{"id":26472,"date":"2021-05-24T23:02:55","date_gmt":"2021-05-24T15:02:55","guid":{"rendered":"https:\/\/swarma.org\/?p=26472"},"modified":"2021-05-24T23:02:55","modified_gmt":"2021-05-24T15:02:55","slug":"%e7%bb%9f%e8%ae%a1%e5%ad%a6%e6%9d%83%e5%a8%81%e7%9b%98%e7%82%b9%e8%bf%87%e5%8e%bb50%e5%b9%b4%e6%9c%80%e9%87%8d%e8%a6%81%e7%9a%84%e7%bb%9f%e8%ae%a1%e5%ad%a6%e6%80%9d%e6%83%b3%ef%bc%8c%e5%9b%a0%e6%9e%9c","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=26472","title":{"rendered":"\u7edf\u8ba1\u5b66\u6743\u5a01\u76d8\u70b9\u8fc7\u53bb50\u5e74\u6700\u91cd\u8981\u7684\u7edf\u8ba1\u5b66\u601d\u60f3\uff0c\u56e0\u679c\u63a8\u7406\u3001bootstrap\u7b49\u4e0a\u699c\uff0cJudea Pearl\u70b9\u8d5e"},"content":{"rendered":"
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\u9648\u5f69\u5a34\u3001Mr Bear | \u4f5c\u8005<\/strong><\/span><\/p>\n

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\u503c\u5f97\u4e00\u63d0\u7684\u662f\uff0cJudea Pearl\u5728\u63a8\u6587\u4e2d\u8868\u793a\uff0c\u201c\u5bf9\u4f5c\u8005\u5c06\u56e0\u679c\u63a8\u7406\u5217\u5165\u5176\u4e2d\u611f\u5230\u6b23\u6170\uff0c\u8fd9\u4e0eStigler\u5728\u300a\u7edf\u8ba1\u5b66\u4e03\u652f\u67f1\u300b\u4e2d\u7684\u603b\u7ed3\u622a\u7136\u4e0d\u540c\uff0c\u540e\u8005\u5b8c\u5168\u6ca1\u6709\u63d0\u5230\u56e0\u679c\u63a8\u7406\u3002\u201d\u53e6\u5916\uff0c\u4ed6\u4e5f\u5bf9\u5927\u5b66\u7edf\u8ba1\u4e13\u4e1a\u5f88\u5c11\u5b89\u6392\u56e0\u679c\u63a8\u7406\u8bfe\u7a0b\u611f\u5230\u62c5\u5fe7\uff0c\u201c\u7edf\u8ba1\u5b66\u53ef\u4ee5\u671f\u5f85\u590d\u5174\u6216\u6539\u9769\u5417\uff1f\u4e0d\u5e78\u7684\u662f\uff0c\u7edf\u8ba1\u7cfb\u4e2d\u63d0\u4f9b\u56e0\u679c\u63a8\u7406\u8bfe\u7a0b\u7684\u975e\u5e38\u5c11\uff0c\u66f4\u4e0d\u7528\u63d0\u6559’The First Law’\u7684\uff0c\u7b80\u76f4\u662f\u65e0\u7a77\u5c11\u3002\u201d<\/span><\/section>\n

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\u5728\u8fd9\u4e2a\u7814\u7a76\u65b9\u5411\u4e0a\uff0c\u5177\u6709\u91cc\u7a0b\u7891\u610f\u4e49\u7684\u5de5\u4f5c\u5305\u62ec Neyman<\/span> (1923)<\/span>\uff0cWelch <\/span>(1937)<\/span>\uff0cRubin <\/span>(1974)<\/span>\uff0cHaavelmo<\/span> (1973) <\/span>\u7b49\u4eba\u7684\u7814\u7a76\u6210\u679c\uff0c\u66f4\u52a0\u8be6\u7ec6\u7684\u7814\u7a76\u80cc\u666f\u8bf7\u53c2\u9605 Heckman \u548c Pinto \u4e8e 2015 \u5e74\u53d1\u8868\u7684\u8bba\u6587\u300cCausal analysis after Haavelmo\u300d\u3002<\/span><\/section>\n

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1.2 bootstrap\u4e0e\u57fa\u4e8e\u6a21\u62df\u7684\u63a8\u7406<\/span><\/strong><\/span><\/section>\n

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\u5728\u8fc7\u53bb\u768450\u5e74\u4e2d\uff0c\u7528\u8ba1\u7b97\u53d6\u4ee3\u6570\u5b66\u5206\u6790\u662f\u7edf\u8ba1\u5b66\u7684\u4e00\u5927\u53d1\u5c55\u8d8b\u52bf\u3002\u8fd9\u4e00\u53d8\u5316\u751a\u81f3\u5728\u300c\u5927\u6570\u636e\u300d\u5206\u6790\u51fa\u73b0\u4e4b\u524d\u5c31\u5f00\u59cb\u4e86\u3002<\/span><\/section>\n

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bootstrap\u662f\u6700\u7eaf\u7cb9\u7684\u57fa\u4e8e\u8ba1\u7b97\u5b9a\u4e49\u7684\u7edf\u8ba1\u65b9\u6cd5\u4e4b\u4e00\uff0c\u5b83\u5b9a\u4e49\u4e86\u4e00\u4e9b\u4f30\u8ba1\u91cf\uff0c\u5e76\u5c06\u5176\u5e94\u7528\u4e8e\u4e00\u7ec4\u968f\u673a\u91cd\u91c7\u6837\u6570\u636e\u96c6\u3002\u5176\u601d\u60f3\u662f\u5c06\u4f30\u8ba1\u503c\u89c6\u4e3a\u6570\u636e\u7684\u4e00\u4e2a\u8fd1\u4f3c\u7684\u5145\u5206\u7edf\u8ba1\u91cf\uff0c\u5e76\u5c06\u81ea\u52a9\u5206\u5e03\u89c6\u4e3a\u5bf9\u6570\u636e\u7684\u91c7\u6837\u5206\u5e03\u7684\u8fd1\u4f3c\u3002<\/strong>\u5728\u6982\u5ff5\u5c42\u9762\u4e0a\uff0c\u4eba\u4eec\u63a8\u5d07\u5c06\u9884\u6d4b\u548c\u91cd\u65b0\u62bd\u6837\u4f5c\u4e3a\u57fa\u672c\u539f\u5219\uff0c\u53ef\u4ee5\u63a8\u5bfc\u51fa\u8bf8\u5982\u504f\u5dee\u6821\u6b63\u548c\u6536\u7f29\u7b49\u7edf\u8ba1\u5b66\u64cd\u4f5c\u3002<\/span><\/section>\n

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1.3 \u8fc7\u53c2\u6570\u5316\u6a21\u578b\u548c\u6b63\u5219\u5316<\/span><\/strong><\/span><\/section>\n

<\/span><\/strong><\/span><\/section>\n<\/h3>\n
\u81ea 20 \u4e16\u7eaa 70 \u5e74\u4ee3\u4ee5\u6765\uff0c\u7edf\u8ba1\u5b66\u53d7\u4e2a\u65b9\u9762\u7684\u5f71\u54cd\uff0c\u53d1\u751f\u4e86\u4e00\u4e2a\u91cd\u5927\u7684\u53d8\u5316\uff0c\u5373\u7528\u4e00\u4e9b\u6b63\u5219\u5316\u8fc7\u7a0b\u5f97\u5230\u7a33\u5b9a\u7684\u4f30\u8ba1\u548c\u826f\u597d\u7684\u9884\u6d4b\u7ed3\u679c\uff0c\u4ece\u800c\u62df\u5408\u5177\u6709\u5927\u91cf\u53c2\u6570<\/span>\uff08\u6709\u65f6\u53c2\u6570\u6bd4\u6570\u636e\u70b9\u66f4\u591a\uff09<\/span>\u7684\u6a21\u578b\u3002\u8be5\u601d\u60f3\u65e8\u5728\u5728\u907f\u514d\u8fc7\u62df\u5408\u95ee\u9898\u7684\u540c\u65f6\uff0c\u83b7\u5f97\u4e00\u79cd\u975e\u53c2\u6570\u5316\u7684\u6216\u9ad8\u5ea6\u53c2\u6570\u5316\u7684\u65b9\u6cd5<\/strong>\u3002\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u9488\u5bf9\u53c2\u6570\u6216\u9884\u6d4b\u66f2\u7ebf\u7684\u60e9\u7f5a\u51fd\u6570\u6765\u5b9e\u73b0\u6b63\u5219\u5316\u3002<\/span><\/section>\n

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\u5728\u4eba\u4eec\u80fd\u591f\u5bb9\u6613\u5730\u83b7\u5f97\u5145\u8db3\u7684\u8ba1\u7b97\u8d44\u6e90\u4e4b\u524d\uff0c\u8fd9\u4e9b\u6a21\u578b\u7684\u4f7f\u7528\u8fd8\u5341\u5206\u6709\u9650\u3002<\/span><\/strong>\u6b64\u540e\uff0c\u56fe\u50cf\u8bc6\u522b\u3001\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u9886\u57df\u4e2d\u7684\u8fc7\u53c2\u6570\u5316\u6a21\u578b\u6301\u7eed\u53d1\u5c55\u3002Hastie\u3001Tibshirani \u4ee5\u53ca Wainwright \u4e8e 2015 \u5e74\u5c06\u8bb8\u591a\u8be5\u9886\u57df\u7684\u5de5\u4f5c\u5b9a\u4e49\u4e3a\u5bf9\u7a00\u758f\u7ed3\u6784\u7684\u4f30\u8ba1\u3002<\/span><\/section>\n

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\u968f\u7740\u7edf\u8ba1\u65b9\u6cd5\u5f97\u5230\u4e86\u53d1\u5c55\uff0c\u5e76\u88ab\u5e94\u7528\u4e8e\u66f4\u5927\u7684\u6570\u636e\u96c6\u4e0a\uff0c\u7814\u7a76\u8005\u4eec\u8fd8\u7814\u53d1\u4e86\u4e00\u4e9b\u8c03\u4f18\u3001\u81ea\u9002\u5e94\uff0c\u4ee5\u53ca\u7ec4\u5408\u6765\u81ea\u591a\u4e2a\u62df\u5408\u7ed3\u679c\u7684\u63a8\u7406<\/span><\/strong>\uff08\u5305\u62ec stacking \u96c6\u6210\u3001\u8d1d\u53f6\u65af\u6a21\u578b\u5e73\u5747\u3001boosting \u96c6\u6210\u3001\u68af\u5ea6\u63d0\u5347\u3001\u968f\u673a\u68ee\u6797\uff09<\/span>\u7684\u65b9\u6cd5\u3002<\/span><\/section>\n

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1.4 \u591a\u5c42\u6a21\u578b<\/span><\/strong><\/span><\/section>\n

<\/span><\/strong><\/span><\/section>\n<\/h3>\n
\u591a\u5c42\u6a21\u578b\u7684\u53c2\u6570\u56e0\u7ec4\u800c\u5f02\uff0c\u5b83\u4f7f\u6a21\u578b\u53ef\u4ee5\u9002\u5e94\u4e8e\u805a\u7c7b\u62bd\u6837\u3001\u7eb5\u5411\u7814\u7a76\u3001\u65f6\u95f4\u5e8f\u5217\u6a2a\u65ad\u9762\u6570\u636e\u3001\u5143\u5206\u6790\u4ee5\u53ca\u5176\u5b83\u7ed3\u6784\u5316\u7684\u73af\u5883\u3002\u5728\u56de\u5f52\u95ee\u9898\u4e2d\uff0c\u4e00\u4e2a\u591a\u5c42\u6a21\u578b\u53ef\u4ee5\u88ab\u770b\u505a\u7279\u5b9a\u53c2\u6570\u5316\u7684\u534f\u65b9\u5dee\u7ed3\u6784\uff0c\u6216\u8005\u662f\u4e00\u4e2a\u53c2\u6570\u6570\u91cf\u968f\u6570\u636e\u6bd4\u4f8b\u589e\u52a0\u7684\u6982\u7387\u5206\u5e03\u3002<\/span><\/section>\n

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\u90e8\u5206\u6c60\u5316\u7684\u601d\u60f3\u5df2\u7ecf\u88ab\u5e94\u7528\u4e8e\u4e00\u4e9b\u7279\u5b9a\u5e94\u7528\u9886\u57df<\/span>\uff08\u4f8b\u5982\uff1a\u52a8\u7269\u80b2\u79cd\uff09<\/span>\u3002\u90e8\u5206\u6c60\u5316\u4e0e\u7edf\u8ba1\u4f30\u8ba1\u95ee\u9898\u4e2d\u7684\u591a\u91cd\u6027\u7684\u4e00\u822c\u5173\u7cfb\u7531\u4e8e James \u548c Stein \u7b49\u4eba\u7684\u5de5\u4f5c\u800c\u5f97\u5230\u4e86\u7406\u8bba\u4e0a\u7684\u91cd\u8981\u8fdb\u5c55\u3002\u6700\u7ec8\uff0c\u8fd9\u542f\u53d1\u4e86\u5fc3\u7406\u5b66\u3001\u836f\u7406\u5b66\u3001\u62bd\u6837\u8c03\u67e5\u7b49\u9886\u57df\u7684\u7814\u7a76\u3002Lindley \u548c Smith \u4e8e 1972 \u5e74\u53d1\u8868\u7684\u8bba\u6587\uff0c\u4ee5\u53ca Lindley \u548c Novick \u4e8e 1981 \u5e74\u53d1\u8868\u7684\u8bba\u6587\u63d0\u4f9b\u4e86\u4e00\u79cd\u57fa\u4e8e\u4f30\u8ba1\u591a\u53d8\u91cf\u6b63\u6001\u5206\u5e03\u7684\u8d85\u53c2\u6570\u7684\u6570\u5b66\u7ed3\u6784\uff0c\u800c Efron \u548c Morris \u7b49\u4eba\u5219\u7ed9\u51fa\u4e86\u76f8\u5e94\u7684\u51b3\u7b56\u7406\u8bba\u65b9\u9762\u7684\u89e3\u91ca\uff0c\u63a5\u7740\u8fd9\u4e9b\u601d\u60f3\u88ab\u878d\u5165\u4e86\u56de\u5f52\u5efa\u6a21\u5e76\u88ab\u5e94\u7528\u4e8e\u5e7f\u6cdb\u7684\u4f7f\u7528\u7ed3\u6784\u5316\u6570\u636e\u7684\u95ee\u9898\u3002<\/span><\/section>\n

