[15,36710,602],{"className":36711},[203],[15,36713],{"className":36714,"style":199},[77],[15,36716,36718,36721,36724,36727,36730,36733,36736],{"className":36717},[58],[15,36719],{"className":36720,"style":124},[62],[15,36722,98],{"className":36723,"style":128},[67,68],[15,36725,102],{"className":36726},[132],[15,36728,534],{"className":36729,"style":563},[67,68],[15,36731],{"className":36732,"style":199},[77],[15,36734,170],{"className":36735},[203],[15,36737],{"className":36738,"style":199},[77],[15,36740,36742,36745,36748],{"className":36741},[58],[15,36743],{"className":36744,"style":124},[62],[15,36746,539],{"className":36747},[67,68],[15,36749,111],{"className":36750},[148],"\n即",[305,36753,36754],{},"干预分布与条件分布重合，观测数据可以直接回答第二层的问题","。用一句话说：",[305,36757,36758],{},"随机化就是人造的 do-算子","——它在物理上执行了定义 3.2 中「删去 ",[15,36761,36763,36776],{"className":36762,"translate":19},[18],[15,36764,36766],{"className":36765},[23],[25,36767,36768],{"xmlns":27},[29,36769,36770,36774],{},[32,36771,36772],{},[35,36773,37],{},[47,36775,37],{"encoding":49},[15,36777,36779],{"className":36778,"ariaHidden":41},[54],[15,36780,36782,36785],{"className":36781},[58],[15,36783],{"className":36784,"style":299},[62],[15,36786,37],{"className":36787,"style":69},[67,68]," 全部入边」这一手术。",[11,36790,36791],{},"这一视角同时划出了 RCT 的边界：",[7923,36793,36794,36800,36807,36843],{},[510,36795,36796,36797,36799],{},"它回答的是第二层问题，",[305,36798,24595],{},"回答个体反事实（见 3.3 节的可识别性边界）；",[510,36801,36802,36803,36806],{},"它识别的是",[305,36804,36805],{},"实际实施的处理版本","，若存在不依从（non-compliance），随机化在图上即被违反，需要借助工具变量等额外结构才能恢复效应估计；",[510,36808,36809,36810,36813,36814,36842],{},"随机化只保证",[305,36811,36812],{},"组间可比","，若存在干扰或溢出效应（SUTVA 违反），",[15,36815,36817,36830],{"className":36816,"translate":19},[18],[15,36818,36820],{"className":36819},[23],[25,36821,36822],{"xmlns":27},[29,36823,36824,36828],{},[32,36825,36826],{},[35,36827,37],{},[47,36829,37],{"encoding":49},[15,36831,36833],{"className":36832,"ariaHidden":41},[54],[15,36834,36836,36839],{"className":36835},[58],[15,36837],{"className":36838,"style":299},[62],[15,36840,37],{"className":36841,"style":69},[67,68]," 与结果之间仍可能经由个体之间的相互影响产生关联；",[510,36844,36845,36846,36849],{},"它保证的是",[305,36847,36848],{},"内部有效性","，外部有效性并不会自动成立——这引出下一小节。",[1309,36851,36853],{"id":36852},"_44-可迁移性与外部有效性","4.4 可迁移性与外部有效性",[11,36855,36856],{},"一个在实践中反复出现的问题是：在某一人群（或地区、时间）中估计出的因果效应，能否搬到另一个人群中去？纯统计框架对这一问题通常只能给出「谨慎泛化」这样的告诫，而因果图可以提供更精确的回答。",[11,36858,36859,36860,2249],{},"Pearl 与 Bareinboim 提出的",[305,36861,36862,36863,36957,36958,36993],{},"可迁移性（transportability）",[305,36864,36865,36866,36896,36897,36956],{},"理论把这类问题形式化如下：设源总体为 ",[15,36867,36869,36884],{"className":36868,"translate":19},[18],[15,36870,36872],{"className":36871},[23],[25,36873,36874],{"xmlns":27},[29,36875,36876,36881],{},[32,36877,36878],{},[35,36879,36880],{},"π",[47,36882,36883],{"encoding":49},"\\pi",[15,36885,36887],{"className":36886,"ariaHidden":41},[54],[15,36888,36890,36893],{"className":36889},[58],[15,36891],{"className":36892,"style":635},[62],[15,36894,36880],{"className":36895,"style":563},[67,68],"、目标总体为 ",[15,36898,36900,36918],{"className":36899,"translate":19},[18],[15,36901,36903],{"className":36902},[23],[25,36904,36905],{"xmlns":27},[29,36906,36907,36915],{},[32,36908,36909],{},[872,36910,36911,36913],{},[35,36912,36880],{},[39,36914,26408],{},[47,36916,36917],{"encoding":49},"\\pi^*",[15,36919,36921],{"className":36920,"ariaHidden":41},[54],[15,36922,36924,36927],{"className":36923},[58],[15,36925],{"className":36926,"style":26653},[62],[15,36928,36930,36933],{"className":36929},[67],[15,36931,36880],{"className":36932,"style":563},[67,68],[15,36934,36936],{"className":36935},[918],[15,36937,36939],{"className":36938},[922],[15,36940,36942],{"className":36941},[927],[15,36943,36945],{"className":36944,"style":26653},[931],[15,36946,36947,36950],{"style":1002},[15,36948],{"className":36949,"style":940},[939],[15,36951,36953],{"className":36952},[944,945,946,947],[15,36954,26408],{"className":36955},[1648,947],"，在","选择图（selection diagram）",[305,36959,36960,36961,36992],{},"中用方框记号 ",[15,36962,36964,36979],{"className":36963,"translate":19},[18],[15,36965,36967],{"className":36966},[23],[25,36968,36969],{"xmlns":27},[29,36970,36971,36976],{},[32,36972,36973],{},[35,36974,36975],{"mathvariant":878},"□",[47,36977,36978],{"encoding":49},"\\square",[15,36980,36982],{"className":36981,"ariaHidden":41},[54],[15,36983,36985,36989],{"className":36984},[58],[15,36986],{"className":36987,"style":36988},[62],"height:0.675em;",[15,36990,36975],{"className":36991},[67,36607]," 标出两个总体之间机制存在差异的节点。