{"id":477963,"date":"2023-08-09T09:23:08","date_gmt":"2023-08-09T09:23:08","guid":{"rendered":""},"modified":"2023-09-05T11:15:45","modified_gmt":"2023-09-05T11:15:45","slug":"markov-chain-monte-carlo-mcmc","status":"publish","type":"wiki","link":"https:\/\/oneproxy.pro\/cn\/wiki\/markov-chain-monte-carlo-mcmc\/","title":{"rendered":"\u9a6c\u5c14\u53ef\u592b\u94fe\u8499\u7279\u5361\u6d1b\uff08MCMC\uff09"},"content":{"rendered":"<p>\u9a6c\u5c14\u53ef\u592b\u94fe\u8499\u7279\u5361\u7f57 (MCMC) \u662f\u4e00\u79cd\u5f3a\u5927\u7684\u8ba1\u7b97\u6280\u672f\uff0c\u7528\u4e8e\u63a2\u7d22\u590d\u6742\u7684\u6982\u7387\u5206\u5e03\u5e76\u5728\u5404\u79cd\u79d1\u5b66\u548c\u5de5\u7a0b\u9886\u57df\u8fdb\u884c\u6570\u503c\u79ef\u5206\u3002\u5b83\u5728\u5904\u7406\u9ad8\u7ef4\u7a7a\u95f4\u6216\u96be\u4ee5\u5904\u7406\u7684\u6982\u7387\u5206\u5e03\u65f6\u7279\u522b\u6709\u4ef7\u503c\u3002MCMC \u5141\u8bb8\u4ece\u76ee\u6807\u5206\u5e03\u4e2d\u91c7\u6837\u70b9\uff0c\u5373\u4f7f\u5176\u5206\u6790\u5f62\u5f0f\u672a\u77e5\u6216\u96be\u4ee5\u8ba1\u7b97\u3002\u8be5\u65b9\u6cd5\u4f9d\u8d56\u4e8e\u9a6c\u5c14\u53ef\u592b\u94fe\u7684\u539f\u7406\u6765\u751f\u6210\u8fd1\u4f3c\u76ee\u6807\u5206\u5e03\u7684\u6837\u672c\u5e8f\u5217\uff0c\u4f7f\u5176\u6210\u4e3a\u8d1d\u53f6\u65af\u63a8\u7406\u3001\u7edf\u8ba1\u5efa\u6a21\u548c\u4f18\u5316\u95ee\u9898\u4e0d\u53ef\u6216\u7f3a\u7684\u5de5\u5177\u3002<\/p>\n<h2>\u9a6c\u5c14\u53ef\u592b\u94fe\u8499\u7279\u5361\u6d1b\uff08MCMC\uff09\u7684\u8d77\u6e90\u5386\u53f2\u53ca\u5176\u9996\u6b21\u63d0\u53ca<\/h2>\n<p>MCMC \u7684\u8d77\u6e90\u53ef\u4ee5\u8ffd\u6eaf\u5230 20 \u4e16\u7eaa\u4e2d\u53f6\u300220 \u4e16\u7eaa 40 \u5e74\u4ee3\uff0c\u65af\u5766\u5c3c\u65af\u62c9\u592b\u00b7\u4e4c\u62c9\u59c6\u548c\u7ea6\u7ff0\u00b7\u51af\u00b7\u8bfa\u4f9d\u66fc\u5728\u7edf\u8ba1\u529b\u5b66\u9886\u57df\u7684\u5de5\u4f5c\u4e3a\u8be5\u65b9\u6cd5\u5960\u5b9a\u4e86\u57fa\u7840\u3002\u4ed6\u4eec\u5f53\u65f6\u6b63\u5728\u7814\u7a76\u683c\u5b50\u4e0a\u7684\u968f\u673a\u6e38\u8d70\u7b97\u6cd5\uff0c\u4ee5\u6b64\u4f5c\u4e3a\u5bf9\u7269\u7406\u7cfb\u7edf\u8fdb\u884c\u5efa\u6a21\u7684\u65b9\u6cd5\u3002\u7136\u800c\uff0c\u76f4\u5230 20 \u4e16\u7eaa 50 \u5e74\u4ee3\u548c 60 \u5e74\u4ee3\uff0c\u8be5\u65b9\u6cd5\u624d\u53d7\u5230\u66f4\u5e7f\u6cdb\u7684\u5173\u6ce8\uff0c\u5e76\u4e0e\u8499\u7279\u5361\u7f57\u6280\u672f\u8054\u7cfb\u5728\u4e00\u8d77\u3002<\/p>\n<p>\u201c\u9a6c\u5c14\u53ef\u592b\u94fe\u8499\u7279\u5361\u7f57\u201d\u8fd9\u4e2a\u672f\u8bed\u672c\u8eab\u662f\u5728 20 \u4e16\u7eaa 50 \u5e74\u4ee3\u521d\u521b\u9020\u7684\uff0c\u5f53\u65f6\u7269\u7406\u5b66\u5bb6 Nicholas Metropolis\u3001Arianna Rosenbluth\u3001Marshall Rosenbluth\u3001Augusta Teller \u548c Edward Teller \u5f15\u5165\u4e86 