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\u4ece\u53e6\u4e00\u4e2a\u65b9\u5411\u6765\u770b\uff0cDonoho \u7b49\u4eba\u4e8e 1995 \u5e74\u7ed9\u51fa\u4e86\u591a\u5143\u53c2\u6570\u6536\u7f29\u7684\u4fe1\u606f\u8bba\u89e3\u91ca\u3002\u6211\u4eec\u66f4\u503e\u5411\u4e8e\u5c06\u591a\u5c42\u6a21\u578b\u770b\u505a\u5c06\u4e0d\u540c\u7684\u4fe1\u606f\u6e90\u8fdb\u884c\u7ec4\u5408\u7684\u6846\u67b6\uff0c\u800c\u4e0d\u662f\u4e00\u4e2a\u7279\u5b9a\u7684\u7edf\u8ba1\u6a21\u578b\u6216\u8ba1\u7b97\u8fc7\u7a0b\u3002<\/strong>\u56e0\u6b64\uff0c\u6bcf\u5f53\u6211\u4eec\u60f3\u8981\u6839\u636e\u6570\u636e\u7684\u5b50\u96c6\u8fdb\u884c\u63a8\u7406<\/span>\uff08\u5c0f\u9762\u79ef\u4f30\u8ba1\uff09<\/span>\u6216\u5c06\u6570\u636e\u6cdb\u5316\u5230\u65b0\u95ee\u9898<\/span>\uff08\u5143\u5206\u6790\uff09<\/span>\u4e0a\u7684\u65f6\u5019\uff0c\u5c31\u53ef\u4ee5\u4f7f\u7528\u8fd9\u79cd\u6a21\u578b\u3002\u7c7b\u4f3c\u5730\uff0c\u8d1d\u53f6\u65af\u63a8\u7406\u7684\u53ef\u8d35\u4e4b\u5904\u5728\u4e8e\uff0c\u5b83\u4e0d\u4ec5\u4ec5\u662f\u4e00\u79cd\u5c06\u5148\u9a8c\u4fe1\u606f\u548c\u6570\u636e\u7ec4\u5408\u8d77\u6765\u7684\u65b9\u6cd5\uff0c\u4e5f\u662f\u4e00\u79cd\u89e3\u91ca\u63a8\u7406\u548c\u51b3\u7b56\u7684\u4e0d\u786e\u5b9a\u6027\u7684\u65b9\u6cd5\u3002<\/strong><\/span><\/section>\n

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\n
1.5 \u6cdb\u578b\u8ba1\u7b97\u65b9\u6cd5<\/span><\/strong><\/span><\/section>\n

<\/span><\/strong><\/span><\/section>\n<\/h3>\n
\u524d\u6587\u4e2d\u8ba8\u8bba\u8fc7\u7684\u5efa\u6a21\u65b9\u9762\u7684\u7814\u7a76\u8fdb\u5c55\u9ad8\u5ea6\u4f9d\u8d56\u4e8e\u73b0\u4ee3\u8ba1\u7b97\u79d1\u5b66\uff0c\u8fd9\u4e0d\u4ec5\u4ec5\u6307\u7684\u662f\u66f4\u5927\u7684\u5185\u5b58\u3001\u66f4\u5feb\u7684 CPU\u3001\u9ad8\u6548\u7684\u77e9\u9635\u8ba1\u7b97\u3001\u5bf9\u7528\u6237\u53cb\u597d\u7684\u8bed\u8a00\uff0c\u4ee5\u53ca\u5176\u5b83\u8ba1\u7b97\u79d1\u5b66\u65b9\u9762\u7684\u521b\u65b0\u3002\u7528\u4e8e\u9ad8\u6548\u8ba1\u7b97\u7684\u7edf\u8ba1\u7b97\u6cd5\u65b9\u9762\u7684\u8fdb\u5c55\u4e5f\u662f\u4e00\u4e2a\u5173\u952e\u7684\u56e0\u7d20\u3002<\/span><\/section>\n

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\u5728\u8fc7\u53bb\u7684 50 \u5e74\u4e2d\uff0c\u5728\u7edf\u8ba1\u95ee\u9898\u7684\u7ed3\u6784\u65b9\u9762\u51fa\u73b0\u4e86\u8bb8\u591a\u5177\u6709\u521b\u65b0\u6027\u7684\u7edf\u8ba1\u7b97\u6cd5\u3002EM \u7b97\u6cd5\u3001Gibbs \u91c7\u6837\u3001\u7c92\u5b50\u6ee4\u6ce2\u3001\u53d8\u5206\u63a8\u65ad\u3001\u671f\u671b\u4f20\u64ad\u4ee5\u4e0d\u540c\u7684\u65b9\u5f0f\u5229\u7528\u4e86\u7edf\u8ba1\u6a21\u578b\u7684\u6761\u4ef6\u72ec\u7acb\u7ed3\u6784\u3002<\/span><\/section>\n

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\u800c Metropolis \u7b97\u6cd5\u3001\u6df7\u5408\u6216 Hamiltonian \u8499\u7279\u5361\u6d1b\u7b97\u6cd5\u5219\u5e76\u6ca1\u6709\u76f4\u63a5\u53d7\u5230\u7edf\u8ba1\u95ee\u9898\u7684\u542f\u53d1\uff0c\u5b83\u4eec\u6700\u521d\u88ab\u63d0\u51fa\u7528\u4e8e\u8ba1\u7b97\u7269\u7406\u5b66\u4e2d\u7684\u9ad8\u7ef4\u6982\u7387\u5206\u5e03\uff0c\u4f46\u662f\u5b83\u4eec\u5df2\u7ecf\u9002\u5e94\u4e86\u7edf\u8ba1\u8ba1\u7b97\uff0c\u8fd9\u4e0e\u5728\u66f4\u65e9\u7684\u65f6\u5019\u88ab\u7528\u4e8e\u8ba1\u7b97\u6700\u5c0f\u4e8c\u4e58\u4ee5\u53ca\u6700\u5927\u4f3c\u7136\u4f30\u8ba1\u7684\u4f18\u5316\u7b97\u6cd5\u76f8\u540c\u3002<\/span><\/section>\n

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\u5f53\u4f3c\u7136\u7684\u89e3\u6790\u5f62\u5f0f\u5f88\u96be\u6c42\u89e3\u6216\u8ba1\u7b97\u5f00\u9500\u975e\u5e38\u5927\u65f6\uff0c\u88ab\u79f0\u4e3a\u8fd1\u4f3c\u8d1d\u53f6\u65af\u8ba1\u7b97\u7684\u65b9\u6cd5<\/span>\uff08\u901a\u8fc7\u751f\u6210\u5f0f\u6a21\u578b\u4eff\u771f\u3001\u800c\u4e0d\u662f\u5bf9\u4f3c\u7136\u51fd\u6570\u8fdb\u884c\u4f30\u8ba1\u5f97\u5230\u540e\u9a8c\u63a8\u7406\uff09<\/span>\u662f\u5341\u5206\u6709\u6548\u7684\u3002<\/span><\/section>\n

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\u7eb5\u89c2\u7edf\u8ba1\u5b66\u7684\u5386\u53f2\uff0c\u6570\u636e\u5206\u6790\u7684\u53d1\u5c55\u3001\u6982\u7387\u5efa\u6a21\u548c\u8ba1\u7b97\u79d1\u5b66\u662f\u5171\u540c\u53d1\u5c55\u7684\u3002<\/span><\/strong>\u65b0\u7684\u6a21\u578b\u4f1a\u6fc0\u53d1\u5177\u6709\u521b\u65b0\u6027\u7684\u8ba1\u7b97\u7b97\u6cd5\uff0c\u800c\u65b0\u7684\u8ba1\u7b97\u6280\u672f\u53c8\u4e3a\u66f4\u52a0\u590d\u6742\u7684\u6a21\u578b\u548c\u65b0\u7684\u63a8\u7406\u601d\u60f3\u5f00\u542f\u4e86\u5927\u95e8<\/span>\uff08\u4f8b\u5982\uff0c\u9ad8\u7ef4\u6b63\u5219\u5316\u3001\u591a\u5c42\u5efa\u6a21\u3001\u81ea\u52a9\u62bd\u6837\u6cd5\uff09<\/span>\u3002\u901a\u7528\u7684\u81ea\u52a8\u63a8\u7406\u7b97\u6cd5\u4f7f\u6211\u4eec\u53ef\u4ee5\u5c06\u6a21\u578b\u7684\u7814\u53d1\u89e3\u8026\u5f00\u6765\uff0c\u8fd9\u6837\u4e00\u6765\u53d8\u66f4\u6a21\u578b\u5e76\u4e0d\u9700\u8981\u5bf9\u7b97\u6cd5\u5b9e\u73b0\u8fdb\u884c\u6539\u53d8\u3002<\/span><\/section>\n

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\n
1.6 \u81ea\u9002\u5e94\u51b3\u7b56\u5206\u6790<\/span><\/strong><\/span><\/section>\n

<\/span><\/section>\n<\/h3>\n
\u81ea 20 \u4e16\u7eaa 40 \u5e74\u4ee3\u81f3 20 \u4e16\u7eaa 60 \u5e74\u4ee3\uff0c\u51b3\u7b56\u7406\u8bba\u5f80\u5f80\u88ab\u8ba4\u4e3a\u662f\u7edf\u8ba1\u5b66\u7684\u57fa\u77f3\uff0c\u4ee3\u8868\u6027\u7684\u5de5\u4f5c\u5305\u62ec\uff1a\u6548\u7528\u6700\u5927\u5316\u3001\u9519\u8bef\u7387\u63a7\u5236\u3001\u4ee5\u53ca\u7ecf\u9a8c\u8d1d\u53f6\u65af\u5206\u6790\u3002<\/span><\/section>\n

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\u8fd1\u5e74\u6765\uff0c\u6cbf\u7740\u4e0a\u8ff0\u5de5\u4f5c\u7684\u65b9\u5411\uff0c\u7814\u7a76\u4eba\u5458\u5728\u8d1d\u53f6\u65af\u51b3\u7b56\u7406\u8bba\u3001\u9519\u8bef\u53d1\u73b0\u7387\u5206\u6790\u7b49\u9886\u57df\u4e5f\u53d6\u5f97\u4e86\u4e00\u7cfb\u5217\u6210\u679c\u3002<\/span><\/strong>\u51b3\u7b56\u7406\u8bba\u8fd8\u53d7\u5230\u4e86\u6709\u5173\u4eba\u7c7b\u51b3\u7b56\u4e2d\u7684\u542f\u53d1\u4e0e\u504f\u89c1\u7684\u5fc3\u7406\u5b66\u7814\u7a76\u7684\u5f71\u54cd\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u51b3\u7b56\u4e5f\u662f\u7edf\u8ba1\u5b66\u7684\u5e94\u7528\u9886\u57df\u4e4b\u4e00\u3002<\/span>\u5728\u7edf\u8ba1\u51b3\u7b56\u5206\u6790\u9886\u57df\u7684\u9886\u57df\u4e2d\uff0c\u91cd\u8981\u7684\u7814\u7a76\u6210\u679c\u5305\u62ec\uff1a\u8d1d\u53f6\u65af\u4f18\u5316\u3001\u5f3a\u5316\u5b66\u4e60\uff0c<\/span><\/strong>\u8fd9\u4e0e\u5de5\u4e1a\u4e2d\u7684 A\/B \u6d4b\u8bd5\u7684\u5b9e\u9a8c\u8bbe\u8ba1\u7684\u590d\u5174\u4ee5\u53ca\u8bb8\u591a\u5de5\u7a0b\u5e94\u7528\u4e2d\u7684\u5728\u7ebf\u5b66\u4e60\u6709\u5173\u3002<\/span><\/section>\n

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\u8ba1\u7b97\u79d1\u5b66\u7684\u6700\u65b0\u8fdb\u5c55\u4f7f\u6211\u4eec\u53ef\u4ee5\u5c06\u9ad8\u65af\u8fc7\u7a0b\u548c\u795e\u7ecf\u7f51\u7edc\u8fd9\u4e9b\u9ad8\u5ea6\u53c2\u6570\u5316\u7684\u6a21\u578b\u7528\u4f5c\u81ea\u9002\u5e94\u51b3\u7b56\u5206\u6790\u4e2d\u7684\u51fd\u6570\u7684\u5148\u9a8c\uff0c\u8fd8\u53ef\u4ee5\u5728\u4eff\u771f\u73af\u5883\u4e2d\u8fdb\u884c\u5927\u89c4\u6a21\u7684\u5f3a\u5316\u5b66\u4e60\uff0c\u4f8b\u5982\uff1a\u521b\u9020\u80fd\u591f\u63a7\u5236\u673a\u5668\u4eba\u3001\u751f\u6210\u6587\u672c\u3001\u4ee5\u53ca\u53c2\u4e0e\u56f4\u68cb\u7b49\u6e38\u620f\u3002<\/span><\/section>\n

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\n
1.7 \u9c81\u68d2\u7684\u63a8\u7406<\/span><\/strong><\/span><\/section>\n

<\/span><\/strong><\/section>\n<\/h3>\n
\u9c81\u68d2\u6027\u601d\u60f3\u662f\u73b0\u4ee3\u7edf\u8ba1\u5b66\u7684\u6838\u5fc3\uff0c\u5b83\u6307\u7684\u662f\uff1a\u5373\u4f7f\u5728\u5047\u8bbe\u9519\u8bef\u7684\u524d\u63d0\u6761\u4ef6\u4e0b\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u4f7f\u7528\u6a21\u578b\u3002<\/span><\/strong>\u5b9e\u9645\u4e0a\uff0c\u5f00\u53d1\u51fa\u80fd\u591f\u5728\u8fdd\u80cc\u4e0a\u8ff0\u5047\u8bbe\u7684\u771f\u5b9e\u573a\u666f\u4e0b\u826f\u597d\u8fd0\u884c\u7684\u6a21\u578b\u5bf9\u4e8e\u7edf\u8ba1\u7406\u8bba\u6765\u8bf4\u662f\u5341\u5206\u91cd\u8981\u7684\u3002<\/span><\/section>\n

<\/span><\/section>\n
Tukey \u66fe\u4e8e 1960 \u5e74\u5728\u8bba\u6587\u300cA survey of sampling from contaminated distributions\u300d\u4e2d\u5bf9\u8be5\u9886\u57df\u7684\u5de5\u4f5c\u8fdb\u884c\u4e86\u7efc\u8ff0\uff0cStigler \u4e5f\u4e8e 2010 \u5e74\u5728\u8bba\u6587\u300cThe changing history of robustness\u300d\u4e2d\u8fdb\u884c\u4e86\u56de\u987e\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u53d7\u5230 Huber \u7b49\u4eba\u5de5\u4f5c\u7684\u5f71\u54cd\uff0c\u7814\u7a76\u8005\u4eec\u5f00\u53d1\u51fa\u4e86\u4e00\u7cfb\u5217\u5728\u73b0\u5b9e\u751f\u6d3b\u4e2d\uff08\u5c24\u5176\u662f\u7ecf\u6d4e\u5b66\u9886\u57df\uff0c\u4eba\u4eec\u5bf9\u7edf\u8ba1\u6a21\u578b\u7684\u7f3a\u9677\u6709\u6df1\u523b\u7684\u8ba4\u8bc6\uff09\u5177\u6709\u4e00\u5b9a\u5f71\u54cd\u529b\u7684\u9c81\u68d2\u65b9\u6cd5\u3002\u5728\u7ecf\u6d4e\u5b66\u7406\u8bba\u4e2d\uff0c\u5b58\u5728\u300cas if\u300d\u5206\u6790\u548c\u7b80\u5316\u6a21\u578b\u7684\u6982\u5ff5\uff0c\u56e0\u6b64\u8ba1\u91cf\u7ecf\u6d4e\u5b66\u5bb6\u4f1a\u5bf9\u5728\u4e00\u7cfb\u5217\u5047\u8bbe\u4e0b\u8fd8\u80fd\u8fd0\u884c\u826f\u597d\u7684\u7edf\u8ba1\u7a0b\u5e8f\u5341\u5206\u611f\u5174\u8da3\u3002\u4f8b\u5982\uff0c\u7ecf\u6d4e\u5b66\u548c\u5176\u5b83\u793e\u4f1a\u79d1\u5b66\u9886\u57df\u7684\u5e94\u7528\u7814\u7a76\u4eba\u5458\u5e7f\u6cdb\u4f7f\u7528\u9c81\u68d2\u6807\u51c6\u8bef\u5dee\u4ee5\u53ca\u90e8\u5206\u8bc6\u522b\u3002<\/span><\/section>\n