有了这一标注，就可以像 do-演算那样通过图上的判定，确定哪些机制可以在两个总体之间共享（因而可以搬运）、哪些必须在目标总体中重新估计，并给出相应的","传输公式（transport formula）",[11,36995,36996,36997,37000],{},"这一工具的意义在于：",[305,36998,36999],{},"外部有效性被从一句笼统的方法论警告，转化为一个在图上可判定的问题。"," 例如，某药物在临床试验人群中的效应能否外推到儿童，取决于两个人群之间的差异所触及的机制是否落在从用药到疗效的因果路径上——若差异只影响与结果无关的变量，效应可以直接搬运；若差异恰好作用于效应的关键中介或调节变量，则必须重新估计。这可以视为 SCM 相对于纯统计框架的一个独有优势。",[1309,37002,37004],{"id":37003},"_45-假设边界与开放问题","4.5 假设边界与开放问题",[11,37006,37007],{},"本文的体系并非无条件成立。把全部预设集中列出，既是诚实，也是使用时的核对清单：",[7923,37009,37010,37106,37224,37310,37381,37387],{},[510,37011,37012,37015,37016,37019,37020,37023,37024,37105],{},[305,37013,37014],{},"无环性","。DAG 假设排除了反馈回路与均衡，但现实中的经济系统（供给与需求互相决定）、生态系统与控制系统本质上是",[305,37017,37018],{},"有环","的。一种自然的放松方向是",[305,37021,37022],{},"有环结构方程模型","：允许 ",[15,37025,37027,37057],{"className":37026,"translate":19},[18],[15,37028,37030],{"className":37029},[23],[25,37031,37032],{"xmlns":27},[29,37033,37034,37054],{},[32,37035,37036,37038,37040,37042,37044,37046,37048,37050,37052],{},[35,37037,1343],{},[39,37039,8863],{},[39,37041,602],{},[35,37043,5724],{},[39,37045,102],{"stretchy":101},[35,37047,1343],{},[39,37049,42],{"separator":41},[35,37051,2458],{},[39,37053,111],{"stretchy":101},[47,37055,37056],{"encoding":49},"V := f(V, U)",[15,37058,37060,37078],{"className":37059,"ariaHidden":41},[54],[15,37061,37063,37066,37069,37072,37075],{"className":37062},[58],[15,37064],{"className":37065,"style":299},[62],[15,37067,1343],{"className":37068,"style":82},[67,68],[15,37070],{"className":37071,"style":199},[77],[15,37073,8899],{"className":37074},[203],[15,37076],{"className":37077,"style":199},[77],[15,37079,37081,37084,37087,37090,37093,37096,37099,37102],{"className":37080},[58],[15,37082],{"className":37083,"style":124},[62],[15,37085,5724],{"className":37086,"style":5772},[67,68],[15,37088,102],{"className":37089},[132],[15,37091,1343],{"className":37092,"style":82},[67,68],[15,37094,42],{"className":37095},[73],[15,37097],{"className":37098,"style":78},[77],[15,37100,2458],{"className":37101,"style":2570},[67,68],[15,37103,111],{"className":37104},[148],"，并以该系统的不动点作为均衡解来定义干预与反事实，此时「因果」的语义变为「均衡状态的移动」。时间序列情形下的动态贝叶斯网络（沿时间维展开后重新成为 DAG）是另一条常见路线。",[510,37107,37108,37111,37112,37140,37141,37169,37170,37173,37174,37223],{},[305,37109,37110],{},"Granger 因果不等于干预因果","。计量经济学中的 Granger 因果检验，其定义是「利用 ",[15,37113,37115,37128],{"className":37114,"translate":19},[18],[15,37116,37118],{"className":37117},[23],[25,37119,37120],{"xmlns":27},[29,37121,37122,37126],{},[32,37123,37124],{},[35,37125,37],{},[47,37127,37],{"encoding":49},[15,37129,37131],{"className":37130,"ariaHidden":41},[54],[15,37132,37134,37137],{"className":37133},[58],[15,37135],{"className":37136,"style":299},[62],[15,37138,37],{"className":37139,"style":69},[67,68]," 的历史能否改善对 ",[15,37142,37144,37157],{"className":37143,"translate":19},[18],[15,37145,37147],{"className":37146},[23],[25,37148,37149],{"xmlns":27},[29,37150,37151,37155],{},[32,37152,37153],{},[35,37154,45],{},[47,37156,45],{"encoding":49},[15,37158,37160],{"className":37159,"ariaHidden":41},[54],[15,37161,37163,37166],{"className":37162},[58],[15,37164],{"className":37165,"style":299},[62],[15,37167,45],{"className":37168,"style":82},[67,68]," 的预测」，这是一个纯粹的",[305,37171,37172],{},"可预测性","概念，与「在 ",[15,37175,37177,37199],{"className":37176,"translate":19},[18],[15,37178,37180],{"className":37179},[23],[25,37181,37182],{"xmlns":27},[29,37183,37184,37196],{},[32,37185,37186,37188,37190,37192,37194],{},[35,37187,696],{},[35,37189,699],{},[39,37191,102],{"stretchy":101},[35,37193,37],{},[39,37195,111],{"stretchy":101},[47,37197,37198],{"encoding":49},"do(X)",[15,37200,37202],{"className":37201,"ariaHidden":41},[54],[15,37203,37205,37208,37211,37214,37217,37220],{"className":37204},[58],[15,37206],{"className":37207,"style":124},[62],[15,37209,696],{"className":37210},[67,68],[15,37212,699],{"className":37213},[67,68],[15,37215,102],{"className":37216},[132],[15,37218,37],{"className":37219,"style":69},[67,68],[15,37221,111],{"className":37222},[148]," 下保持不变」的机制性因果概念分属两个不同的层级。在存在共同驱动因素（尤其是同时驱动二者但滞后不同的因素）时，Granger 因果会给出与干预无关的结论。把二者等同，是应用中最常见的概念混淆之一。",[510,37225,37226,37229,37230,37309],{},[305,37227,37228],{},"忠实性不可检验","。1.3 节的「当且仅当」版本依赖忠实性假设，即分布中不存在的独立性都不是参数偶然相消的产物。然而参数相消（例如路径系数恰好满足 ",[15,37231,37233,37259],{"className":37232,"translate":19},[18],[15,37234,37236],{"className":37235},[23],[25,37237,37238],{"xmlns":27},[29,37239,37240,37256],{},[32,37241,37242,37244,37247,37249,37252,37254],{},[35,37243,10218],{},[35,37245,37246],{},"b",[39,37248,2894],{},[35,37250,37251],{},"c",[39,37253,602],{},[1425,37255,2461],{},[47,37257,37258],{"encoding":49},"ab + c = 0",[15,37260,37262,37282,37300],{"className":37261,"ariaHidden":41},[54],[15,37263,37265,37269,37273,37276,37279],{"className":37264},[58],[15,37266],{"className":37267,"style":37268},[62],"height:0.7778em;vertical-align:-0.0833em;",[15,37270,37272],{"className":37271},[67,68],"ab",[15,37274],{"className":37275,"style":82},[77],[15,37277,2894],{"className":37278},[1648],[15,37280],{"className":37281,"style":82},[77],[15,37283,37285,37288,37291,37294,37297],{"className":37284},[58],[15,37286],{"className":37287,"style":635},[62],[15,37289,37251],{"className":37290},[67,68],[15,37292],{"className":37293,"style":199},[77],[15,37295,602],{"className":37296},[203],[15,37298],{"className":37299,"style":199},[77],[15,37301,37303,37306],{"className":37302},[58],[15,37304],{"className":37305,"style":3149},[62],[15,37307,2461],{"className":37308},[67],"）在数学上完全合法，且在某些自然的参数化下（如线性高斯模型的某些先验）几乎必然发生。忠实性无法从数据中检验，只能被接受或拒绝。",[510,37311,37312,37315,37316,37319,37320,431,37348,37376,37377,37380],{},[305,37313,37314],{},"马尔可夫型假设与不可识别性","。本文默认不存在未观测的混杂（2.1 节）。3.5 节的前门准则可以在",[305,37317,37318],{},"特定的中介结构","下绕过这一限制，但它远非一般性的解决方案。对一般的半马尔可夫型 SCM，存在根本不可识别的结构（例如 ",[15,37321,37323,37336],{"className":37322,"translate":19},[18],[15,37324,37326],{"className":37325},[23],[25,37327,37328],{"xmlns":27},[29,37329,37330,37334],{},[32,37331,37332],{},[35,37333,37],{},[47,37335,37],{"encoding":49},[15,37337,37339],{"className":37338,"ariaHidden":41},[54],[15,37340,37342,37345],{"className":37341},[58],[15,37343],{"className":37344,"style":299},[62],[15,37346,37],{"className":37347,"style":69},[67,68],[15,37349,37351,37364],{"className":37350,"translate":19},[18],[15,37352,37354],{"className":37353},[23],[25,37355,37356],{"xmlns":27},[29,37357,37358,37362],{},[32,37359,37360],{},[35,37361,45],{},[47,37363,45],{"encoding":49},[15,37365,37367],{"className":37366,"ariaHidden":41},[54],[15,37368,37370,37373],{"className":37369},[58],[15,37371],{"className":37372,"style":299},[62],[15,37374,45],{"className":37375,"style":82},[67,68]," 之间存在未观测混杂、且不存在满足前门条件的中介），此时唯一的出路是用",[305,37378,37379],{},"部分识别","方法给出效应的上下界，而非一个点估计。",[510,37382,37383,37386],{},[305,37384,37385],{},"选择与缺失","。d-分离的判据默认全部相关变量均已被观测，而样本选择本身就是在某些节点上做条件化——例 1.4 的伯克森悖论正是选择偏差的图论根源。同理，缺失数据的机制（MCAR \u002F MAR \u002F MNAR）在因果图中对应何种结构、会对可识别性造成何种影响，是一条自然而且实用的延伸方向。",[510,37388,37389,37392,37393,37396],{},[305,37390,37391],{},"因果发现的可扩展性","。1.4 节所述的算法在假设成立、样本充分时具有理论保证，但在有限样本下，条件独立检验的误差会逐层累积，输出的图往往并不稳定；同时这些算法对忠实性、无隐变量、函数类等假设相当敏感，其输出应当被当作",[305,37394,37395],{},"待检验的假设候选","，而不是结论。",[11,37398,37399,37400],{},"以上限制并未削弱这套理论的价值，反而界定了它的使用条件：",[305,37401,37402],{},"因果推断的可靠程度，等于你愿意且能够承担的假设的强度。",[1305,37404,37405],{"id":37405},"其他结语",[11,37407,37408],{},"回顾全文，因果图、结构因果模型、结构方程三者并非彼此独立的工具，而是同一理论体系在不同抽象层级上的展开：",[507,37410,37411,37423,37489],{},[510,37412,37413,7760,37415,37418,37419,37422],{},[305,37414,1307],{},[305,37416,37417],{},"定性层面","编码「谁影响谁」。它给出 d-分离这一可在图上机械判定的独立性判据，从而把「该控制哪些变量」从一个凭经验判断的问题，转化为一个组合问题；而它最主要的信息量，恰恰集中在那些",[305,37420,37421],{},"没有被画出来的边","上。",[510,37424,37425,7760,37427,37430,37431,37459,37460,37488],{},[305,37426,9435],{},[305,37428,37429],{},"生成层面","把图提升为一个可以生成数据的机制。