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\u4e00\u822c\u6765\u8bf4\uff0c\u6b63\u5982\u5728 Bernardo \u548c Smith \u4e8e 1994 \u5e74\u6240\u63d0\u51fa\u7684 \u300cM-\u5f00\u653e\u4e16\u754c\u300d<\/span>\uff08\u5728\u8fd9\u4e2a\u4e16\u754c\u4e2d\uff0c\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u4e0d\u5c5e\u4e8e\u62df\u5408\u7684\u6982\u7387\u6a21\u578b\uff09<\/span>\u4e0b\u8bc4\u4f30\u7edf\u8ba1\u8fc7\u7a0b\u7684\u60f3\u6cd5\u4e00\u6837\uff0c\u7edf\u8ba1\u7814\u7a76\u4e2d\u7684\u9c81\u68d2\u6027\u7684\u4e3b\u8981\u5f71\u54cd\u5e76\u4e0d\u5728\u4e8e\u5bf9\u7279\u5b9a\u65b9\u6cd5\u7684\u53d1\u5c55\u3002Greenland \u8ba4\u4e3a\uff0c\u7814\u7a76\u8005\u9700\u8981\u663e\u5f0f\u5730\u89e3\u91ca\u4f20\u7edf\u7edf\u8ba1\u6a21\u578b\u4e2d\u6ca1\u6709\u8003\u8651\u7684\u8bef\u5dee\u6765\u6e90\u3002\u5bf9\u9c81\u68d2\u6027\u7684\u5173\u6ce8\u4e0e\u9ad8\u5ea6\u53c2\u6570\u5316\u7684\u6a21\u578b\u76f8\u5173\uff0c\u8fd9\u662f\u73b0\u4ee3\u7edf\u8ba1\u5b66\u7684\u7279\u70b9\uff0c\u5bf9\u6a21\u578b\u8bc4\u4f30\u6709\u66f4\u666e\u904d\u7684\u5f71\u54cd\u3002<\/strong><\/span><\/section>\n

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1.8 \u63a2\u7d22\u6027\u6570\u636e\u5206\u6790<\/span><\/strong><\/span><\/section>\n

<\/span><\/strong><\/span><\/section>\n<\/h3>\n
\u4e0a\u6587\u8ba8\u8bba\u7684\u7edf\u8ba1\u601d\u60f3\u90fd\u6d89\u53ca\u5bc6\u96c6\u7684\u7406\u8bba\u548c\u8ba1\u7b97\u7684\u7ed3\u5408\u3002<\/span><\/strong>\u4ece\u53e6\u4e00\u4e2a\u5b8c\u5168\u4e0d\u540c\u7684\u65b9\u5411\u6765\u770b\uff0c\u7814\u7a76\u4eba\u5458\u4eec\u8fdb\u884c\u4e86\u4e00\u79cd\u5177\u6709\u5f71\u54cd\u529b\u7684\u300c\u56de\u5f52\u5230\u672c\u8d28\u300d\u7684\u63a2\u7d22\uff0c\u4ed6\u4eec\u8df3\u51fa\u6982\u7387\u6a21\u578b\uff0c\u91cd\u70b9\u5173\u6ce8\u6570\u636e\u7684\u56fe\u5f62\u53ef\u89c6\u5316\u3002<\/strong><\/span><\/section>\n

<\/span><\/section>\n
Tukey \u548c Tufte \u7b49\u4eba\u5728\u4ed6\u4eec\u7684\u8457\u4f5c\u4e2d\u66fe\u5bf9\u7edf\u8ba1\u56fe\u7684\u4f18\u70b9\u8fdb\u884c\u4e86\u8ba8\u8bba\uff0c\u800c\u8bb8\u591a\u8fd9\u6837\u7684\u601d\u60f3\u901a\u8fc7\u4ed6\u4eec\u5728\u6570\u636e\u5206\u6790\u73af\u5883 S<\/span>\uff08\u76ee\u524d\u5728\u7edf\u8ba1\u5b66\u53ca\u5176\u5e94\u7528\u9886\u57df\u5360\u636e\u4e3b\u5bfc\u5730\u4f4d\u7684 R \u8bed\u8a00\u7684\u524d\u8eab\uff09<\/span>\u4e2d\u7684\u5b9e\u73b0\u5f00\u5c55\u4e86\u7edf\u8ba1\u5b9e\u8df5\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u5728 Tukey \u4e4b\u540e\uff0c\u63a2\u7d22\u6027\u6570\u636e\u5206\u6790\u7684\u62e5\u8db8\u91cd\u70b9\u8bf4\u660e\u4e86\u6e10\u8fdb\u7406\u8bba\u7684\u5c40\u9650\u6027\u4ee5\u53ca\u5f00\u653e\u5f0f\u63a2\u7d22\u548c\u901a\u4fe1\u7684\u597d\u5904\uff0c\u5e76\u4e14\u9610\u660e\u4e86\u8d85\u8d8a\u7edf\u8ba1\u7406\u8bba\u7684\u5bf9\u7edf\u8ba1\u79d1\u5b66\u7684\u66f4\u4e00\u822c\u7684\u89c2\u70b9\u3002\u8fd9\u4e0e\u66f4\u52a0\u5173\u6ce8\u53d1\u73b0\u800c\u975e\u68c0\u9a8c\u56fa\u5b9a\u5047\u8bbe\u7684\u7edf\u8ba1\u5efa\u6a21\u89c2\u70b9\u4e0d\u8c0b\u800c\u5408\u3002<\/strong><\/span><\/section>\n

<\/span><\/section>\n
\u540c\u65f6\uff0c\u5b83\u4e0d\u4ec5\u5728\u7279\u5b9a\u7684\u56fe\u5f62\u5316\u65b9\u6cd5\u7684\u53d1\u5c55\u4e2d\u5341\u5206\u5177\u6709\u5f71\u54cd\u529b\uff0c\u4e5f\u4ece\u79d1\u5b66\u7684\u6570\u636e\u4e2d\u5b66\u4e60\uff0c\u5c06\u7edf\u8ba1\u5b66\u4ece\u5b9a\u7406\u8bc1\u660e\u8f6c\u5411\u66f4\u5f00\u653e\u3001\u66f4\u5065\u5eb7\u7684\u89d2\u5ea6\u3002<\/span><\/strong>\u4e3e\u4f8b\u800c\u8a00\uff0c\u5728\u533b\u5b66\u7edf\u8ba1\u5b66\u9886\u57df\u4e2d\uff0cBland \u548c Altman \u4e8e 1986 \u5e74\u53d1\u8868\u7684\u4e00\u7bc7\u9ad8\u88ab\u5f15\u8bba\u6587\u63a8\u8350\u4eba\u4eec\u5c06\u56fe\u5f62\u5316\u65b9\u6cd5\u7528\u4e8e\u6570\u636e\u5bf9\u6bd4\uff0c\u4ece\u800c\u66ff\u6362\u5173\u8054\u6027\u548c\u56de\u5f52\u5206\u6790\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u6b64\u5916\uff0c\u7814\u7a76\u4eba\u5458\u8bd5\u56fe\u5f62\u5f0f\u5316\u5b9a\u4e49\u63a2\u7d22\u6027\u6570\u636e\u5206\u6790\uff1aGelman \u5c06\u6570\u636e\u5c55\u793a\u4e0e\u8d1d\u53f6\u65af\u9884\u6d4b\u68c0\u67e5\u7684\u53ef\u89c6\u5316\u76f8\u7ed3\u5408\uff0cWilkinson \u5f62\u5f0f\u5316\u5b9a\u4e49\u4e86\u7edf\u8ba1\u56fe\u4e2d\u56fa\u6709\u7684\u5bf9\u6bd4\u548c\u6570\u636e\u7ed3\u6784\uff0c\u800c Wickham \u901a\u8fc7\u8fd9\u79cd\u65b9\u5f0f\u5f97\u4ee5\u5b9e\u73b0\u4e86\u4e00\u4e2a\u6781\u5177\u5f71\u54cd\u529b\u7684 R \u8bed\u8a00\u7a0b\u5e8f\u5305\uff0c\u4ece\u800c\u5728\u8bb8\u591a\u9886\u57df\u4e2d\u6539\u53d8\u4e86\u7edf\u8ba1\u5b66\u5b9e\u8df5\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u8ba1\u7b97\u7684\u8fdb\u6b65\u4f7f\u4ece\u4e1a\u8005\u4eec\u80fd\u591f\u5feb\u901f\u6784\u5efa\u5927\u578b\u7684\u590d\u6742\u6a21\u578b\uff0c\u5176\u4e2d\u5728\u7406\u89e3\u6570\u636e\u3001\u62df\u5408\u7684\u6a21\u578b\u3001\u9884\u6d4b\u7ed3\u679c\u4e4b\u95f4\u7684\u5173\u7cfb\u65f6\uff0c\u7edf\u8ba1\u56fe\u662f\u5341\u5206\u6709\u7528\u7684\u3002<\/span><\/strong>\u300c\u63a2\u7d22\u6027\u6a21\u578b\u5206\u6790\u300d\u6709\u65f6\u88ab\u7528\u6765\u83b7\u53d6\u6570\u636e\u5206\u6790\u8fc7\u7a0b\u7684\u5b9e\u9a8c\u7279\u6027\u3002\u7814\u7a76\u4eba\u5458\u4eec\u4e5f\u4e00\u76f4\u8fdb\u884c\u7740\u5c06\u53ef\u89c6\u5316\u56ca\u62ec\u5728\u6a21\u578b\u6784\u5efa\u548c\u6570\u636e\u5206\u6790\u8fc7\u7a0b\u4e2d\u7684\u7814\u7a76\u5de5\u4f5c\u3002<\/span><\/section>\n<\/section>\n

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2.\u76f8\u540c\u70b9\u4e0e\u4e0d\u540c\u70b9<\/strong><\/strong><\/span><\/p>\n<\/section>\n

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<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n

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2.1 \u601d\u60f3\u80fd\u4ea7\u751f\u65b9\u6cd5\u4e0e\u5de5\u4f5c\u6d41\u7a0b<\/span><\/strong><\/span><\/section>\n

<\/span><\/section>\n<\/h4>\n
\u6211\u4eec\u4e4b\u6240\u4ee5\u8ba4\u4e3a\u4e0a\u9762\u5217\u51fa\u7684\u601d\u60f3\u91cd\u8981\uff0c\u662f\u56e0\u4e3a\u5b83\u4eec\u4e0d\u4ec5\u89e3\u51b3\u4e86\u73b0\u6709\u95ee\u9898\uff0c\u8fd8\u5efa\u7acb\u4e86\u65b0\u7684\u7edf\u8ba1\u601d\u7ef4\u65b9\u5f0f\u548c\u6570\u636e\u5206\u6790\u65b9\u5f0f\u3002<\/span><\/strong>\u6362\u53e5\u8bdd\u8bf4\uff0c\u4e0a\u8ff0\u7684\u6bcf\u4e00\u79cd\u601d\u60f3\u90fd\u662f\u4e00\u90e8\u6cd5\u5178\uff0c\u5176\u65b9\u6cd5\u4e0d\u4ec5\u5c40\u9650\u4e8e\u7edf\u8ba1\u5b66\uff0c\u800c\u66f4\u50cf\u662f\u4e00\u79cd\u201c\u7814\u7a76\u54c1\u5473\u201d\u6216\u201c\u54f2\u5b66\u601d\u60f3\u201d\uff1a<\/span><\/section>\n

<\/span><\/section>\n
\u2022 \u53cd\u4e8b\u5b9e\u673a\u5236\u5c06\u56e0\u679c\u63a8\u7406\u7f6e\u4e8e\u7edf\u8ba1\u6216\u9884\u6d4b\u7684\u6846\u67b6\u4e2d\uff0c\u5176\u4e2d\uff0c\u56e0\u679c\u4f30\u91cf<\/span>\uff08causal estimands\uff09<\/span>\u53ef\u4ee5\u6839\u636e\u7edf\u8ba1\u6a21\u578b\u4e2d\u672a\u89c2\u5bdf\u5230\u7684\u6570\u636e\u7cbe\u786e\u5b9a\u4e49\u548c\u8868\u8fbe\uff0c\u5e76\u4e0e\u8c03\u67e5\u62bd\u6837\u548c\u7f3a\u5931\u6570\u636e\u63a8\u7b97\u7684\u601d\u60f3\u8054\u7cfb\u8d77\u6765\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u2022 Boostrap \u6253\u5f00\u4e86\u9690\u5f0f\u975e\u53c2\u6570\u5efa\u6a21<\/span>\uff08implicit nonparametric modeling\uff09<\/span>\u7684\u5927\u95e8\u3002<\/span><\/section>\n
\u2022 \u8fc7\u53c2\u6570\u5316\u7684\u6a21\u578b\u548c\u6b63\u5219\u5316\u57fa\u4e8e\u4ece\u6570\u636e\u4e2d\u4f30\u8ba1\u6a21\u578b\u53c2\u6570\u7684\u80fd\u529b\uff0c\u5c06\u9650\u5236\u6a21\u578b\u5927\u5c0f\u7684\u73b0\u6709\u505a\u6cd5\u5f62\u5f0f\u5316\u548c\u6cdb\u5316\uff0c\u8fd9\u4e0e\u4ea4\u53c9\u9a8c\u8bc1\u548c\u4fe1\u606f\u6807\u51c6\u6709\u5173\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u2022 \u591a\u5c42\u6a21\u578b\u5c06\u4ece\u6570\u636e\u4f30\u8ba1\u5148\u9a8c\u5206\u5e03\u7684\u201c\u7ecf\u9a8c\u8d1d\u53f6\u65af\u201d\u6280\u672f\u5f62\u5f0f\u5316\uff0c\u4f7f\u8fd9\u79cd\u65b9\u6cd5\u5728\u7c7b\u522b\u66f4\u5e7f\u6cdb\u7684\u95ee\u9898\u4e2d\u4f7f\u7528\u65f6\u5177\u5907\u66f4\u9ad8\u7684\u8ba1\u7b97\u4e0e\u63a8\u7406\u7a33\u5b9a\u6027\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u2022 \u6cdb\u578b\u8ba1\u7b97\u7b97\u6cd5\u4f7f\u5b9e\u8df5\u8005\u80fd\u591f\u5feb\u901f\u62df\u5408\u7528\u4e8e\u56e0\u679c\u63a8\u7406\u3001\u591a\u5c42\u6b21\u5206\u6790\u3001\u5f3a\u5316\u5b66\u4e60\u548c\u5176\u4ed6\u8bb8\u591a\u9886\u57df\u7684\u9ad8\u7ea7\u6a21\u578b\uff0c\u4f7f\u6838\u5fc3\u601d\u60f3\u5728\u7edf\u8ba1\u5b66\u548c\u673a\u5668\u5b66\u4e60\u4e2d\u4ea7\u751f\u66f4\u5e7f\u6cdb\u7684\u5f71\u54cd\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u2022 \u81ea\u9002\u5e94\u51b3\u7b56\u5206\u6790\u5c06\u6700\u4f73\u63a7\u5236\u7684\u5de5\u7a0b\u95ee\u9898\u4e0e\u7edf\u8ba1\u5b66\u4e60\u9886\u57df\u8054\u7cfb\u5728\u4e00\u8d77\uff0c\u8fdc\u8fdc\u8d85\u51fa\u4e86\u7ecf\u5178\u7684\u5b9e\u9a8c\u8bbe\u8ba1\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u2022 \u9c81\u68d2\u63a8\u7406\u5c06\u5bf9\u63a8\u7406\u7a33\u5b9a\u6027\u7684\u76f4\u89c9\u5f62\u5f0f\u5316\uff0c\u5728\u8868\u8fbe\u8fd9\u4e9b\u95ee\u9898\u65f6\u53ef\u4ee5\u5bf9\u4e0d\u540c\u7a0b\u5e8f\u8fdb\u884c\u6b63\u5f0f\u8bc4\u4f30\u548c\u5efa\u6a21\uff0c\u4ee5\u5904\u7406\u5bf9\u5f02\u5e38\u503c\u548c\u6a21\u578b\u9519\u8bef\u8bf4\u660e\u7684\u6f5c\u5728\u62c5\u5fe7\u3002\u6b64\u5916\uff0c\u9c81\u68d2\u63a8\u7406\u7684\u601d\u60f3\u4e5f\u4e3a\u975e\u53c2\u6570\u4f30\u8ba1\u63d0\u4f9b\u4e86\u4fe1\u606f\u3002<\/span><\/section>\n