它通过外生变量 ",[15,37432,37434,37447],{"className":37433,"translate":19},[18],[15,37435,37437],{"className":37436},[23],[25,37438,37439],{"xmlns":27},[29,37440,37441,37445],{},[32,37442,37443],{},[35,37444,2458],{},[47,37446,2458],{"encoding":49},[15,37448,37450],{"className":37449,"ariaHidden":41},[54],[15,37451,37453,37456],{"className":37452},[58],[15,37454],{"className":37455,"style":299},[62],[15,37457,2458],{"className":37458,"style":2570},[67,68]," 与结构方程 ",[15,37461,37463,37476],{"className":37462,"translate":19},[18],[15,37464,37466],{"className":37465},[23],[25,37467,37468],{"xmlns":27},[29,37469,37470,37474],{},[32,37471,37472],{},[35,37473,9484],{},[47,37475,9484],{"encoding":49},[15,37477,37479],{"className":37478,"ariaHidden":41},[54],[15,37480,37482,37485],{"className":37481},[58],[15,37483],{"className":37484,"style":299},[62],[15,37486,9484],{"className":37487,"style":128},[67,68]," 明确了「观测分布」与「干预分布」的区别，使第二层的问题第一次拥有了明确的数学对象。",[510,37490,37491,7760,37494,37497,37498,37528,37529,37633,37634,37719],{},[305,37492,37493],{},"结构方程",[305,37495,37496],{},"操作层面","给出这套机制的可改写形式。非对称的 ",[15,37499,37501,37516],{"className":37500,"translate":19},[18],[15,37502,37504],{"className":37503},[23],[25,37505,37506],{"xmlns":27},[29,37507,37508,37514],{},[32,37509,37510,37512],{},[39,37511,8863],{},[39,37513,602],{},[47,37515,8899],{"encoding":49},[15,37517,37519],{"className":37518,"ariaHidden":41},[54],[15,37520,37522,37525],{"className":37521},[58],[15,37523],{"className":37524,"style":635},[62],[15,37526,8899],{"className":37527},[203]," 使得 do-算子可以理解为一次对机制的手术式局部替换（",[15,37530,37532,37553],{"className":37531,"translate":19},[18],[15,37533,37535],{"className":37534},[23],[25,37536,37537],{"xmlns":27},[29,37538,37539,37551],{},[32,37540,37541],{},[863,37542,37543,37545],{},[35,37544,1336],{},[18639,37546,37547,37549],{"accent":41},[35,37548,37],{},[39,37550,18645],{"stretchy":41},[47,37552,18648],{"encoding":49},[15,37554,37556],{"className":37555,"ariaHidden":41},[54],[15,37557,37559,37562],{"className":37558},[58],[15,37560],{"className":37561,"style":18658},[62],[15,37563,37565,37568],{"className":37564},[67],[15,37566,1336],{"className":37567},[67,68],[15,37569,37571],{"className":37570},[918],[15,37572,37574,37625],{"className":37573},[922,923],[15,37575,37577,37622],{"className":37576},[927],[15,37578,37580],{"className":37579,"style":18677},[931],[15,37581,37582,37585],{"style":18680},[15,37583],{"className":37584,"style":18684},[939],[15,37586,37588],{"className":37587},[944,945,946,947],[15,37589,37591],{"className":37590},[67,947],[15,37592,37594],{"className":37593},[67,18694,947],[15,37595,37597],{"className":37596},[922],[15,37598,37600],{"className":37599},[927],[15,37601,37603,37614],{"className":37602,"style":18704},[931],[15,37604,37605,37608],{"style":18707},[15,37606],{"className":37607,"style":18684},[939],[15,37609,37611],{"className":37610},[67,947],[15,37612,37],{"className":37613,"style":69},[67,68,947],[15,37615,37616,37619],{"style":18719},[15,37617],{"className":37618,"style":18684},[939],[15,37620],{"className":37621,"style":18727},[18726,947],[15,37623,955],{"className":37624},[954],[15,37626,37628],{"className":37627},[927],[15,37629,37631],{"className":37630,"style":18737},[931],[15,37632],{},"），并经潜在结果 ",[15,37635,37637,37661],{"className":37636,"translate":19},[18],[15,37638,37640],{"className":37639},[23],[25,37641,37642],{"xmlns":27},[29,37643,37644,37658],{},[32,37645,37646,37652,37654,37656],{},[863,37647,37648,37650],{},[35,37649,45],{},[35,37651,539],{},[39,37653,102],{"stretchy":101},[35,37655,13778],{},[39,37657,111],{"stretchy":101},[47,37659,37660],{"encoding":49},"Y_x(u)",[15,37662,37664],{"className":37663,"ariaHidden":41},[54],[15,37665,37667,37670,37710,37713,37716],{"className":37666},[58],[15,37668],{"className":37669,"style":124},[62],[15,37671,37673,37676],{"className":37672},[67],[15,37674,45],{"className":37675,"style":82},[67,68],[15,37677,37679],{"className":37678},[918],[15,37680,37682,37702],{"className":37681},[922,923],[15,37683,37685,37699],{"className":37684},[927],[15,37686,37688],{"className":37687,"style":932},[931],[15,37689,37690,37693],{"style":1499},[15,37691],{"className":37692,"style":940},[939],[15,37694,37696],{"className":37695},[944,945,946,947],[15,37697,539],{"className":37698},[67,68,947],[15,37700,955],{"className":37701},[954],[15,37703,37705],{"className":37704},[927],[15,37706,37708],{"className":37707,"style":962},[931],[15,37709],{},[15,37711,102],{"className":37712},[132],[15,37714,13778],{"className":37715},[67,68],[15,37717,111],{"className":37718},[148]," 通向第三层的反事实。",[11,37721,37722],{},"第四部分则表明，这一体系与潜在结果框架、传统结构方程模型之间并无高下之分，而是对同一批问题的不同表述：本文的框架以图换取「该控制什么」的可判定性，潜在结果框架以概率表述换取成熟的估计工具，而传统 SEM 关心的始终是协方差结构能否被一个路径图解释；至于随机化实验，其全部因果语义就是一次在物理上实施的 do-算子。",[11,37724,37725,37726,37729],{},"这一体系最深刻的洞见在于：",[305,37727,37728],{},"因果知识本质上是关于「世界如何生成数据」的知识，而非「数据本身呈现出何种模式」的知识","。正因如此，仅凭再大规模、再高维度的观测数据，也无法在没有结构性假设（即因果图）的前提下唯一确定因果效应——这既是因果推断这一领域存在的根本原因，也是它与纯粹的统计学习、机器学习范式在认识论上的分界线所在。",[11,37731,37732],{},"同时也应记住 4.5 节列出的代价：这套理论的可识别性结论，无一例外地建立在无环、忠实、无未观测混杂等假设之上，而其中若干假设本身并不能由数据检验。因此使用因果图时最值得追问的，往往不是「这张图算出了什么」，而是「这张图凭什么长成这样」，以及「若换一张同样合理的图，结论是否仍然成立」。",{"title":4127,"searchDepth":37734,"depth":37734,"links":37735},2,[37736,37743,37748,37755,37762],{"id":1307,"depth":37734,"text":1307,"children":37737},[37738,37740,37741,37742],{"id":1311,"depth":37739,"text":1312},3,{"id":4191,"depth":37739,"text":4192},{"id":6342,"depth":37739,"text":6343},{"id":7917,"depth":37739,"text":7918},{"id":9435,"depth":37734,"text":9435,"children":37744},[37745,37746,37747],{"id":9445,"depth":37739,"text":9446},{"id":11951,"depth":37739,"text":11952},{"id":13632,"depth":37739,"text":13633},{"id":16076,"depth":37734,"text":16076,"children":37749},[37750,37751,37752,37753,37754],{"id":16127,"depth":37739,"text":16128},{"id":17174,"depth":37739,"text":17175},{"id":21999,"depth":37739,"text":22000},{"id":25997,"depth":37739,"text":25998},{"id":29710,"depth":37739,"text":29711},{"id":34549,"depth":37734,"text":34549,"children":37756},[37757,37758,37759,37760,37761],{"id":34555,"depth":37739,"text":34556},{"id":36307,"depth":37739,"text":36308},{"id":36484,"depth":37739,"text":36485},{"id":36852,"depth":37739,"text":36853},{"id":37003,"depth":37739,"text":37004},{"id":37405,"depth":37734,"text":37405},"为什么概率论不足以回答因果问题？设 X,YX, YX,Y 为两个随机变量，概率论所能给出的全部工具是联合分布 P(X,Y)P(X,Y)P(X,Y)、条件分布 P(Y∣X)P(Y\\mid X)P(Y∣X)，以及由此导出的独立性关系 X⊥ ⁣ ⁣ ⁣⊥YX \\perp\\!\\!\\!\\perp YX⊥⊥Y。这套语言在数学上是自洽的，但存在一个根本性的表达力缺陷：概率分布对「对称性」是不敏感的。若已知 P(X,Y)P(X,Y)P(X,Y)，则 P(Y∣X)P(Y\\mid X)P(Y∣X) 与 P(X∣Y)P(X\\mid Y)P(X∣Y) 皆可通过贝叶斯定理相互推出，二者在信息量上完全等价，谁也不比谁更「根本」。然而在实际世界中，「气压下降导致下雨」与「下雨导致气压下降」显然不是对称的两种表述——只有前者是对的。这种方向性、非对称性的知识，是概率分布本身无法编码的，必须由额外的结构承载。",false,true,"md","甘肃兰州",{},null,"\u002Fblog\u002F2026\u002F0005-yin-guo-jie-gou-mo-xing-jian-lun",{"title":6,"description":37763},"blog\u002F2026\u002F0005-yin-guo-jie-gou-mo-xing-jian-lun","为什么概率论不足以回答因果问题？本文以 Judea Pearl 的因果推断阶梯为线索，依次展开因果图、结构因果模型与结构方程这三层层层递进的形式化工具，进而讨论因果发现、中介分析、do-演算与前门准则，并对照潜在结果框架与传统结构方程模型，梳理这一体系成立所依赖的假设与适用边界。",[37775],"machine-learning","2026-09-20T23:05:13+08:00","9Ui90_cj3io7V35nrGJl0F-SOCQb6hzZNEryfszpPTM",{"id":37779,"title":37780,"body":37781,"description":4127,"draft":37764,"enableComment":37765,"extension":37766,"image":4127,"important":37764,"location":37769,"meta":38058,"navigation":37765,"ogImage":37769,"path":38059,"seo":38060,"stem":38061,"summary":38062,"tags":38063,"time":38065,"__hash__":38066},"blog\u002Fblog\u002F2026\u002F0002-brief-biography-of-von-neumann.md","冯 · 诺依曼小传",{"type":8,"value":37782,"toc":38048},[37783,37786,37789,37792,37799,37802,37805,37808,37811,37814,37817,37820,37823,37826,37829,37832,37835,37838,37841,37844,37847,37850,37853,37856,37859,37862,37865,37868,37871,37874,37877,37880,37883,37886,37889,37895,37898,37901,37904,37907,37910,37913,37916,37919,37922,37925,37928,37931,37934,37937,37940,37943,37946,37949,37952,37955,37958,37961,37964,37967,37970,37973,37976,37979,37982,37985,37988,37991,37994,37997,38000,38003,38006,38009,38012,38015,38018,38021,38024,38027,38030,38033,38036,38039,38042,38045],[1305,37784,37785],{"id":37785},"布达佩斯",[11,37787,37788],{},"匈牙利，1903 年 12 月 28 日，布达佩斯的一户殷实人家添了第一个男孩。父亲马克斯·诺依曼是位银行家，母亲玛吉特·肯恩出身富商之家。家里人叫他「扬奇」——匈牙利名字扬诺什的昵称。他还有两个弟弟，米哈伊和米克洛什。",[11,37790,37791],{},"扬奇从小就不太寻常——别的小孩还在学数数，他已经能用古希腊语跟父亲互相打趣了。他后来懂六种以上语言：匈牙利语、德语、法语、英语、拉丁语、古希腊语，晚年还学一点西班牙语。乌拉姆回忆，他用英语写论文时，已经能写出比大多数美国数学家更地道的英文散文。他学新语言的路子，跟解数学题是同一个路数——有同事回忆，他拿到一本新语言的语法书，先翻动词变位表，自己把规则推演出来，再拿例句验证。",[11,37793,37794],{},[37795,37796],"img",{"alt":37797,"src":37798},"童年时的约翰 · 冯 · 诺依曼","https:\u002F\u002Fimage-assets.dreams.plus\u002F202609020248182.png",[11,37800,37801],{},"六岁那年，他在心里算两个八位数的除法，速度快得让在座的客人怀疑是提前排练的把戏。他母亲有一次在饭桌上一时兴起，随口考他：「你说，你要是盯着窗外看，脑子里能想什么？」扬奇想都没想地回答出一堆答案，逗得全家人哈哈大笑——这大概是他这辈子第一次在饭桌上「表演」，后来这种饭桌高谈阔论的习惯，他保持了一辈子。",[11,37803,37804],{},"一九一三年，皇帝弗朗茨·约瑟夫册封马克斯为贵族，授予世袭的「玛尔吉泰」头衔——大致相当于德语里的「冯」。