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\u2022 \u63a2\u7d22\u6027\u6570\u636e\u5206\u6790\u4f7f\u56fe\u5f62\u6280\u672f\u548c\u53d1\u73b0\u6210\u4e3a\u7edf\u8ba1\u5b9e\u8df5\u7684\u4e3b\u6d41\uff0c\u56e0\u4e3a\u8fd9\u4e9b\u5de5\u5177\u6b63\u597d\u53ef\u4ee5\u7528\u4e8e\u66f4\u597d\u5730\u7406\u89e3\u548c\u8bca\u65ad\u6b63\u5728\u4e0e\u6570\u636e\u8fdb\u884c\u62df\u5408\u7684\u6982\u7387\u6a21\u578b\u7684\u65b0\u578b\u590d\u6742\u7c7b\u522b\u3002<\/span><\/section>\n

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2.2. \u8ba1\u7b97\u4e0a\u7684\u8fdb\u6b65<\/span><\/strong><\/span><\/section>\n

<\/span><\/section>\n<\/h4>\n
\u5143\u7b97\u6cd5<\/span>\uff08\u5229\u7528\u73b0\u6709\u6a21\u578b\u548c\u63a8\u7406\u6b65\u9aa4\u7684\u5de5\u4f5c\u6d41\uff09<\/span>\u5728\u7edf\u8ba1\u5b66\u4e2d\u88ab\u5e7f\u6cdb\u4f7f\u7528\uff0c\u6bd4\u5982\u6700\u5c0f\u4e8c\u4e58\u6cd5\uff0c\u77e9\u4f30\u8ba1<\/span>\uff08the method of moments\uff09<\/span>\uff0c\u6700\u5927\u4f3c\u7136\uff0c\u7b49\u7b49\u3002<\/span><\/section>\n

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\u5728\u8fc7\u53bb 50 \u5e74\u91cc\u6240\u5f00\u53d1\u7684\u8bb8\u591a\u673a\u5668\u5b66\u4e60\u5143\u7b97\u6cd5\u90fd\u6709\u4e00\u4e2a\u7279\u5f81\uff0c\u5c31\u662f\u5b83\u4eec\u4f1a\u4ee5\u67d0\u79cd\u65b9\u5f0f\u62c6\u5206\u6570\u636e\u6216\u6a21\u578b\u3002<\/span><\/strong>\u5b66\u4e60\u5143\u7b97\u6cd5<\/span>\uff08Learning Meta-Algorithms\uff09<\/span>\u4e0e\u5206\u6cbb\u8ba1\u7b97\u65b9\u6cd5\u76f8\u5173\uff0c\u6700\u8457\u540d\u7684\u662f\u53d8\u5206\u8d1d\u53f6\u65af\u548c\u671f\u671b\u4f20\u64ad\u7b97\u6cd5\u3002<\/span><\/section>\n

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\u5143\u7b97\u6cd5\u548c\u8fed\u4ee3\u8ba1\u7b97\u5728\u7edf\u8ba1\u5b66\u4e2d\u4e4b\u6240\u4ee5\u91cd\u8981\uff0c\u4e3b\u8981\u662f\u6709\u4e24\u4e2a\u539f\u56e0\uff1a1\uff09\u9664\u4e86\u6700\u521d\u5f00\u53d1\u7684\u5143\u7b97\u6cd5\u793a\u4f8b\u4ee5\u5916\uff0c\u901a\u8fc7\u591a\u4e2a\u6765\u6e90\u6574\u5408\u4fe1\u606f\uff0c\u6216\u901a\u8fc7\u6574\u5408\u5f31\u5206\u7c7b\u5668<\/span>\uff08weak learner\uff09<\/span>\u6765\u521b\u5efa\u5f3a\u5206\u7c7b\u5668\u7684\u901a\u7528\u60f3\u6cd5\u53ef\u4ee5\u5f97\u5230\u5e7f\u6cdb\u5e94\u7528\uff1b2\uff09\u81ea\u9002\u5e94\u7b97\u6cd5\u5728\u5728\u7ebf\u5b66\u4e60\u4e2d\u53d1\u6325\u4e86\u5f88\u597d\u7684\u4f5c\u7528\uff0c\u6700\u7ec8\u88ab\u8ba4\u4e3a\u4ee3\u8868\u4e86\u73b0\u4ee3\u7edf\u8ba1\u89c2\u70b9\uff1a\u6570\u636e\u548c\u8ba1\u7b97\u5206\u5f00\uff0c\u4fe1\u606f\u4ea4\u6362\u548c\u8ba1\u7b97\u67b6\u6784\u662f\u5143\u6a21\u578b\u6216\u63a8\u7406\u8fc7\u7a0b\u7684\u4e00\u90e8\u5206\u3002<\/span><\/section>\n

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\u65b0\u65b9\u6cd5\u4f7f\u7528\u65b0\u6280\u672f\u5de5\u5177\u5e76\u4e0d\u7a00\u5947\uff1a\u968f\u7740\u8ba1\u7b97\u901f\u5ea6\u8d8a\u5feb\u3001\u8ba1\u7b97\u8303\u56f4\u8d8a\u5e7f\uff0c\u7edf\u8ba1\u5b66\u5bb6\u4e0d\u518d\u5c40\u9650\u4e8e\u5177\u5907\u89e3\u6790\u65b9\u6848\u7684\u7b80\u5355\u6a21\u578b\u4e0e\u7b80\u5355\u7684\u5c01\u95ed\u5f0f\u7b97\u6cd5<\/span>\uff08\u5982\u6700\u5c0f\u4e8c\u4e58\u6cd5\uff09<\/span>\u3002<\/span><\/strong>\u6211\u4eec\u53ef\u4ee5\u7b80\u8981\u8bf4\u4e00\u4e0b\u4e0a\u8ff0\u601d\u60f3\u662f\u5982\u4f55\u5229\u7528\u73b0\u4ee3\u8ba1\u7b97\uff1a<\/span><\/section>\n

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\u2022 \u4e00\u4e9b\u601d\u60f3<\/span>\uff08boostrapping\uff0c\u8d85\u53c2\u6570\u5316\u6a21\u578b\u548c\u673a\u5668\u5b66\u4e60\u5143\u5206\u6790\uff09<\/span>\u76f4\u63a5\u5229\u7528\u4e86\u8ba1\u7b97\u901f\u5ea6\uff0c\u8fd9\u5728\u8ba1\u7b97\u673a\u51fa\u73b0\u4e4b\u524d\u96be\u4ee5\u60f3\u8c61\u3002\u4f8b\u5982\uff0c\u76f4\u5230\u5f15\u5165\u9ad8\u6548\u7684GPU\u5361\u548c\u4e91\u8ba1\u7b97\u4e4b\u540e\uff0c\u795e\u7ecf\u7f51\u7edc\u624d\u66f4\u52a0\u6d41\u884c\u8d77\u6765\u3002<\/span><\/section>\n

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\u2022 \u9664\u4e86\u8ba1\u7b97\u80fd\u529b\u4ee5\u5916\uff0c\u8ba1\u7b97\u8d44\u6e90\u7684\u5206\u6563\u4e5f\u5f88\u91cd\u8981\uff1a\u53f0\u5f0f\u8ba1\u7b97\u673a\u80fd\u8ba9\u7edf\u8ba1\u5b66\u5bb6\u548c\u8ba1\u7b97\u673a\u79d1\u5b66\u5bb6\u5c1d\u8bd5\u65b0\u65b9\u6cd5\uff0c\u7136\u540e\u7531\u4ece\u4e1a\u4eba\u5458\u4f7f\u7528\u8fd9\u4e9b\u65b0\u65b9\u6cd5\u3002<\/span><\/section>\n

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\u2022 \u63a2\u7d22\u6027\u6570\u636e\u5206\u6790\u6700\u521d\u662f\u4ece\u7eb8\u7b14\u56fe\u5f62\u5f00\u59cb\uff0c\u4f46\u968f\u7740\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u7684\u53d1\u5c55\uff0c\u63a2\u7d22\u6027\u6570\u636e\u5206\u6790\u5df2\u7ecf\u5386\u5f7b\u5e95\u6539\u53d8\u3002<\/span><\/section>\n

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\u2022 \u8fc7\u53bb\uff0c\u8d1d\u53f6\u65af\u63a8\u7406\u4ec5\u9650\u4e8e\u53ef\u4ee5\u901a\u8fc7\u5206\u6790\u89e3\u51b3\u7684\u7b80\u5355\u6a21\u578b\u3002\u968f\u7740\u8ba1\u7b97\u80fd\u529b\u7684\u63d0\u9ad8\uff0c\u53d8\u5206\u548c\u9a6c\u5c14\u53ef\u592b\u94fe\u6a21\u62df\u65b9\u6cd5\u4f7f\u5f97\u6a21\u578b\u6784\u5efa\u548c\u63a8\u7406\u7b97\u6cd5\u5f00\u53d1\u7684\u5206\u79bb\u6210\u4e3a\u53ef\u80fd\uff0c\u6982\u7387\u7f16\u7a0b\u4e5f\u56e0\u6b64\u5141\u8bb8\u4e0d\u540c\u9886\u57df\u7684\u4e13\u5bb6\u80fd\u591f\u4e13\u6ce8\u4e8e\u6a21\u578b\u6784\u5efa\u5e76\u81ea\u52a8\u5b8c\u6210\u63a8\u7406\u3002\u8fd9\u5bfc\u81f4\u4e86\u8d1d\u53f6\u65af\u65b9\u6cd5\u57281990\u5e74\u5f00\u59cb\u5728\u8bb8\u591a\u5e94\u7528\u9886\u57df\u53d8\u5f97\u666e\u53ca\u3002<\/span><\/section>\n

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\u2022 \u81ea\u9002\u5e94\u51b3\u7b56\u5206\u6790\uff0c\u8d1d\u53f6\u65af\u4f18\u5316\u548c\u5728\u7ebf\u5b66\u4e60\u5e94\u7528\u4e8e\u8ba1\u7b97\u548c\u6570\u636e\u5bc6\u96c6\u578b\u95ee\u9898\uff0c\u4f8b\u5982\u4f18\u5316\u5927\u578b\u673a\u5668\u5b66\u4e60\u548c\u795e\u7ecf\u7f51\u7edc\u6a21\u578b\uff0c\u5b9e\u65f6\u56fe\u50cf\u5904\u7406\u548c\u81ea\u7136\u8bed\u8a00\u5904\u7406\u3002<\/span><\/section>\n

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\u2022 \u9c81\u68d2\u7684\u7edf\u8ba1\u5b66\u4e0d\u4e00\u5b9a\u9700\u8981\u5927\u91cf\u8ba1\u7b97\uff0c\u4f46\u5b83\u7684\u4f7f\u7528\u5728\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u7531\u8ba1\u7b97\u9a71\u52a8\uff0c\u4e0e\u5c01\u95ed\u5f0f\u4f30\u8ba1<\/span>\uff08\u5982\u6700\u5c0f\u4e8c\u4e58\u6cd5\uff09<\/span>\u6709\u6240\u533a\u522b\u3002Andrews\u7b49\u4eba\u66fe\u4f7f\u7528\u5927\u91cf\u8ba1\u7b97\u8fdb\u884c\u4e86\u4e00\u9879\u6a21\u62df\u7814\u7a76\uff0c\u4fc3\u8fdb\u4e86\u5bf9\u9c81\u68d2\u65b9\u6cd5\u7684\u5f00\u53d1\u548c\u7406\u89e3\u3002<\/span><\/section>\n

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\u2022 \u51cf\u5c11\u591a\u5143\u63a8\u7406\u7684\u5408\u7406\u6027\u4e0d\u4ec5\u53ef\u4ee5\u901a\u8fc7\u7edf\u8ba1\u6548\u7387\u6765\u8bc1\u660e\uff0c\u8fd8\u53ef\u4ee5\u4ece\u8ba1\u7b97\u5c42\u9762\u8bc1\u660e\uff1a\u6fc0\u53d1\u4e86\u4e00\u79cd\u65b0\u7684\u6e10\u8fd1\u7406\u8bba\u3002<\/span><\/section>\n

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\u2022 \u53cd\u4e8b\u5b9e\u56e0\u679c\u63a8\u7406\u7684\u5173\u952e\u601d\u60f3\u4e0e\u7406\u8bba\u76f8\u5173\uff0c\u800c\u4e0d\u662f\u8ba1\u7b97\u76f8\u5173\u3002\u4f46\u662f\uff0c\u8fd1\u5e74\u6765\uff0c\u56e0\u679c\u63a8\u7406\u5728\u4f7f\u7528\u8ba1\u7b97\u5bc6\u96c6\u7684\u975e\u53c2\u6570\u65b9\u6cd5\u540e\u5df2\u6709\u4e86\u53d1\u5c55\uff0c\u4fc3\u8fdb\u4e86\u7edf\u8ba1\u5b66\u3001\u7ecf\u6d4e\u5b66\u548c\u673a\u5668\u5b66\u4e60\u4e2d\u56e0\u679c\u548c\u9884\u6d4b\u6a21\u578b\u7684\u7edf\u4e00\u3002<\/span><\/section>\n