父亲自己没把这个头衔当回事，倒是儿子后来在德文论文上署起了「冯·诺依曼」的名字，一路用到了美国。",[11,37806,37807],{},"十岁那年，家里给他请了数学家教。没多久，一位名叫费凯特的匈牙利数学家登门找他讨论高等数学——据说聊到后来，这位比他大十几岁的年轻人被眼前的少年感动得眼眶发热。费凯特后来成了他学术生涯的引路人之一，两人还合写了他最早的一篇论文。",[11,37809,37810],{},"也是在十来岁的年纪，他一头扎进家里一套四十八卷本的《世界历史》，几个月就啃完了，之后养成一个爱好：拿当下报纸上的新闻，跟历史上某场战役类比，一本正经地讨论两边的战术优劣，仿佛在分析一盘棋局。他的记性好得被家人和师长传成奇谈——据说他能背下一整本小说，能记住电话簿里连续好几页的号码，谁想考他，报个页码就行。多年以后，普林斯顿一位专攻拜占庭史的教授私下承认，聊起拜占庭历史的细节，三十多岁的诺依曼懂得比他这个专业教授还多——而这只是诺依曼的一个业余爱好。",[11,37812,37813],{},"不过，扬奇不是散养出来的神童。马克斯给儿子请的不是普通家教，而是布达佩斯大学的年轻数学家和科学家，让他们定期来家里上课；诺依曼的弟弟后来回忆，家里餐厅的椅子常常被拉到书房去，因为「上课的人太多了」。父亲自己没受过多少正规科学训练，但他知道什么值得花钱——他给儿子买的，是一整套经过设计的私人教育。",[11,37815,37816],{},"这样的家教安排，在那个年代的布达佩斯并不罕见。二十世纪初，布达佩斯的一批犹太中产家庭把数学和语言教育当成头等大事，舍得为下一代花钱；诺依曼、维格纳、西拉德、特勒、冯·卡门——这些后来跟原子弹、氢弹、航空这些词紧紧绑在一起的名字——都出自同一个城市、相近的阶层。这群人中间后来流传一个玩笑：火星上的侦察兵在布达佩斯落脚，跟当地人通婚，留下孩子，又回了火星，于是有了这批「不像地球人」的科学家。玩笑归玩笑，背景是实的：诺依曼和维格纳上的是同一所路德中学，教过他们数学的是同一位老师——拉茨·拉斯洛。诺依曼不是孤例，他只是这一批人里算得最快、路走得最宽的一个。",[11,37818,37819],{},"家里原本盘算让他子承父业，将来接银行的班，至少学门「正经手艺」。至于数学，父亲倒也不反对，只是觉得那门手艺养活不了人。",[1305,37821,37822],{"id":37822},"从化学到量子力学",[11,37824,37825],{},"于是，他一边挂名在苏黎世联邦理工学院读化学工程，一边偷偷跑去旁听数学课，每学期还要跑回布达佩斯参加考试。两条腿走路，两头都没耽误：二十岁上下，他先后拿到了苏黎世的化学工程文凭和布达佩斯大学的数学博士学位，论文题目是《集合论的公理化》，那年他二十二岁。头一篇正式发表的论文，其实早在中学时代就出来了——一九二二年，还不满十八岁的他和费凯特合写了一篇文章，讨论一类极小多项式零点的位置，把切比雪夫多项式的一个经典结果往前推了一步。",[11,37827,37828],{},"父亲的心愿和儿子自己的兴趣，算是用一种曲线救国的方式两全了。那套化学工程的训练他后来几乎没再用过，倒是养成了他一辈子的习惯：把物理问题先翻译成数学，再拿数学去对付它。",[11,37830,37831],{},"博士毕业那年秋天，他拿了一笔洛克菲勒奖学金去了哥廷根，在大卫·希尔伯特身边做研究。那时候量子力学刚成形不过几年，海森堡的矩阵力学、薛定谔的波动力学、玻恩的概率诠释，各家表述五花八门，物理学家正吵得不可开交。诺依曼在哥廷根那几年，做的一桩费力的事：把量子力学翻译成严格的数学语言。他用希尔伯特空间搭起统一框架，讨论观测量的谱分解，还头一回把「测量」写成一个数学过程——一九三二年出版的德文专著《量子力学的数学基础》，成了这个领域绕不过去的一本书。这套「给年轻学科搭骨架」的本事，往后他还会用很多次。",[11,37833,37834],{},"一九三〇年九月，在哥尼斯堡的一场学术会议上，一位叫库尔特·哥德尔的年轻逻辑学家报告了一个令人不安的结果：任何足够强的一致公理系统里，都有既不能证明也不能证伪的命题——这就是后来著名的「不完备定理」。台下大多数听众没太当回事，诺依曼却当场就抓住了证明的要害。散会之后他顺着想下去，琢磨出一个哥德尔当时还没说透的推论：这样的系统连「自身是一致的」这件事都无法证明。他写了一封信给哥德尔，信里把这个结论完整地推了一遍。等哥德尔的回信到了，他才得知，哥德尔本人也已经发现了这个结果，正在把它写进次年发表的文章里。诺依曼没有争这个先后，后来还在公开场合把功劳归给哥德尔。",[11,37836,37837],{},"在柏林和汉堡当讲师的那些年，他一边教课一边写，算子理论、遍历理论、测度论，到处都有他插手的痕迹。",[1305,37839,37840],{"id":37840},"研究院与博弈论",[11,37842,37843],{},"一九三〇年，他应普林斯顿大学的邀请跨过大西洋去讲学。一九三三年，新成立的普林斯顿高等研究院聘他做创始教授——第一批六位教授里，有爱因斯坦，有外尔，有刚从纳粹德国跑出来的哥德尔。诺依曼是最年轻的一个。",[11,37845,37846],{},"三十年代是他学术上最密集的一段时间。他跟弗朗西斯·默里合作，把「算子代数」这门学科从无到有地搭起来——后来这套东西被称作「冯·诺依曼代数」，至今仍是数学和量子物理交叉处的重要工具。他还把集合论里「序数」的定义做了现代化处理，证明了紧群上哈默测度的唯一性；一九三二年，他又证明了动力系统里一个关于时间平均的定理——后来被称作「平均遍历定理」，成了统计物理的基本工具。光是在普林斯顿的头十年，他横跨的领域多得让同行咋舌——但「咋舌」是我们这些后来的读者会用的词，当时他身边人的反应往往是：又来了。",[11,37848,37849],{},"一九二八年，他还在柏林时就发表过一篇讨论博弈的文章，研究两人零和博弈，证明了著名的「极小极大定理」——玩家在最坏情况下求最好结果的策略，跟对方的策略同时达成平衡。这篇论文当时在数学圈里没掀起多少波澜。真正让它出圈，要等他和一位经济学家奥卡·莫根施特恩的合作。莫根施特恩是奥地利人，一九三八年逃到普林斯顿，两人一拍即合，一九四四年出版了《博弈论与经济行为》——一本经济学史和数学史上都绕不过去的大书。把「博弈」变成一门有严格结构的学科，跟当年给量子力学搭骨架，是同一个路数。",[11,37851,37852],{},"研究院边上，他的生活渐渐固定下来。家里几乎每周都要开派对，客厅里高朋满座，他自己端着酒杯一圈一圈地敬酒讲笑话，笑话大多带点荤腥，气氛总能被他搅得热闹非凡。据好友乌拉姆回忆，他喜欢昂贵的西装、烈酒和跑车，是那种谁都愿意请去撑场面的座上宾。",[11,37854,37855],{},"他跟哥德尔的交情值得一提。哥德尔是出了名的孤僻，在研究院里少有人能跟他真正说上话，诺依曼是少数几个。两人常在普林斯顿的林间小道上一起散步，一聊就是很久——聊的什么，旁人很少知道，大约是逻辑与数学的底细。研究院里的气氛并不总是一团和气：他跟外尔能合作，跟爱因斯坦之间却谈不上热络，两人对许多事情的看法相去甚远，尤其是在战争与核武器的问题上。",[11,37857,37858],{},"还有一件后来才被翻出来的小事。一九三八年春天，一位名叫艾伦·图灵的英国青年在普林斯顿完成了他的博士论文——那篇论文后来被称为「图灵机」的构想。诺依曼读过之后，提出让他留在高等研究院给自己当助手，年薪一千五百美元。图灵谢绝了，他说剑桥国王学院的职位更合意，然后乘船回了英国。多年以后人们回头翻这段旧账，常常感叹：如果当时图灵留了下来，计算机的早期历史也许会换一副样子。",[11,37860,37861],{},"一九三七年，他入了美国籍。也是那段时间，他离了婚，娶了第二任妻子克拉拉·丹。第一段婚姻的另一位主角玛丽埃特是布达佩斯人，两人婚后有个女儿玛丽娜，生于一九三五年。离婚后，玛丽娜先在母亲身边长大，后来又回到父亲身边。分隔两地的时候，他给女儿写很长的信；玛丽娜在回忆录里写道，有一封信，头八页都在劝她别急着结婚，后面才转到她的论文，再扯到他自己对历史的看法，顺手引了几段法文史料。玛丽娜后来读了经济学，一九七二年被尼克松任命为总统经济顾问委员会成员——是头一个坐上那个位子的女性。她晚年给回忆录起名《火星人的女儿》，写的就是前面那批「火星人」里的她父亲。",[11,37863,37864],{},"战争还没打起来，他的顾问身份就先忙上了。一九三七年之后，他先后给陆军和海军当顾问，处理弹道、炸药和空气动力学的问题。他参与改进了「聚能装药」——一种把炸药能量聚焦成射流来击穿装甲的设计，后来成了反坦克武器的原理。这些事他做得不声不响，连研究院里的同事都未必清楚。同一时期，他那几个布达佩斯老同乡也在为同一件事奔走——一九三九年，西拉德、维格纳和特勒三个人起草了一封给罗斯福的信，借爱因斯坦的名字签了出去，提醒美国政府注意铀裂变的前景；诺依曼没有在这封信上署名，但布达佩斯这群人之间，消息向来是通的。",[1305,37866,37867],{"id":37867},"原子弹的算盘",[11,37869,37870],{},"一九四三年，奥本海默把诺依曼请到了洛斯阿拉莫斯。名义上他是顾问，实际上他很快成了原子弹设计里「算」这一环的关键人物。",[11,37872,37873],{},"原子弹的临界质量怎么算？炸药怎么聚爆才对称？冲击波在水里、在空气里怎么传播？这些在诺依曼到来之前，许多还停留在估算阶段。他把流体力学和数值方法带进了洛斯阿拉莫斯，一起带进去的还有他那张出了名的「活计算器」。聚爆方案最初是另一位物理学家奈德迈耶提出的大胆设想，但把设想变成能用的设计，需要算清楚球面聚爆的流体力学细节——诺依曼接过这一摊，跟化学家基斯塔科夫斯基合作，把炸药透镜的配方和几何一点点调出来。他还算过另一种打法：把核弹在高空引爆，让冲击波在更大的面积上均匀压下来，造成的破坏比地面引爆大得多。广岛和长崎的投弹高度，就参考了这套计算。",[11,37875,37876],{},"一九四五年七月十六日凌晨，新墨西哥州阿拉莫戈多沙漠，人类第一次核爆试验——「三位一体」——在那里进行。诺依曼就站在观看的人群里，看着那颗以他的方程为基础的炸弹把自己烧成白光。他回去之后说了什么，没有可靠的记载；能确认的是，他给这次试验做过大量的计算，也为此吸收了不少辐射。在洛斯阿拉莫斯那段日子，他跟费米、费曼这些人在食堂里一桌吃饭、插科打诨，照样是那身讲究的打扮。原子弹的严肃和这些日常混在一起，在他身上并不显得矛盾。",[11,37878,37879],{},"战后他留在这个圈子里。氢弹的「超级」方案，他是最早的推动者之一；一九四六年他跟乌拉姆一起，在洛斯阿拉莫斯继续做数值计算。这些工作后来凝结成了他冷战幕僚生涯的一部分。",[1305,37881,37882],{"id":37882},"从算数到思考",[11,37884,37885],{},"战争还没结束，另一条线索已经悄悄接上了。",[11,37887,37888],{},"一九四四年夏天，在阿伯丁的火车站台上，诺依曼碰上了陆军派到宾夕法尼亚大学的联络官赫曼·哥德斯坦。哥德斯坦随口说起，大学里正在建造一台叫 ENIAC 的电子计算机——一万八千个真空管，用来算火炮射表。诺依曼听完，没过多久就出现在摩尔学院的每次设计会上。那一年正是曼哈顿计划最紧的时候，他两头跑；他很快意识到，这种「机器自动算」的路子，正是洛斯阿拉莫斯需要的。",[11,37890,37891],{},[37795,37892],{"alt":37893,"src":37894},"埃尼阿克计算机","https:\u002F\u002Fimage-assets.dreams.plus\u002F202609020249186.png",[11,37896,37897],{},"一九四五年六月，他起草了一份报告，题目叫《EDVAC 报告初稿》，把「存储程序」的思想写成白纸黑字——程序和数据一样放进内存，机器读一条执行一条，不必再靠插拔接线来「改程序」。",[11,37899,37900],{},"这份打印稿在圈子里私下流传，日后被称作「冯·诺依曼架构」的雏形。",[11,37902,37903],{},"严格说，「存储程序」是小组讨论的产物，不全是他的发明；但把它提炼成一份清晰的文件，又一路推动它付诸实现的，是他。这一步的关键不在算得快，而在想得远：机器从此不只是算数的工具，程序本身也成了可以被读写的东西。",[11,37905,37906],{},"战后他在高等研究院主持电子计算机项目，一九五二年，那台「IAS 机」正式跑了起来。这台机器的图纸流传出去，成了好几家机构机器的蓝本——兰德公司照着造的那台，直接被人叫作「约翰尼艾克」。",[11,37908,37909],{},"为了让机器有正经事干，他和乌拉姆、梅特罗波利斯一起，把一种用随机数抽样逼近复杂计算的「蒙特卡洛方法」搬上了机器，用来算中子的扩散。",[11,37911,37912],{},"他一边算，一边开玩笑：任何想用确定性办法产生随机数的人，都是「活在罪孽之中」。这句玩笑后来成了统计学家们的名言。顺带一提，他的第二任妻子克拉拉·丹也是这台机器背后的早期程序员之一，替蒙特卡洛计算写过代码。",[11,37914,37915],{},"他还惦记着用机器预报天气。四十年代他就反复对人说，天气预报是计算机最有价值的用途之一，甚至把人工造雨、控制气候也算进计算的版图。一九五二年前后，他拉了几位气象学家，真的在 IAS 机上跑起了数值天气预报——那台机器算一次要用很久，但方向算是立住了。",[11,37917,37918],{},"从「机器能算什么」到「机器到底是什么」，这条路他一路走到了底。他琢磨「自动机」能不能自我复制，设计过一个理论上能复制自身的自动机，还在一次研讨会上做过一场题为《自动机的逻辑理论》的演讲，讨论机器与人脑的关系。",[11,37920,37921],{},"一九五二年一月，他在加州理工连讲五讲，题目是《概率逻辑与由不可靠元件合成可靠有机体》。灵感来自脑子：神经元单个来看并不牢靠，可整颗脑子照样运转稳定——问题是，怎么用一堆不可靠的零件，拼出一台可靠到能算能记的机器。",[11,37923,37924],{},"这份讲稿后来在《自动机研究》上刊出，成了后世「容错计算」最早的理论基础之一。他一辈子都在跟「系统内部的不可靠」打交道，从集合论里的不完备，到神经元的不稳定，说到底像是同一件事。",[11,37926,37927],{},"这些想法他生前没有写完，身后被整理成《自复制自动机理论》一书。他给耶鲁预备的最后一份讲稿，题目就叫《计算机与人脑》，讲的还是同一个执念：机器和脑子，到底谁跟谁学。",[11,37929,37930],{},"有一次，记者问他正在想什么。他说：「我在想一件比炸弹重要得多的事——我在想计算机。」这话流传得很广，因为说这话的人，炸弹和计算机两样都参与得很深。",[1305,37932,37933],{"id":37933},"冷战幕僚",[11,37935,37936],{},"同一时期，他的另一副面孔也在忙碌。",[11,37938,37939],{},"学术这边，他把博弈论从桌上的游戏推向对人类决策的一般描述。跟莫根施特恩合著的《博弈论与经济行为》一九四四年出版，一开始读者寥寥——经济学家嫌它太数学，数学家嫌它太经济学。",[11,37941,37942],{},"诺依曼没太在意，照样在各种场合宣传这套东西「能描述一切有利益冲突的人类活动」。一九四七年十月，一个叫乔治·丹齐格的年轻人带着一道卡了自己很久的线性规划题来见他。",[11,37944,37945],{},"诺依曼看了一眼，说了句「哦，这个啊」，然后当场在黑板前面讲了一个多小时，把线性规划的「对偶性」从头推到尾——这个结论，丹齐格之前翻遍了文献也没找到。丹齐格后来回忆，自己当场就学会了法卡斯引理和对偶理论。而这场即兴讲座的另一个副产品，是把博弈论和线性规划这两种此前不搭界的数学连到了一起。",[11,37947,37948],{},"公共事务这边，他越来越深地卷进冷战。他是空军科学顾问委员会的成员，是兰德公司的顾问——兰德公司在加州的圣莫尼卡，他战后常去那边——还替原子能委员会出谋划策。",[11,37950,37951],{},"博弈论在这里找到了最严肃的用武之地：核威慑，本质上被他说成一场玩家之间不停盘算对方底牌的博弈。他的政治立场之强硬，在当时的科学家里也属于突出的那一档——一九五〇年，他私下对不少人讲过，美国应该趁苏联还没造出氢弹，先发制人。",[11,37953,37954],{},"这个主张在研究院的同僚里并不讨喜，研究院里也有不少人跟他观点相左，但在白宫和五角大楼的走廊里，他的话很受用。",[11,37956,37957],{},"一九五四年，奥本海默的安全听证会开庭。诺依曼和奥本海默在氢弹问题上站得正相反，可他还是去做了证人。听证官问他对奥本海默的忠诚怎么看，他说：毫无疑问，没有任何怀疑。他又当着听证官的面把两件事分开——反对氢弹是一回事，忠诚是另一回事；他还提醒，这套安全体系有个危险，就是把技术上的不同意见，误当成政治上的异心。听证会的结果没有因为他的证词而改变：奥本海默还是被吊销了安全许可，从此离开了决策圈。",[11,37959,37960],{},"同年，他主持的一个委员会（因为代号而被称为「茶壶委员会」）向空军提交了一份报告，建议美国大力发展洲际弹道导弹——后来美国的第一代洲际导弹，多少都算这份报告的产物。一九五五年，艾森豪威尔把他任命为原子能委员会委员——委员会里像他这样以科学家身份直接坐进决策层的，并不多见。",[11,37962,37963],{},"他经手的事务，大多与核武器的设计和导弹的部署有关：他那个委员会算过一笔账，一枚能装进洲际导弹的一兆吨氢弹，足以把两英里内的一切抹平；于是氢弹的小型化跟洲际导弹一起，成了他这边推进的两件事。",[11,37965,37966],{},"一九五六年，比基尼环礁上进行了新的一轮核试验，第一枚「袖珍氢弹」就是在那轮试验里炸响的——那时候，他坐在委员会里，离权力中心很近。据说不管对面坐着的是将军还是总统，他都能一样谈笑风生、自信从容；艾森豪威尔后来回忆过，给他颁发总统自由勋章那次，这位科学家的风趣谈吐给自己留下了很深的印象。",[1305,37968,37969],{"id":37969},"灵感",[11,37971,37972],{},"工作之外，穿着讲究到有点固执：常年穿着马甲，口袋里插一块手绢，外套的扣子永远扣得整整齐齐——即便是在新墨西哥沙漠里搞原子弹的洛斯阿拉莫斯，别人穿着短袖短裤在酷热里晃悠，他也照样西装革履。他喜欢精巧的小玩意，复杂的机械玩具、稀奇古怪的小装置，只要摆在他面前，他都要摆弄一番。",[11,37974,37975],{},"工作起来他是不折不扣的工作狂，一个问题不解决，他能一直死磕下去，半夜里灵感一来，翻身就爬起来接着算。可一旦离开书桌，他对生活琐事的粗心大意也是出了名的。据说有一次，他生病卧床的妻子想让他倒杯水，诺依曼却愣是想不起杯子放在哪儿——而那时候他已经在那栋房子里住了整整十七年。",[11,37977,37978],{},"开车对他来说更是一场持续多年的灾难。他几乎每年都要报废一辆车，熟人们甚至专门给他反复出事故的那个路口起了个外号，叫「冯·诺依曼转角」。他喜欢把车开得飞快，据他身边人的说法，那是把拥挤的路段当成一道多体问题，边开边在心里算最优路线——至于算得好不好，看事故率就知道。",[11,37980,37981],{},"他其实从没考下过驾照，连着几次没过之后，还是在妻子的建议下使了点手段，才拿到执照。他开的是凯迪拉克，问他为什么挑这个牌子，他说：因为没人肯卖给我坦克。据说他跟保险公司解释事故经过时说过一句流传很广的话：路边的树本来排得整整齐齐地朝我迎面而来，一直都挺好的，直到有一棵没躲开。",[11,37983,37984],{},"他食量也惊人。在洛斯阿拉莫斯搞原子弹那几年，他常常开车一百二十英里，专程跑去一家墨西哥餐馆撮一顿，吃完再开一百二十英里回来——对他而言，这大概不算什么特别麻烦的事。",[11,37986,37987],{},"他的算术快到经常让身边人下不来台。