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2.3 \u5927\u6570\u636e<\/span><\/strong><\/span><\/section>\n

<\/span><\/strong><\/span><\/section>\n<\/h4>\n
\u9664\u4e86\u4e3a\u7edf\u8ba1\u5206\u6790\u5f00\u62d3\u53d1\u5c55\u7a7a\u95f4\u4ee5\u5916\uff0c\u73b0\u4ee3\u8ba1\u7b97\u8fd8\u542f\u53d1\u4e86\u65b0\u7edf\u8ba1\u65b9\u6cd5\u7684\u5e94\u7528\u548c\u5f00\u53d1\uff0c\u4ece\u800c\u4ea7\u751f\u4e86\u5927\u6570\u636e\uff0c\u4f8b\u5b50\u6709\uff1a\u57fa\u56e0\u9635\u5217\uff0c\u6d41\u56fe\u50cf\u548c\u6587\u672c\u6570\u636e\uff0c\u4ee5\u53ca\u5728\u7ebf\u63a7\u5236\u95ee\u9898\uff0c\u5982\u81ea\u52a8\u9a7e\u9a76\u6c7d\u8f66\u3002\u4e8b\u5b9e\u4e0a\uff0c\u201c\u6570\u636e\u79d1\u5b66\u201d\u6d41\u884c\u7684\u539f\u56e0\u4e4b\u4e00\u5c31\u662f\u56e0\u4e3a\uff0c\u5728\u6b64\u7c7b\u95ee\u9898\u4e2d\uff0c\u6570\u636e\u5904\u7406\u548c\u9ad8\u6548\u8ba1\u7b97\u662f\u4e0e\u7528\u4e8e\u62df\u5408\u6570\u636e\u7684\u7edf\u8ba1\u65b9\u6cd5\u4e00\u6837\u91cd\u8981\u7684\u3002<\/strong><\/span><\/section>\n

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\u8fd9\u4e0e Hal Stern \u7684\u89c2\u70b9\u76f8\u5173\uff1a\u7edf\u8ba1\u5206\u6790\u6700\u91cd\u8981\u7684\u65b9\u9762\u4e0d\u662f\u5bf9\u6570\u636e\u8fdb\u884c\u7684\u64cd\u4f5c\uff0c\u800c\u662f\u4f60\u6240\u4f7f\u7528\u7684\u6570\u636e\u662f\u4ec0\u4e48\u3002<\/strong>\u4e0e\u5148\u524d\u7684\u65b9\u6cd5\u76f8\u6bd4\uff0c\u672c\u6587\u8ba8\u8bba\u7684\u6240\u6709\u601d\u60f3\u90fd\u6709\u4e00\u4e2a\u5171\u540c\u7279\u5f81\uff0c\u5373\u6709\u52a9\u4e8e\u4f7f\u7528\u66f4\u591a\u7684\u6570\u636e\uff1a<\/span><\/section>\n

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\u2022 \u53cd\u4e8b\u5b9e\u6846\u67b6\u5141\u8bb8\u4f7f\u7528\u7528\u4e8e\u5bf9\u53d7\u63a7\u5b9e\u9a8c\u5efa\u6a21\u7684\u76f8\u540c\u7ed3\u6784\u4ece\u89c2\u6d4b\u6570\u636e\u4e2d\u8fdb\u884c\u56e0\u679c\u63a8\u65ad\u3002<\/span><\/section>\n

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\u2022 Bootstrapping \u53ef\u7528\u4e8e\u7ea0\u6b63\u504f\u5dee\uff0c\u4e0e\u5728\u5206\u6790\u8ba1\u7b97\u65e0\u6cd5\u8fdb\u884c\u7684\u590d\u6742\u8c03\u67e5\u3001\u5b9e\u9a8c\u8bbe\u8ba1\u548c\u5176\u4ed6\u6570\u636e\u7ed3\u6784\u4e0a\u8fdb\u884c\u65b9\u5dee\u4f30\u8ba1\u3002<\/span><\/section>\n

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\u2022 \u6b63\u5219\u5316\u5141\u8bb8\u7528\u6237\u5728\u6a21\u578b\u4e2d\u52a0\u5165\u66f4\u591a\u9884\u6d4b\u53d8\u91cf\uff0c\u800c\u4e0d\u5fc5\u62c5\u5fc3\u8fc7\u5ea6\u62df\u5408\u3002<\/span><\/section>\n

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\u2022 \u591a\u5c42\u6a21\u578b\u4f7f\u7528\u90e8\u5206\u6c47\u96c6\u6765\u5408\u5e76\u6765\u6e90\u4e0d\u540c\u7684\u4fe1\u606f\uff0c\u4ece\u800c\u66f4\u5e7f\u6cdb\u5e94\u7528\u5143\u5206\u6790\u7684\u539f\u7406\u3002<\/span><\/section>\n

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\u2022 \u6cdb\u578b\u8ba1\u7b97\u7b97\u6cd5\u5141\u8bb8\u7528\u6237\u62df\u5408\u66f4\u5927\u7684\u6a21\u578b\uff0c\u8fd9\u5bf9\u5c06\u53ef\u7528\u6570\u636e\u8fde\u63a5\u5230\u91cd\u8981\u7684\u57fa\u672c\u95ee\u9898\u6765\u8bf4\u53ef\u80fd\u662f\u6709\u5fc5\u8981\u7684\u3002<\/span><\/section>\n

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\u2022 \u81ea\u9002\u5e94\u51b3\u7b56\u5206\u6790\u5229\u7528\u5728\u6570\u503c\u5206\u6790\u4e2d\u5f00\u53d1\u7684\u968f\u673a\u4f18\u5316\u65b9\u6cd5\u3002<\/span><\/section>\n

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\u2022 \u9c81\u68d2\u63a8\u7406\u53ef\u4ee5\u66f4\u5e38\u89c4\u5730\u4f7f\u7528\u5177\u6709\u5f02\u5e38\u503c\u3001\u76f8\u5173\u6027\u548c\u5176\u4ed6\u53ef\u80fd\u963b\u788d\u5e38\u89c4\u7edf\u8ba1\u5efa\u6a21\u7684\u6570\u636e\u3002<\/span><\/section>\n

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\u2022 \u63a2\u7d22\u6027\u6570\u636e\u5206\u6790\u4e3a\u590d\u6742\u6570\u636e\u96c6\u7684\u53ef\u89c6\u5316\u6253\u5f00\u4e86\u5927\u95e8\uff0c\u5e76\u63a8\u52a8\u4e86\u6574\u6d01\u6570\u636e\u5206\u6790<\/span>\uff08tidy data analysis\uff09<\/span>\u7684\u53d1\u5c55\uff0c\u4ee5\u53ca\u7edf\u8ba1\u5206\u6790\u3001\u8ba1\u7b97\u548c\u901a\u4fe1\u7684\u96c6\u6210\u3002<\/span><\/section>\n

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\u5728\u8fc7\u53bb\u768450 \u5e74\u91cc\uff0c\u7edf\u8ba1\u7f16\u7a0b\u73af\u5883\u4e5f\u6709\u4e86\u5f88\u5927\u7684\u53d1\u5c55\uff0c\u6700\u8457\u540d\u7684\u662fS\u8bed\u8a00\u3001R\u8bed\u8a00\uff0c\u8fd8\u6709\u4ee5 BUGS \u5f00\u5934\u547d\u540d\u7684\u901a\u7528\u63a8\u7406\u5f15\u64ce\u53ca\u5176\u540e\u7ee7\u8005\u3002\u8fd1\u65e5\uff0c\u6570\u503c\u5206\u6790\u3001\u81ea\u52a8\u63a8\u7406\u548c\u7edf\u8ba1\u8ba1\u7b97\u7684\u601d\u60f3\u5f00\u59cb\u4ee5\u53ef\u590d\u5236\u7684\u7814\u7a76\u73af\u5883<\/span>\uff08\u5982Jupyter notebook\uff09<\/span>\u548c\u6982\u7387\u7f16\u7a0b\u73af\u5883<\/span>\uff08\u5982Stan\uff0cTensorflow\u548cPyro\uff09<\/span>\u7684\u5f62\u5f0f\u6df7\u5408\u5728\u4e00\u8d77\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u81f3\u5c11\u53ef\u4ee5\u9884\u8ba1\u63a8\u7406\u548c\u8ba1\u7b97\u65b9\u6cd5\u7684\u90e8\u5206\u7edf\u4e00\uff0c\u4f8b\u5982\u4f7f\u7528\u81ea\u52a8\u5fae\u5206\u8fdb\u884c\u4f18\u5316\u3001\u91c7\u6837\u548c\u7075\u654f\u5ea6\u5206\u6790\u3002<\/span><\/section>\n

<\/span><\/section>\n

\n
2.4 \u8fd9\u4e9b\u601d\u60f3\u7684\u5173\u8054\u4e0e\u4ea4\u4e92<\/span><\/strong><\/span><\/section>\n

<\/span><\/section>\n<\/h4>\n
Stigler \u5728 2016 \u5e74\u63d0\u51fa\uff0c\u4e00\u4e9b\u660e\u663e\u4e0d\u540c\u7684\u7edf\u8ba1\u9886\u57df\u80cc\u540e\u5b58\u5728\u67d0\u4e9b\u5171\u540c\u4e3b\u9898\u7684\u76f8\u5173\u6027\u3002<\/strong>\u8fd9\u4e00\u4e92\u76f8\u8054\u7cfb\u7684\u601d\u60f3\u4e5f\u53ef\u4ee5\u7528\u4e8e\u6700\u8fd1\u7684\u53d1\u5c55\u3002\u4f8b\u5982\uff0c\u9c81\u68d2\u7edf\u8ba1\u5b66<\/span>\uff08\u4fa7\u91cd\u4e8e\u504f\u79bb\u7279\u5b9a\u6a21\u578b\u5047\u8bbe\uff09<\/span>\u548c\u63a2\u7d22\u6027\u6570\u636e\u5206\u6790<\/span>\uff08\u4f20\u7edf\u4e0a\u88ab\u8ba4\u4e3a\u5bf9\u6a21\u578b\u6839\u672c\u4e0d\u611f\u5174\u8da3\uff09<\/span>\u4e4b\u95f4\u6709\u4ec0\u4e48\u8054\u7cfb\uff1f<\/span><\/section>\n

<\/span><\/section>\n
\u63a2\u7d22\u6027\u65b9\u6cd5<\/span>\uff08\u5982\u6b8b\u5dee\u56fe\u548c hanging rootograms \uff09<\/span>\u53ef\u4ee5\u4ece\u7279\u5b9a\u7684\u6a21\u578b\u5206\u7c7b<\/span>\uff08\u5206\u522b\u662f\u7d2f\u8ba1\u56de\u5f52\u548c\u6cca\u677e\u5206\u5e03\uff09<\/span>\u4e2d\u83b7\u5f97\uff0c\u4f46\u662f\uff0c\u5b83\u4eec\u7684\u4ef7\u503c\u5728\u5f88\u5927\u7a0b\u5ea6\u4e0a\u662f\u5728\u4e8e\u5176\u53ef\u89e3\u91ca\u6027\uff0c\u5373\u65e0\u9700\u53c2\u8003\u542f\u53d1\u5b83\u4eec\u7684\u6a21\u578b\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u540c\u6837\uff0c\u4f60\u53ef\u4ee5\u5355\u72ec\u5c06\u4e00\u79cd\u65b9\u6cd5<\/span>\uff08\u5982\u6700\u5c0f\u4e8c\u4e58\u6cd5\uff09<\/span>\u770b\u4f5c\u5bf9\u6570\u636e\u7684\u8fd0\u7b97\uff0c\u7136\u540e\u7814\u7a76\u8868\u73b0\u597d\u7684\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u7684\u7c7b\u522b\uff0c\u518d\u4f7f\u7528\u8fd9\u79cd\u7406\u8bba\u5206\u6790\u7684\u7ed3\u679c\u6765\u63d0\u51fa\u66f4\u9c81\u68d2\u7684\u7a0b\u5e8f\uff0c\u80fd\u591f\u62d3\u5c55\u65e0\u8bba\u662f\u57fa\u4e8e\u6545\u969c\u70b9<\/span>\uff08breakdown point\uff09<\/span>\uff0c\u6781\u5c0f\u5316\u6781\u5927\u98ce\u9669\u6216\u5176\u4ed6\u65b9\u5f0f\u5b9a\u4e49\u7684\u9002\u7528\u8303\u56f4\u3002\u76f8\u53cd\uff0c\u7eaf\u7cb9\u7684\u8ba1\u7b97\u65b9\u6cd5<\/span>\uff08\u4f8b\u5982\u8499\u7279\u5361\u6d1b\u79ef\u5206\u4f30\u7b97\uff09<\/span>\u53ef\u4ee5\u88ab\u6709\u6548\u89e3\u91ca\u4e3a\u7edf\u8ba1\u63a8\u7406\u95ee\u9898\u7684\u89e3\u51b3\u65b9\u6848\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u53e6\u4e00\u4e2a\u8054\u7cfb\u662f\uff0c\u56e0\u679c\u63a8\u7406\u7684\u6f5c\u5728\u7ed3\u679c\u6846\u67b6\u5bf9\u4eba\u7fa4\u4e2d\u7684\u6bcf\u4e2a\u5355\u5143\u90fd\u6709\u4e0d\u540c\u7684\u5904\u7406\u6548\u5e94\uff0c\u56e0\u6b64\u81ea\u7136\u800c\u7136\u5c31\u91c7\u7528\u4e86\u4e00\u79cd\u5143\u5206\u6790\u65b9\u6cd5\u5c06\u6548\u5e94\u591a\u6837\u5316\uff0c\u5e76\u4f7f\u7528\u5728\u5b9e\u9a8c\u6216\u89c2\u5bdf\u6027\u7814\u7a76\u5206\u6790\u4e2d\u4f7f\u7528\u591a\u5c42\u6b21\u56de\u5f52\u8fdb\u884c\u5efa\u6a21\u3002<\/span><\/section>\n

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\u56de\u8fc7\u5934\u6765\u770b\uff0c\u7814\u7a76 bootstrap \u53ef\u4ee5\u4e3a\u6211\u4eec\u63d0\u4f9b\u4e00\u79cd\u65b0\u89c2\u70b9\uff1a\u5c06\u7ecf\u9a8c\u8d1d\u53f6\u65af<\/span>\uff08\u591a\u5c42\u6b21\uff09<\/span>\u63a8\u7406\u770b\u4f5c\u975e\u900f\u89c6\u65b9\u6cd5\u3002\u5728\u8be5\u65b9\u6cd5\u4e2d\uff0c\u6b63\u6001\u5206\u5e03\u6216\u5176\u4ed6\u53c2\u6570\u6a21\u578b\u7528\u4e8e\u90e8\u5206\u6c47\u96c6\uff0c\u4f46\u6700\u7ec8\u4f30\u8ba1\u503c\u4e0d\u5c40\u9650\u4e8e\u4efb\u4f55\u53c2\u6570\u5f62\u5f0f\u3002\u5bf9\u5c0f\u6ce2<\/span>\uff08wavelets\uff09<\/span>\u548c\u5176\u4ed6\u4e30\u5bcc\u53c2\u6570\u5316\u6a21\u578b\u8fdb\u884c\u6b63\u5219\u5316\u7684\u7814\u7a76\u4e0e\u5728\u9c81\u68d2\u80cc\u666f\u4e0b\u5f00\u53d1\u7684\u7a33\u5b9a\u63a8\u7406\u7a0b\u5e8f\u4e4b\u95f4\u5b58\u5728\u610f\u60f3\u4e0d\u5230\u7684\u8054\u7cfb\u3002<\/span><\/section>\n

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\u5176\u4ed6\u65b9\u6cd5\u8bba\u7684\u8054\u7cfb\u66f4\u4e3a\u660e\u663e\u3002\u6b63\u5219\u5316\u7684\u8fc7\u53c2\u6570\u5316\u6a21\u578b\u4f7f\u7528\u673a\u5668\u5b66\u4e60\u5143\u7b97\u6cd5\u8fdb\u884c\u4e86\u4f18\u5316\uff0c\u53cd\u8fc7\u6765\u53c8\u53ef\u4ee5\u5f97\u51fa\u5bf9 contamination \u5177\u6709\u9c81\u68d2\u6027\u7684\u63a8\u8bba\u3002\u8fd9\u4e9b\u8fde\u63a5\u53ef\u4ee5\u7528\u5176\u4ed6\u65b9\u5f0f\u8868\u793a\uff0c\u9c81\u68d2\u56de\u5f52\u6a21\u578b\u5bf9\u5e94\u6df7\u5408\u5206\u5e03\uff0c\u6df7\u5408\u5206\u5e03\u53ef\u4ee5\u89c6\u4e3a\u591a\u5c42\u6b21\u6a21\u578b\uff0c\u8fd8\u53ef\u4ee5\u4f7f\u7528\u8d1d\u53f6\u65af\u63a8\u7406\u8fdb\u884c\u62df\u5408\u3002\u6df1\u5ea6\u5b66\u4e60\u6a21\u578b\u4e0e\u4e00\u79cd\u591a\u5c42\u6b21\u903b\u8f91\u56de\u5f52\u76f8\u5173\uff0c\u4e5f\u4e0e\u590d\u73b0\u6838\u5fc3\u7684 Hilbert \u7a7a\u95f4<\/span>\uff08\u5728\u6837\u6761\u4e2d\u4f7f\u7528\uff0c\u652f\u6301\u5411\u91cf\u673a\uff09<\/span>\u76f8\u5173\u3002<\/span><\/section>\n

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\u9ad8\u5ea6\u53c2\u6570\u5316\u7684\u673a\u5668\u5b66\u4e60\u65b9\u6cd5\u53ef\u4ee5\u6784\u5efa\u4e3a\u8d1d\u53f6\u65af\u5206\u5c42\u6a21\u578b\uff0c\u5176\u4e2d\u5c06\u60e9\u7f5a\u51fd\u6570\u6b63\u5219\u5316\u4e0e\u8d85\u5148\u9a8c\u76f8\u4e00\u81f4\uff0c\u65e0\u76d1\u7763\u5b66\u4e60\u6a21\u578b\u4e5f\u53ef\u4ee5\u88ab\u6784\u5efa\u4e3a\u5177\u6709\u672a\u77e5\u7ec4\u5458\u7684\u6df7\u5408\u6a21\u578b\u3002\u5728\u8bb8\u591a\u60c5\u51b5\u4e0b\uff0c\u662f\u5426\u4f7f\u7528\u8d1d\u53f6\u65af\u751f\u6210\u6846\u67b6\u662f\u53d6\u51b3\u4e8e\u8ba1\u7b97\uff0c\u8fd9\u4e5f\u662f\u53cc\u5411\u8fdb\u884c\uff1a\u8d1d\u53f6\u65af\u8ba1\u7b97\u65b9\u6cd5\u53ef\u4ee5\u5e2e\u52a9\u638c\u63e1\u63a8\u7406\u548c\u9884\u6d4b\u4e2d\u7684\u4e0d\u786e\u5b9a\u6027\uff0c\u9ad8\u6548\u4f18\u5316\u7b97\u6cd5\u4e5f\u53ef\u4ee5\u7528\u4e8e\u8fd1\u4f3c\u57fa\u4e8e\u6a21\u578b\u7684\u63a8\u7406 \u3002<\/span><\/section>\n

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\u8bb8\u591a\u88ab\u5e7f\u6cdb\u8ba8\u8bba\u7684\u601d\u60f3\u90fd\u6d89\u53ca\u5230\u4e30\u5bcc\u7684\u53c2\u6570\u5316\uff0c\u5e76\u4f34\u968f\u4e00\u4e9b\u7528\u4e8e\u6b63\u5219\u5316\u7684\u7edf\u8ba1\u6216\u8ba1\u7b97\u5de5\u5177\u3002\u56e0\u6b64\uff0c\u5b83\u4eec\u53ef\u4ee5\u88ab\u8ba4\u4e3a\u662f\u7ecf\u7b5b\u9009\u601d\u60f3\u7684\u66f4\u5e7f\u6cdb\u5b9e\u73b0\uff1a\u968f\u7740\u53ef\u7528\u6570\u636e\u7684\u589e\u52a0\uff0c\u6a21\u578b\u4f1a\u53d8\u5f97\u66f4\u5927\u3002<\/span><\/strong><\/span><\/section>\n

<\/span><\/section>\n

\n
2.5 \u7406\u8bba\u4fc3\u8fdb\u5e94\u7528\uff0c\u53cd\u4e4b\u4ea6\u7136<\/span><\/strong><\/section>\n

<\/span><\/section>\n<\/h4>\n
\u53ef\u4ee5\u8bf4\u6240\u6709\u8fd9\u4e9b\u65b9\u6cd5\u7684\u5171\u540c\u7279\u5f81\u662f\u6613\u8bb0\u7684\u540d\u79f0\u548c\u826f\u597d\u7684\u4f20\u64ad\u3002\u4f46\u662f\u4f5c\u8005\u6000\u7591\u8fd9\u4e9b\u65b9\u6cd5\u7684\u540d\u79f0\u4ec5\u5728\u56de\u987e\u65f6\u4f1a\u5f15\u8d77\u6ce8\u610f\u3002\u8bf8\u5982\u201c\u53cd\u4e8b\u5b9e\u201d\u3001\u201c\u5f15\u5bfc\u7a0b\u5e8f\u201d\u3001\u201c\u5806\u53e0\u201d\u548c\u201c\u589e\u5f3a\u201d\u4e4b\u7c7b\u7684\u672f\u8bed\u542c\u8d77\u6765\u5f88\u4e13\u4e1a\uff0c\u800c\u4e0d\u662f\u4ee4\u4eba\u5370\u8c61\u6df1\u523b\uff0c\u4f5c\u8005\u8ba4\u4e3a\u662f\u65b9\u6cd5\u7684\u4ef7\u503c\u4f7f\u8fd9\u4e9b\u540d\u5b57\u53d8\u5f97\u54cd\u4eae\u3002<\/strong><\/span><\/section>\n

<\/span><\/section>\n
\u521b\u65b0\u7684\u60f3\u6cd5\u7ecf\u5e38\u4f1a\u9047\u5230\u963b\u529b\uff0c\u8fd9\u4e5f\u662f\u672c\u6587\u4e2d\u8ba8\u8bba\u7684\u8fd9\u4e9b\u6709\u5f71\u54cd\u529b\u7684\u60f3\u6cd5\u7684\u547d\u8fd0\u3002\u5982\u679c\u4e00\u4e2a\u65b0\u601d\u60f3\u8d77\u6e90\u4e8e\u4e00\u4e2a\u5e94\u7528\u9886\u57df\uff0c\u90a3\u4e48\u8981\u8bf4\u670d\u7406\u8bba\u5bb6\u76f8\u4fe1\u5b83\u7684\u4ef7\u503c\u53ef\u80fd\u4f1a\u9047\u5230\u5f88\u5927\u6311\u6218\u3002\u76f8\u53cd\uff0c\u6279\u8bc4\u65b0\u65b9\u6cd5\u5728\u7406\u8bba\u4e0a\u662f\u6709\u7528\u7684\uff0c\u4f46\u5728\u5b9e\u8df5\u4e2d\u6ca1\u6709\u7528\uff0c\u5012\u662f\u5f88\u5bb9\u6613\u3002<\/strong><\/span><\/section>\n

<\/span><\/section>\n
\u6211\u4eec\u5e94\u8be5\u6f84\u6e05\uff0c\u6240\u8c13\u201c\u53cd\u5bf9\u201d\u4e0d\u4e00\u5b9a\u610f\u5473\u7740\u79ef\u6781\u53cd\u5bf9\u3002\u4e0e\u5176\u4ed6\u4e00\u4e9b\u5b66\u672f\u9886\u57df\u76f8\u6bd4\uff0c\u7edf\u8ba1\u6570\u636e\u4e0d\u662f\u5f88\u653f\u6cbb\u5316\uff1a<\/strong>\u5b66\u672f\u754c\u3001\u653f\u5e9c\u548c\u884c\u4e1a\u5185\u90e8\u5bf9\u7edf\u8ba1\u9886\u57df\u7684\u53d1\u5c55\u5f88\u5bbd\u5bb9\uff0c\u751a\u81f3\u8fb9\u7f18\u601d\u60f3\u4e5f\u88ab\u5141\u8bb8\u53d1\u5c55\u3002\u6b64\u5904\u8ba8\u8bba\u7684\u8bb8\u591a\u65b9\u6cd5<\/span>\uff08\u4f8b\u5982\u5f15\u5bfc\u7a0b\u5e8f\uff0classo\u548c\u591a\u5c42\u6a21\u578b\uff09<\/span>\u5728\u7edf\u8ba1\u548c\u5404\u79cd\u5e94\u7528\u9886\u57df\u4e2d\u90fd\u7acb\u5373\u6d41\u884c\u8d77\u6765\uff0c\u4f46\u5373\u4f7f\u662f\u8fd9\u4e9b\u601d\u60f3\u4e5f\u9762\u4e34\u7740\u963b\u529b\uff0c\u5373\u5c40\u5916\u4eba\u9700\u8981\u786e\u4fe1\u5176\u5e94\u7528\u7684\u5fc5\u8981\u6027\u3002<\/span><\/section>\n

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\u7406\u8bba\u7edf\u8ba1\u5b66\u662f\u5e94\u7528\u7edf\u8ba1\u5b66\u7684\u7406\u8bba\uff0c\u8fd9\u5728\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u5f97\u76ca\u4e8e\u8bf8\u5982Cox\u7684\u201cPlanning of Experiments\u201d\uff0cBox and Tiao\u7684\u201cBayesian Inference in Statistical Analysis\u201d\uff0cCox and Hinkley\u7684\u201cTheoretical Statistics\u201d\uff0cBox\uff0cHunter\u548cHunter\u7684\u201cStatistics for Experimenters\u201d\u7b49\u6709\u5f71\u54cd\u529b\u7684\u8457\u4f5c\uff0c\u5e2e\u52a9\u6211\u4eec\u8de8\u8d8a\u4e86\u7406\u8bba\u548c\u5e94\u7528\u4e4b\u95f4\u7684\u9e3f\u6c9f\u3002<\/span><\/section>\n

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\u4e0d\u540c\u4e8e\u7eaf\u6570\u5b66\uff0c\u4e0d\u5b58\u5728\u7eaf\u7cb9\u7684\u7edf\u8ba1\u3002<\/span><\/strong>\u6ca1\u9519\uff0c\u4e00\u4e9b\u7edf\u8ba1\u601d\u60f3\u662f\u6df1\u523b\u800c\u4f18\u7f8e\u7684\uff0c\u5e76\u4e14\u4e0e\u6570\u5b66\u4e00\u6837\uff0c\u8fd9\u4e9b\u601d\u60f3\u4e5f\u5177\u6709\u57fa\u672c\u7684\u8054\u7cfb\u3002\u4f8b\u5982\uff0c\u56de\u5f52\u548c\u5747\u503c\u4e4b\u95f4\u7684\u8054\u7cfb\uff0c\u6700\u5c0f\u4e8c\u4e58\u548c\u90e8\u5206\u6c60\u5316\u4e4b\u95f4\u7684\u8054\u7cfb\uff0c\u4f46\u5b83\u4eec\u4ecd\u4e0e\u7279\u5b9a\u4e3b\u9898\u76f8\u5173\u3002\u5c31\u50cf\u6458\u4e0b\u7684\u82f9\u679c\u4e00\u6837\uff0c\u8131\u79bb\u5176\u8425\u517b\u6765\u6e90\u540e\uff0c\u7406\u8bba\u7edf\u8ba1\u7814\u7a76\u8d8b\u4e8e\u67af\u7aed\u3002\u6570\u5b66\u4e5f\u662f\u5982\u6b64\uff0c\u4f46\u662f\u7eaf\u6570\u5b66\u4e2d\u7684\u601d\u60f3\u4f3c\u4e4e\u53ef\u4ee5\u5b58\u5728\u66f4\u957f\u7684\u65f6\u95f4\uff0c\u5e76\u4e14\u80fd\u4ee5\u5b64\u7acb\u7684\u7814\u7a76\u5b58\u5728\uff0c\u800c\u7edf\u8ba1\u5b66\u601d\u60f3\u5219\u65e0\u6cd5\u5982\u6b64\u3002<\/span><\/section>\n

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\u5e94\u7528\u7edf\u8ba1\u7406\u8bba\u5e26\u6765\u7684\u597d\u5904\u662f\u663e\u800c\u6613\u89c1\u7684\u3002\u4eba\u4eec\u53ef\u4ee5\u5c06\u7406\u8bba\u89c6\u4e3a\u8ba1\u7b97\u7684\u6377\u5f84\u3002<\/strong>\u6211\u4eec\u603b\u662f\u9700\u8981\u8fd9\u6837\u7684\u6377\u5f84\uff1a\u5efa\u6a21\u7684\u9700\u6c42\u4e0d\u53ef\u907f\u514d\u5730\u968f\u7740\u8ba1\u7b97\u80fd\u529b\u7684\u589e\u957f\u800c\u589e\u52a0\uff0c\u56e0\u6b64\u6211\u4eec\u9700\u8981\u5206\u6790\u538b\u7f29\u548c\u903c\u8fd1\u7684\u4ef7\u503c\u3002\u6b64\u5916\uff0c\u7406\u8bba\u53ef\u4ee5\u5e2e\u52a9\u6211\u4eec\u7406\u89e3\u7edf\u8ba1\u65b9\u6cd5\u7684\u5de5\u4f5c\u539f\u7406\uff0c\u800c\u6570\u5b66\u903b\u8f91\u53ef\u4ee5\u542f\u53d1\u65b0\u7684\u6a21\u578b\u548c\u6570\u636e\u5206\u6790\u65b9\u6cd5\u3002<\/span><\/section>\n