他上课喜欢直接在黑板上写答案，中间的推导过程一概省略，学生们常常一脸茫然。有一回一个学生不死心，追问他这道题是不是还有别的解法，诺依曼愣了一下，一本正经地点头说：「有。」然后就没了下文——那个所谓「另一种解法」，大概永远留在他自己脑子里了。",[11,37989,37990],{},"还有一次，麻省理工的一个学生在走廊里拦住他，请教一道积分题。诺依曼瞄了一眼题目，脱口而出答案。学生说，教授，我知道书后面写的答案就是这个，我是想请您讲讲怎么算出来的。诺依曼又看了一眼题目，想了想，把答案又报了一遍。学生急了，反复解释自己要的是过程。诺依曼摊摊手，一脸无辜地说：「你还想怎样，我可是用了两种不同的方法才验算出这个答案的。」",[11,37992,37993],{},"他的心算速度还成就了一个流传很广的派对段子：一次晚宴上，女主人出了道题考他——两列火车相距一英里，各以每小时三十英里的速度迎面开来，一只苍蝇栖在其中一列车头，以每小时六十英里的速度朝对面飞去，碰到之后立刻折返，如此来回，直到两车相撞，问苍蝇一共飞了多少英里。",[11,37995,37996],{},"大多数懂点数学的人，第一反应是去算一个无穷级数求和，麻烦但也不难；诺依曼几乎没停顿就报出了正确答案。提问的人有点失望地说，其实有个巧办法——先算出两车相撞要多久（正好一分钟），再乘以苍蝇的速度就行，用不着算级数。诺依曼有点意外地反问：「可是我刚才算的就是级数啊。」",[11,37998,37999],{},"还有个流传更广的故事：福特汽车厂里一台发电机坏了，工程师们查了半天也没找出毛病，慕名请诺依曼来看。他围着机器转了一圈，用粉笔在外壳上画了一条线，让工人从那儿拆开检查——问题果然就出在那儿。福特问他要多少钱，诺依曼开了一张五千美元的账单，还附上明细：「画一条线，一美元；知道该画在哪儿，四千九百九十九美元。」（这则轶事在另一位工程师身上也有相似的版本，流传得久了，人们总爱把它安在算得最快的人头上。）",[11,38001,38002],{},"还有一件小事。象棋这件事，他其实也早就想过了。他一九二八年的极小极大定理，写的是两个人如何在博弈里各取最优；后来计算机下棋所用的那套搜索方法，追根溯源，都是从那棵博弈树长出来的。一九五六年，洛斯阿拉莫斯的一台机器第一次用它下赢了业余棋手。他连这个都已经想过了。",[11,38004,38005],{},"战后，一位在洛斯阿拉莫斯工作的物理学家碰到一道棘手的题，跑去请教这位顾问。诺依曼说：简单，用特征线法就能解。物理学家老老实实说，我不懂特征线法。诺依曼看着他：「年轻人，在数学里，你不需要理解什么，你只需要习惯它们。」这句话后来被记了下来，成了许多数学系学生自我安慰的箴言。",[1305,38007,38008],{"id":38008},"病床上的最后一年",[11,38010,38011],{},"一九五五年，诺依曼被查出癌症——多半是骨癌，具体是什么，各种说法都有，但大家普遍认为，跟他这些年没少亲临核试验现场、接触辐射脱不了关系。",[11,38013,38014],{},"诊断没有让他停下来。他坐着轮椅照常去五角大楼开会，担任的原子能委员会委员一直当到生命的最后，躺在病床上还在口述那部没写完的手稿。",[11,38016,38017],{},"病床边的一些细节，是身边人后来才慢慢讲出来的。一向对宗教毫不在意的他，主动请来一位天主教神父，安排了临终仪式——不过那位神父私下说，自己也说不准这场仪式究竟有没有真的抚慰到这位科学家。",[11,38019,38020],{},"这件事让很多老朋友意外——他这辈子对宗教既不信，也不讨论，更不反对，只是像对待一套不感兴趣的数学公理一样，敬而远之。",[11,38022,38023],{},"诺依曼对仪式的配合，更像是完成一项程序：到了这个阶段，该走的步骤走一遍。他问过诺依曼是否想谈谈上帝。诺依曼的回答很短，大意是：如果有一种更高级的存在，它大概不会用我们这种语言说话。",[11,38025,38026],{},"这话既是拒绝，也没有完全关上。像他晚年的很多判断一样——保留可能性，不给出承诺。",[11,38028,38029],{},"乌拉姆后来回忆，诺依曼在病中有一阵子确实表现出对死亡的恐惧，那种恐惧比周围人预想的更具体，也更不「体面」。他会长时间地计算自己还剩多少时间，问医生每种治疗方案的概率，像在评估一个项目的失败风险。死亡对他而言不是哲学问题，是一道突然摆在面前的、信息不完备的决策题。",[11,38031,38032],{},"而宗教能提供的，恰恰是他一生都在绕开的那种东西：不确定、不可验证、不要求算清楚。他的理性是他最锋利的工具，也是他的边界。临终前他愿意走一遍仪式，却无法交出那个「信任的跳跃」。",[11,38034,38035],{},"这大概是一个一生都在把世界翻译成数学的人，最后发现，有些东西翻译不过去。这个人太理性了，一生理性的他，宗教抚慰很难走进他的内心。",[11,38037,38038],{},"因为他脑子里装着太多国防机密，弥留之际，军方甚至派了警卫守在病房门口，生怕他意识模糊时无意间说漏了嘴。",[11,38040,38041],{},"乌拉姆在他去世后写的纪念文章里，回忆了一次谈话：诺依曼谈到技术的加速进步，说人类的处境正在逼近某种「本质上的奇点」——越过那个点之后，按我们熟悉的方式运转的人类事务，恐怕难以继续下去。这话经由乌拉姆的笔传下来，成了「技术奇点」这个概念最早的出处之一。",[11,38043,38044],{},"一九五七年二月八日，诺依曼在华盛顿的沃尔特·里德陆军医院去世，享年五十三岁，葬在新泽西州普林斯顿。他女儿玛丽娜后来在回忆录里写道，父亲弥留之际说过一句话：「没有人真正理解另一个人。」——这是那种让人没法反驳、也让人没法安心的句子。",[11,38046,38047],{},"去世六年后，同样来自匈牙利的诺贝尔物理学奖得主尤金·维格纳在一次演讲后被人问：匈牙利怎么在同一个年代冒出这么多天才？维格纳想都没想地回答——只有冯·诺依曼一个人是天才，别人不过是脑子比较好使的普通人罢了。据说在场没人反驳这句话，尽管诺依曼这辈子从没拿过什么重量级的科学奖章。",{"title":4127,"searchDepth":37734,"depth":37734,"links":38049},[38050,38051,38052,38053,38054,38055,38056,38057],{"id":37785,"depth":37734,"text":37785},{"id":37822,"depth":37734,"text":37822},{"id":37840,"depth":37734,"text":37840},{"id":37867,"depth":37734,"text":37867},{"id":37882,"depth":37734,"text":37882},{"id":37933,"depth":37734,"text":37933},{"id":37969,"depth":37734,"text":37969},{"id":38008,"depth":37734,"text":38008},{},"\u002Fblog\u002F2026\u002F0002-brief-biography-of-von-neumann",{"title":37780,"description":4127},"blog\u002F2026\u002F0002-brief-biography-of-von-neumann","从 1903 年布达佩斯的银行家之子，到 1957 年华盛顿病床上的原子能委员。他留下的不是一尊天才的神像，而是一道冷峻的背影——一个快得让时代跟不上的头脑，一个把理性用到极致、也走到理性尽头的人。",[38064],"thoughts","2026-09-02T02:45:47+08:00","KFRWCJxndsMPsD1egcxGn8kEmxXpjHfYKLPgx7E-qNw",{"left":38068,"top":38068,"width":38069,"height":38069,"rotate":38068,"vFlip":37764,"hFlip":37764,"body":38070},0,24,"\u003Cpath fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"round\" stroke-linejoin=\"round\" stroke-width=\"2\" d=\"M12 7v5l3 3m6-3a9 9 0 1 1-18 0a9 9 0 0 1 18 0\"\u002F>",{"left":38068,"top":38068,"width":38069,"height":38069,"rotate":38068,"vFlip":37764,"hFlip":37764,"body":38072},"\u003Cpath fill=\"currentColor\" d=\"M16 10c0-2.21-1.79-4-4-4s-4 1.79-4 4s1.79 4 4 4s4-1.79 4-4m-6 0c0-1.1.9-2 2-2s2 .9 2 2s-.9 2-2 2s-2-.9-2-2\"\u002F>\u003Cpath fill=\"currentColor\" d=\"M11.42 21.81c.17.12.38.19.58.19s.41-.06.58-.19c.3-.22 7.45-5.37 7.42-11.82c0-4.41-3.59-8-8-8s-8 3.59-8 8c-.03 6.44 7.12 11.6 7.42 11.82M12 4c3.31 0 6 2.69 6 6c.02 4.44-4.39 8.43-6 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