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2.6 \u548c\u7edf\u8ba1\u9886\u57df\u5176\u4ed6\u8fdb\u5c55\u7684\u5173\u8054<\/span><\/strong><\/span><\/span><\/section>\n

<\/span><\/section>\n<\/h4>\n
\u7279\u5b9a\u7684\u7edf\u8ba1\u6a21\u578b\u4e0e\u8fd9\u4e9b\u91cd\u8981\u601d\u60f3\u662f\u4ec0\u4e48\u8054\u7cfb\uff1f\u5728\u8fd9\u91cc\uff0c\u4f5c\u8005\u8003\u8651\u7684\u662f\u6709\u5f71\u54cd\u529b\u7684\u5de5\u4f5c\uff0c\u4f8b\u5982\u98ce\u9669\u56de\u5f52\u3001\u5e7f\u4e49\u7ebf\u6027\u6a21\u578b\u3001\u7a7a\u95f4\u81ea\u56de\u5f52\u3001\u7ed3\u6784\u65b9\u7a0b\u6a21\u578b\u3001\u6f5c\u5728\u5206\u7c7b\u3001\u9ad8\u65af\u8fc7\u7a0b\u548c\u6df1\u5ea6\u5b66\u4e60\u3002\u5982\u4e0a\u6240\u8ff0\uff0c\u5728\u8fc7\u53bb\u7684\u534a\u4e2a\u4e16\u7eaa\u4e2d\uff0c\u7edf\u8ba1\u63a8\u65ad\u548c\u8ba1\u7b97\u9886\u57df\u51fa\u73b0\u4e86\u8bb8\u591a\u91cd\u8981\u7684\u53d1\u5c55\uff0c\u8fd9\u4e9b\u53d1\u5c55\u90fd\u53d7\u5230\u4e86\u4e0a\u9762\u8ba8\u8bba\u7684\u65b0\u6a21\u578b\u548c\u63a8\u65ad\u601d\u60f3\u7684\u542f\u53d1\u548c\u63a8\u52a8\u3002\u6a21\u578b\u3001\u65b9\u6cd5\u3001\u5e94\u7528\u7a0b\u5e8f\u548c\u8ba1\u7b97\u90fd\u7ed3\u5408\u5728\u4e00\u8d77\u3002<\/span><\/section>\n

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\u8ba8\u8bba\u4e0d\u540c\u6982\u5ff5\u53d1\u5c55\u4e4b\u95f4\u7684\u8054\u7cfb\uff0c\u5e76\u4e0d\u610f\u5473\u7740\u5173\u4e8e\u9002\u5f53\u4f7f\u7528\u548c\u89e3\u91ca\u7edf\u8ba1\u65b9\u6cd5\u7684\u4e89\u8bba\u4ecd\u7136\u5b58\u5728\u3002<\/span><\/strong>\u4f8b\u5982\uff0c\u9519\u8bef\u53d1\u73b0\u7387<\/span>\uff08false discovery rate\uff09<\/span>\u4e0e\u591a\u5c42\u6a21\u578b\u4e4b\u95f4\u5b58\u5728\u53cc\u91cd\u6027\uff0c\u4f46\u662f\u57fa\u4e8e\u8fd9\u4e9b\u4e0d\u540c\u539f\u7406\u7684\u8fc7\u7a0b\u53ef\u4ee5\u7ed9\u51fa\u4e0d\u540c\u7684\u7ed3\u679c\u3002\u901a\u5e38\u4f7f\u7528\u8d1d\u53f6\u65af\u65b9\u6cd5\u6765\u62df\u5408\u591a\u5c42\u6a21\u578b\uff0c\u5e76\u4e14\u5728\u540e\u9a8c\u5206\u5e03\u4e2d\uff0c\u6ca1\u6709\u4efb\u4f55\u4e1c\u897f\u4f1a\u4e00\u76f4\u6536\u655b\u5230\u96f6\u3002<\/span><\/section>\n

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\u76f8\u53cd\uff0c\u9519\u8bef\u53d1\u73b0\u7387\u65b9\u6cd5\u901a\u5e38\u4f7f\u7528p\u503c\u9608\u503c\uff0c\u76ee\u7684\u662f\u8bc6\u522b\u5c11\u91cf\u7edf\u8ba1\u4e0a\u663e\u8457\u7684\u975e\u96f6\u7ed3\u679c\u3002\u518d\u4f8b\u5982\uff0c\u5728\u56e0\u679c\u63a8\u7406\u4e2d\uff0c\u4eba\u4eec\u8d8a\u6765\u8d8a\u5173\u6ce8\u5bc6\u96c6\u53c2\u6570\u5316\u7684\u673a\u5668\u5b66\u4e60\u9884\u6d4b\uff0c\u7136\u540e\u8fdb\u884c\u540e\u5206\u5c42<\/span>\uff08poststratification\uff09<\/span>\u4ee5\u83b7\u5f97\u7279\u5b9a\u7684\u56e0\u679c\u4f30\u8ba1\uff0c\u4f46\u662f\u5728\u66f4\u5f00\u653e\u7684\u73af\u5883\u4e2d\uff0c\u9700\u8981\u53d1\u73b0\u975e\u96f6\u56e0\u679c\u5173\u7cfb\u3002\u540c\u6837\uff0c\u6839\u636e\u76ee\u6807\u662f\u5bc6\u96c6\u9884\u6d4b\u8fd8\u662f\u7a00\u758f\u9884\u6d4b\uff0c\u4f7f\u7528\u4e86\u4e0d\u540c\u7684\u65b9\u6cd5\u3002<\/span><\/section>\n

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\u6700\u540e\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u7edf\u8ba1\u65b9\u6cd5\u7684\u7814\u7a76\u4e0e\u79d1\u5b66\u548c\u5de5\u7a0b\u5b66\u4e2d\u7edf\u8ba1\u5e94\u7528\u7684\u8d8b\u52bf\u8054\u7cfb\u8d77\u6765\u3002\u5728\u8fd9\u91cc\uff0c\u4f5c\u8005\u63d0\u5230\u4e86\u751f\u7269\u5b66\u3001\u5fc3\u7406\u5b66\u3001\u7ecf\u6d4e\u5b66\u548c\u5176\u4ed6\u79d1\u5b66\u9886\u57df\u7684\u590d\u73b0\u5371\u673a\u6216\u53ef\u590d\u73b0\u6027\u9769\u547d\uff0c\u8fd9\u4e9b\u9886\u57df\u7684\u53d8\u5f02\u8303\u56f4\u8db3\u591f\u5927\uff0c\u9700\u8981\u6839\u636e\u7edf\u8ba1\u8bc1\u636e\u5f97\u51fa\u7ed3\u8bba\u3002<\/strong><\/span><\/section>\n

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\u5728\u53ef\u590d\u73b0\u6027\u9769\u547d\u4e2d\uff0c\u5177\u6709\u91cc\u7a0b\u7891\u610f\u4e49\u7684\u8bba\u6587\u5305\u62ec\uff1a<\/span><\/section>\n

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Meehl\u53d1\u8868\u7684\u201cTheoretical risks and tabular asterisks: Sir Karl, Sir Ronald, and the slow progress of soft psychology\u201d\uff0c\u6982\u8ff0\u4e86\u5728\u539f\u5047\u8bbe\u91cd\u8981\u6027\u68c0\u9a8c\u7684\u6807\u51c6\u7528\u6cd5\u4e2d\u63d0\u51fa\u79d1\u5b66\u4e3b\u5f20\u7684\u54f2\u5b66\u7f3a\u9677\u3002<\/span><\/section>\n

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Ioannidis\u53d1\u8868\u7684\u201cWhy most published research findings are false\u201d\uff0c\u5176\u8ba4\u4e3a\uff0c\u533b\u5b66\u4e0a\u5927\u591a\u6570\u5df2\u53d1\u8868\u7684\u7814\u7a76\u90fd\u5728\u4f7f\u5f97\u7ed3\u8bba\u4e0d\u53d7\u5176\u7edf\u8ba1\u6570\u636e\u7684\u652f\u6301\u3002<\/span><\/section>\n

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Simmons\uff0cNelson\u548cSimonsohn\u53d1\u8868\u7684\u201cFalse-positive psychology: Undisclosed flexibility in data collection and analysis allow presenting anything as significant \u201d\uff0c\u89e3\u91ca\u4e86\u201c\u7814\u7a76\u4eba\u5458\u7684\u81ea\u7531\u5ea6\u201d\u5982\u4f55\u4f7f\u7814\u7a76\u4eba\u5458\u5373\u4f7f\u4ece\u7eaf\u566a\u58f0\u6570\u636e\u4e2d\u4e5f\u80fd\u5e38\u89c4\u83b7\u5f97\u7edf\u8ba1\u610f\u4e49\u3002<\/span><\/section>\n

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\u4e00\u4e9b\u8865\u6551\u63aa\u65bd\u662f\u7a0b\u5e8f\u6027\u7684\uff0c\u4f8b\u5982Amrhein\uff0cGreenland\u548cMcShane\u53d1\u8868\u7684\u201cScientists rise up against statistical significance\u201d\u3002<\/span><\/section>\n

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\u4f46\u4e5f\u6709\u4eba\u5efa\u8bae\u53ef\u4ee5\u4f7f\u7528\u591a\u5c42\u6a21\u578b\u89e3\u51b3\u4e0d\u53ef\u590d\u73b0\u7814\u7a76\u7684\u67d0\u4e9b\u95ee\u9898\uff0c\u5c06\u4f30\u8ba1\u503c\u90e8\u5206\u5f52\u96f6\u4ee5\u66f4\u597d\u5730\u53cd\u6620\u7814\u7a76\u4e2d\u7684\u6548\u5e94\u603b\u91cf\uff0c\u4f8b\u5982van Zwet\uff0cSchwab\u548cSenn\u53d1\u8868\u7684\u201cThe statistical properties of RCTs and a proposal for shrinkage\u201d\u3002<\/span><\/section>\n

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\u53ef\u518d\u73b0\u6027\u548c\u7a33\u5b9a\u6027\u95ee\u9898\u4e5f\u76f4\u63a5\u6d89\u53ca\u5230\u5f15\u5bfc\u7a0b\u5e8f\u548c\u53ef\u9760\u7684\u7edf\u8ba1\u6570\u636e\uff0c\u53c2\u89c1Yu. B.\u53d1\u8868\u7684\u201cStability.\u201d\u3002<\/span><\/section>\n
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3.\u672a\u6765\u51e0\u5341\u5e74\u7684\u91cd\u8981\u7edf\u8ba1\u601d\u60f3\u4f1a\u662f\u4ec0\u4e48\uff1f<\/strong><\/strong><\/span><\/p>\n<\/section>\n

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3.1 \u56de\u987e<\/span><\/strong><\/section>\n

<\/span><\/section>\n<\/h4>\n
\u5728\u8003\u8651\u81ea1970\u5e74\u4ee5\u6765\u6700\u91cd\u8981\u7684\u53d1\u5c55\u65f6\uff0c\u56de\u987e\u4e00\u4e0b1920-1970\u5e74\u7684\u91cd\u8981\u7edf\u8ba1\u601d\u60f3\uff08\u5305\u62ec\u8d28\u91cf\u63a7\u5236\u3001\u6f5c\u5728\u53d8\u91cf\u5efa\u6a21\u3001\u62bd\u6837\u7406\u8bba\u3001\u5b9e\u9a8c\u8bbe\u8ba1\u3001\u7ecf\u5178\u548c\u8d1d\u53f6\u65af\u51b3\u7b56\u5206\u6790\u3001\u7f6e\u4fe1\u533a\u95f4\u548c\u5047\u8bbe\u68c0\u9a8c\u3001\u6700\u5927\u4f3c\u7136\u3001\u65b9\u5dee\u5206\u6790\u548c\u5ba2\u89c2\u8d1d\u53f6\u65af\u63a8\u7406\uff09\u4e5f\u5f88\u6709\u610f\u4e49\u3002\u5f53\u7136\u8fd8\u67091870\u5e74\u81f31920\u5e74\uff08\u6982\u7387\u5206\u5e03\u5206\u7c7b\u3001\u5747\u503c\u56de\u5f52\u3001\u6570\u636e\u73b0\u8c61\u5b66\u5efa\u6a21\uff09\uff0c\u4ee5\u53caStigler\u5728\u300aThe History of Statistics\u300b\u4e2d\u63d0\u5230\u7684\u66f4\u65e9\u5e74\u4ee3\u7684\u7edf\u8ba1\u601d\u60f3\u3002<\/span><\/section>\n

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\u5728\u672c\u6587\u4e2d\uff0c\u4f5c\u8005\u8bd5\u56fe\u63d0\u4f9b\u4e00\u4e2a\u5e7f\u6cdb\u7684\u89c6\u89d2\uff0c\u4ee5\u53cd\u6620\u4e0d\u540c\u7684\u89c2\u70b9\u3002\u4f46\u662f\u5176\u4ed6\u4eba\u53ef\u80fd\u5bf9\u8fc7\u53bb\u4e94\u5341\u5e74\u6765\u6700\u91cd\u8981\u7684\u7edf\u8ba1\u601d\u60f3\u6709\u81ea\u5df1\u7684\u770b\u6cd5\u3002\u786e\u5b9e\uff0c\u95ee\u8fd9\u4e2a\u95ee\u9898\u4e3b\u8981\u662f\u5f15\u8d77\u4eba\u4eec\u5bf9\u7edf\u8ba1\u5b66\u89c2\u5ff5\u7684\u91cd\u8981\u6027\u7684\u8ba8\u8bba\u3002\u5728\u672c\u6587\u4e2d\uff0c\u4f5c\u8005\u907f\u514d\u4e86\u4f7f\u7528\u5f15\u6587\u8ba1\u6570\u6216\u5176\u4ed6\u6570\u503c\u65b9\u6cd5\u5bf9\u8bba\u6587\u8fdb\u884c\u6392\u540d\uff0c\u4f46\u662f\u4ed6\u4eec\u9690\u542b\u5730\u4ee5\u7c7b\u4f3cpage-rank\u7684\u65b9\u5f0f\u6765\u8861\u91cf\u5f71\u54cd\u529b\uff0c\u56e0\u4e3a\u4ed6\u4eec\u8bd5\u56fe\u5c06\u6ce8\u610f\u529b\u96c6\u4e2d\u5728\u90a3\u4e9b\u5f71\u54cd\u4e86\u7edf\u8ba1\u5b9e\u8df5\u7684\u65b9\u6cd5\u53d1\u5c55\u7684\u601d\u60f3\u4e0a\u3002<\/span><\/section>\n

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3.2 \u5c55\u671b<\/span><\/strong><\/span><\/section>\n

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\u63a5\u4e0b\u6765\u4f1a\u53d1\u751f\u4ec0\u4e48\uff1f<\/span>\u4f5c\u8005\u540c\u610f\u5361\u5c14\u00b7\u6ce2\u666e\u5c14<\/span>\uff08Karl Popper\uff09<\/span>\u7684\u89c2\u70b9\uff0c\u5373\u4eba\u4eec\u65e0\u6cd5\u9884\u89c1\u6240\u6709\u672a\u6765\u7684\u79d1\u5b66\u53d1\u5c55\uff0c\u4f46\u662f\u6211\u4eec\u53ef\u80fd\u5bf9\u5f53\u524d\u7684\u8d8b\u52bf\u5c06\u5982\u4f55\u6301\u7eed\u6709\u6bd4\u8f83\u53ef\u9760\u7684\u89c1\u89e3\u3002<\/span><\/strong><\/span><\/section>\n

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\u6700\u5b89\u5168\u7684\u9009\u62e9\u662f\uff0c\u5728\u73b0\u6709\u65b9\u6cd5\u7ec4\u5408\u4e0a\u6301\u7eed\u53d6\u5f97\u8fdb\u5c55\uff1a<\/span><\/strong>\u5bf9\u6f5c\u5728\u8f93\u51fa\u7684\u4e30\u5bcc\u6a21\u578b\u8fdb\u884c\u56e0\u679c\u63a8\u7406\uff0c\u5e76\u4f7f\u7528\u6b63\u5219\u5316\u4f30\u8ba1\uff1b\u7ed3\u6784\u5316\u6570\u636e\u7684\u590d\u6742\u6a21\u578b\uff0c\u4f8b\u5982\u968f\u65f6\u95f4\u6f14\u53d8\u7684\u7f51\u7edc\uff0c\u5bf9\u591a\u5c42\u6a21\u578b\u7684\u53ef\u9760\u63a8\u65ad\uff1b\u5bf9\u8d85\u53c2\u6570\u5316\u6a21\u578b\u7684\u63a2\u7d22\u6027\u6570\u636e\u5206\u6790\uff1b\u7528\u4e8e\u4e0d\u540c\u8ba1\u7b97\u95ee\u9898\u7684\u5b50\u96c6<\/span>\uff08subsetting\uff09<\/span>\u548c\u673a\u5668\u5b66\u4e60\u5143\u7b97\u6cd5\u7b49\u7b49\u3002\u6b64\u5916\uff0c\u4f5c\u8005\u671f\u671b\u5728\u7ed3\u6784\u5316\u6570\u636e\u7684\u5b9e\u9a8c\u8bbe\u8ba1\u548c\u91c7\u6837\u65b9\u9762\u53d6\u5f97\u8fdb\u5c55\u3002<\/span><\/section>\n

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\u53e6\u4e00\u4e2a\u6210\u719f\u7684\u53d1\u5c55\u9886\u57df\u662f\u6a21\u578b\u7406\u89e3\uff0c\u6709\u65f6\u4e5f\u79f0\u4e3a\u53ef\u89e3\u91ca\u673a\u5668\u5b66\u4e60\u3002<\/span><\/strong>\u8fd9\u91cc\u7684\u77db\u76fe\u4e4b\u5904\u5728\u4e8e\uff0c\u7406\u89e3\u590d\u6742\u6a21\u578b\u7684\u6700\u4f73\u65b9\u6cd5\u901a\u5e38\u662f\u4f7f\u7528\u7b80\u5355\u6a21\u578b\u5bf9\u5176\u8fdb\u884c\u8fd1\u4f3c\u3002\u4f46\u95ee\u9898\u662f\uff0c\u5728\u8fd9\u8fc7\u7a0b\u4e2d\u662f\u4ec0\u4e48\u5728\u8fdb\u884c\u4ea4\u6d41\uff1f\u4e00\u79cd\u53ef\u80fd\u6709\u7528\u7684\u65b9\u6cd5\u662f\u8ba1\u7b97\u5bf9\u6570\u636e\u548c\u6a21\u578b\u53c2\u6570\u6270\u52a8\u7684\u63a8\u65ad\u654f\u611f\u6027\uff0c\u5c06\u9c81\u68d2\u6027\u548c\u6b63\u5219\u5316\u7684\u601d\u60f3\u4e0e\u57fa\u4e8e\u68af\u5ea6\u7684\u8ba1\u7b97\u65b9\u6cd5\u76f8\u7ed3\u5408\uff0c\u8be5\u65b9\u6cd5\u5728\u8bb8\u591a\u4e0d\u540c\u7684\u7edf\u8ba1\u7b97\u6cd5\u4e2d\u4f7f\u7528\u3002<\/span><\/section>\n

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\u6700\u540e\uff0c\u9274\u4e8e\u51e0\u4e4e\u6240\u6709\u65b0\u7684\u7edf\u8ba1\u548c\u6570\u636e\u79d1\u5b66\u601d\u60f3\u5728\u8ba1\u7b97\u4e0a\u90fd\u662f\u6602\u8d35\u7684\uff0c\u56e0\u6b64\uff0c\u4f5c\u8005\u8bbe\u60f3\u4e86\u5bf9\u63a8\u8bba\u65b9\u6cd5\u9a8c\u8bc1\u7684\u672a\u6765\u7814\u7a76\uff0c\u5c06\u8bf8\u5982\u8f6f\u4ef6\u5de5\u7a0b\u4e2d\u7684\u5355\u5143\u6d4b\u8bd5\u4e4b\u7c7b\u7684\u601d\u60f3\u5e94\u7528\u5230\u4ece\u566a\u58f0\u6570\u636e\u4e2d\u5b66\u4e60\u7684\u95ee\u9898\u4e2d\u3002\u968f\u7740\u7edf\u8ba1\u65b9\u6cd5\u53d8\u5f97\u8d8a\u6765\u8d8a\u5148\u8fdb\uff0c\u7406\u89e3\u6570\u636e\u3001\u6a21\u578b\u548c\u5b9e\u4f53\u7406\u8bba\u4e4b\u95f4\u7684\u8054\u7cfb\u5c06\u53d8\u5f97\u8d8a\u6765\u8d8a\u91cd\u8981\u3002<\/strong><\/span><\/section>\n

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\u4f5c\u8005\u7b80\u4ecb\uff1a<\/strong><\/span>
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Andrew Gelman\uff0c\u7f8e\u56fd\u7edf\u8ba1\u5b66\u5bb6\uff0c\u54e5\u4f26\u6bd4\u4e9a\u5927\u5b66\u7edf\u8ba1\u5b66\u548c\u653f\u6cbb\u5b66\u6559\u6388\u3002\u4ed61986\u5e74\u83b7\u5f97\u9ebb\u7701\u7406\u5de5\u5b66\u9662\u6570\u5b66\u548c\u7269\u7406\u5b66\u535a\u58eb\u5b66\u4f4d\u3002\u968f\u540e\uff0c\u4ed6\u83b7\u5f97\u4e86\u535a\u58eb\u5b66\u4f4d\u3002\u5728\u54c8\u4f5b\u5927\u5b66\u7edf\u8ba1\u5b66\u8363\u8a89\u9000\u4f11\u6559\u6388Donald Rubin\u7684\u6307\u5bfc\u4e0b\uff0c\u4e8e1990\u5e74\u4ece\u54c8\u4f5b\u5927\u5b66\u83b7\u5f97\u7edf\u8ba1\u5b66\u535a\u58eb\u5b66\u4f4d\u3002\u4ed6\u662f\u7f8e\u56fd\u7edf\u8ba1\u534f\u4f1a\u4e0e\u6570\u7406\u7edf\u8ba1\u5b66\u4f1a\u7684\u9662\u58eb\uff0c\u66fe\u4e09\u5ea6\u83b7\u5f97\u7f8e\u56fd\u7edf\u8ba1\u534f\u4f1a\u9881\u53d1\u7684\u201c\u6770\u51fa\u7edf\u8ba1\u5e94\u7528\u5956\u201d\uff0c\u8c37\u6b4c\u5b66\u672f\u663e\u793a\uff0c\u4ed6\u7684\u8bba\u6587\u603b\u5f15\u7528\u91cf\u8d85\u8fc712\u4e07\uff0ch-index\u4e3a110\u3002<\/span><\/section>\n

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<\/section>\n
Aki Vehtari\uff0c\u963f\u5c14\u6258\u5927\u5b66\u8ba1\u7b97\u673a\u79d1\u5b66\u7cfb\u526f\u6559\u6388\uff0c\u4e3b\u8981\u7814\u7a76\u9886\u57df\u4e3a\u8d1d\u53f6\u65af\u6982\u7387\u7406\u8bba\u548c\u65b9\u6cd5\u3001\u8d1d\u53f6\u65af\u5de5\u4f5c\u6d41\u3001\u6982\u7387\u7f16\u7a0b\u3001\u63a8\u7406\u65b9\u6cd5\uff08\u4f8b\u5982Laplace\uff0cEP\uff0cVB\uff0cMC\uff09\u3001\u63a8\u7406\u548c\u6a21\u578b\u8bca\u65ad\u3001\u6a21\u578b\u8bc4\u4f30\u548c\u9009\u62e9\u3001\u9ad8\u65af\u8fc7\u7a0b\u4ee5\u53ca\u5206\u5c42\u6a21\u578b\u3002\u8c37\u6b4c\u5b66\u672f\u663e\u793a\uff0c\u4ed6\u7684\u8bba\u6587\u603b\u5f15\u7528\u91cf\u8fd14\u4e07\u3002\u4ed6\u548cAndrew Gelman\u90fd\u662f\u300a\u8d1d\u53f6\u65af\u6570\u636e\u5206\u6790\u300b\u7684\u4f5c\u8005\uff0c\u8fd9\u672c\u4e66\u56e0\u5728\u6570\u636e\u5206\u6790\u3001\u7814\u7a76\u89e3\u51b3\u96be\u9898\u65b9\u9762\u7684\u53ef\u8bfb\u6027\u3001\u5b9e\u7528\u6027\u800c\u5e7f\u53d7\u8bfb\u8005\u597d\u8bc4\uff0c\u88ab\u8ba4\u4e3a\u662f\u8d1d\u53f6\u65af\u65b9\u6cd5\u9886\u57df\u7684\u4f18\u79c0\u4e4b\u4f5c\u3002<\/span><\/section>\n

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\u56e0\u679c\u79d1\u5b66\u7b2c\u4e8c\u5b63\u8bfb\u4e66\u4f1a\u62a5\u540d\u4e2d<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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<\/section>\n<\/h2>\n
\u56e0\u679c\u63a8\u65ad\u4e0e\u673a\u5668\u5b66\u4e60\u9886\u57df\u7684\u7ed3\u5408\u5df2\u7ecf\u5438\u5f15\u4e86\u8d8a\u6765\u8d8a\u591a\u6765\u81ea\u5b66\u754c\u4e1a\u754c\u7684\u5173\u6ce8\uff0c\u4e3a\u6df1\u5165\u63a2\u8ba8\u3001\u666e\u53ca\u63a8\u5e7f\u56e0\u679c\u79d1\u5b66\u8bae\u9898\uff0c\u667a\u6e90\u793e\u533a\u643a\u624b\u96c6\u667a\u4ff1\u4e50\u90e8\u5c06\u4e3e\u529e\u7b2c\u4e8c\u5b63\u300c<\/span>\u56e0\u679c\u79d1\u5b66\u4e0eCausalAI\u8bfb\u4e66\u4f1a<\/a><\/span>\u300d\u3002\u672c\u671f\u8bfb\u4e66\u4f1a\u7740\u529b\u4e8e\u5b9e\u64cd\u6027\u3001\u57fa\u7840\u6027\uff0c\u5c06\u5e26\u9886\u5927\u5bb6\u7cbe\u8bfb\u56e0\u679c\u79d1\u5b66\u65b9\u5411\u4e24\u672c\u975e\u5e38\u53d7\u5e7f\u6cdb\u8ba4\u53ef\u7684\u5165\u95e8\u6559\u6750\u3002<\/span><\/section>\n

<\/section>\n
1. Pearl, Judea, Madelyn Glymour, and Nicholas P. Jewell. Causal inference in statistics: A primer. John Wiley & Sons, 2016.<\/span>\uff08\u672c\u4e66\u4e2d\u8bd1\u7248\u300a\u7edf\u8ba1\u56e0\u679c\u63a8\u7406\u5165\u95e8\uff08\u7ffb\u8bd1\u7248\uff09\u300b\u5df2\u7531\u9ad8\u7b49\u6559\u80b2\u51fa\u7248\u793e\u51fa\u7248\uff09<\/span><\/section>\n

<\/section>\n
2. Peters, Jonas, Dominik Janzing, and Bernhard Sch\u00f6lkopf. Elements of causal inference: foundations and learning algorithms. The MIT Press, 2017.<\/span><\/section>\n

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\u8bfb\u4e66\u4f1a\u6bcf\u5468\u5c06\u8fdb\u884c\u76f4\u64ad\u8ba8\u8bba\uff0c\u8fdb\u884c\u95ee\u9898\u4ea4\u6d41\u3001\u91cd\u70b9\u6982\u5ff5\u5206\u4eab\u3001\u9605\u8bfb\u6982\u89c8\u548c\u7f16\u7a0b\u5b9e\u8df5\u5185\u5bb9\u5206\u6790\u3002\u975e\u5e38\u9002\u5408\u6709\u673a\u5668\u5b66\u4e60\u80cc\u666f\uff0c\u5e0c\u671b\u6df1\u5165\u5b66\u4e60\u56e0\u679c\u79d1\u5b66\u57fa\u7840\u77e5\u8bc6\u548c\u91cd\u8981\u6a21\u578b\u65b9\u6cd5\uff0c\u5bfb\u6c42\u89e3\u51b3\u76f8\u5173\u7814\u7a76\u95ee\u9898\u7684\u670b\u53cb\u53c2\u52a0\u3002<\/span><\/section>\n

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\u76ee\u524d\u56e0\u679c\u79d1\u5b66\u8bfb\u4e66\u4f1a\u7cfb\u5217\uff0c\u5df2\u7ecf\u6709\u63a5\u8fd1400\u591a\u4f4d\u7684\u6d77\u5185\u5916\u9ad8\u6821\u79d1\u7814\u9662\u6240\u7684\u4e00\u7ebf\u79d1\u7814\u5de5\u4f5c\u8005\u4ee5\u53ca\u4e92\u8054\u7f51\u4e00\u7ebf\u4ece\u4e1a\u4eba\u5458\u53c2\u4e0e\uff0c\u5438\u5f15\u4e86\u56fd\u5185\u548c\u56fd\u9645\u4e0a\u5927\u90e8\u5206\u7684\u56e0\u679c\u79d1\u5b66\u9886\u57df\u7684\u4e13\u4e1a\u79d1\u7814\u4eba\u5458\uff0c\u5982\u679c\u4f60\u4e5f\u5bf9\u8fd9\u4e2a\u4e3b\u9898\u611f\u5174\u8da3\uff0c\u60f3\u8981\u6df1\u5ea6\u5730\u53c2\u4e0e\uff0c\u5c31\u5feb\u52a0\u5165\u6211\u4eec\u5427\uff01<\/span><\/section>\n

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\u8fde\u63a5\u7edf\u8ba1\u5b66\u3001\u673a\u5668\u5b66\u4e60\u4e0e\u81ea\u52a8\u63a8\u7406\u7684\u65b0\u5174\u4ea4\u53c9\u9886\u57df\u2014\u2014\u56e0\u679c\u79d1\u5b66\u8bfb\u4e66\u4f1a\u518d\u8d77\u822a<\/span><\/strong><\/a><\/section>\n
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