Metropolis-Hastings \u7b97\u6cd5\u3002\u8be5\u7b97\u6cd5\u65e8\u5728\u5728\u7edf\u8ba1\u529b\u5b66\u6a21\u62df\u4e2d\u9ad8\u6548\u5730\u5bf9\u73bb\u5c14\u5179\u66fc\u5206\u5e03\u8fdb\u884c\u91c7\u6837\uff0c\u4e3a MCMC \u7684\u73b0\u4ee3\u53d1\u5c55\u94fa\u5e73\u4e86\u9053\u8def\u3002<\/p>\n<h2>\u6709\u5173\u9a6c\u5c14\u53ef\u592b\u94fe\u8499\u7279\u5361\u6d1b\uff08MCMC\uff09\u7684\u8be6\u7ec6\u4fe1\u606f<\/h2>\n<p>MCMC \u662f\u4e00\u7c7b\u7b97\u6cd5\uff0c\u901a\u8fc7\u751f\u6210\u9a6c\u5c14\u53ef\u592b\u94fe\u6765\u8fd1\u4f3c\u76ee\u6807\u6982\u7387\u5206\u5e03\uff0c\u9a6c\u5c14\u53ef\u592b\u94fe\u7684\u5e73\u7a33\u5206\u5e03\u5373\u4e3a\u6240\u9700\u6982\u7387\u5206\u5e03\u3002MCMC \u80cc\u540e\u7684\u4e3b\u8981\u601d\u60f3\u662f\u6784\u5efa\u4e00\u4e2a\u9a6c\u5c14\u53ef\u592b\u94fe\uff0c\u968f\u7740\u8fed\u4ee3\u6b21\u6570\u8d8b\u8fd1\u4e8e\u65e0\u7a77\u5927\uff0c\u8be5\u94fe\u4f1a\u6536\u655b\u5230\u76ee\u6807\u5206\u5e03\u3002<\/p>\n<h3>\u9a6c\u5c14\u53ef\u592b\u94fe\u8499\u7279\u5361\u6d1b\uff08MCMC\uff09\u7684\u5185\u90e8\u7ed3\u6784\u53ca\u5176\u5de5\u4f5c\u539f\u7406<\/h3>\n<p>MCMC \u7684\u6838\u5fc3\u601d\u60f3\u662f\u901a\u8fc7\u8fed\u4ee3\u5730\u63d0\u51fa\u65b0\u72b6\u6001\u5e76\u6839\u636e\u5176\u76f8\u5bf9\u6982\u7387\u63a5\u53d7\u6216\u62d2\u7edd\u5b83\u4eec\u6765\u63a2\u7d22\u76ee\u6807\u5206\u5e03\u7684\u72b6\u6001\u7a7a\u95f4\u3002\u8be5\u8fc7\u7a0b\u53ef\u5206\u4e3a\u4ee5\u4e0b\u6b65\u9aa4\uff1a<\/p>\n<ol>\n<li>\n<p><strong>\u521d\u59cb\u5316<\/strong>\uff1a\u4ece\u76ee\u6807\u5206\u5e03\u7684\u521d\u59cb\u72b6\u6001\u6216\u6837\u672c\u5f00\u59cb\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u63d0\u6848\u6b65\u9aa4<\/strong>\uff1a\u6839\u636e\u63d0\u8bae\u5206\u5e03\u751f\u6210\u5019\u9009\u72b6\u6001\u3002\u8be5\u5206\u5e03\u51b3\u5b9a\u4e86\u65b0\u72b6\u6001\u7684\u751f\u6210\u65b9\u5f0f\uff0c\u5bf9 MCMC \u7684\u6548\u7387\u8d77\u7740\u81f3\u5173\u91cd\u8981\u7684\u4f5c\u7528\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u9a8c\u6536\u6b65\u9aa4<\/strong>\uff1a\u8ba1\u7b97\u8003\u8651\u5f53\u524d\u72b6\u6001\u548c\u5efa\u8bae\u72b6\u6001\u6982\u7387\u7684\u63a5\u53d7\u7387\u3002\u6b64\u6bd4\u7387\u7528\u4e8e\u786e\u5b9a\u662f\u5426\u63a5\u53d7\u6216\u62d2\u7edd\u5efa\u8bae\u72b6\u6001\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u66f4\u65b0\u6b65\u9aa4<\/strong>\uff1a\u5982\u679c\u63d0\u8bae\u72b6\u6001\u88ab\u63a5\u53d7\uff0c\u5219\u5c06\u5f53\u524d\u72b6\u6001\u66f4\u65b0\u4e3a\u65b0\u72b6\u6001\u3002\u5426\u5219\uff0c\u4fdd\u6301\u5f53\u524d\u72b6\u6001\u4e0d\u53d8\u3002<\/p>\n<\/li>\n<\/ol>\n<p>\u901a\u8fc7\u91cd\u590d\u9075\u5faa\u8fd9\u4e9b\u6b65\u9aa4\uff0c\u9a6c\u5c14\u53ef\u592b\u94fe\u63a2\u7d22\u72b6\u6001\u7a7a\u95f4\uff0c\u7ecf\u8fc7\u8db3\u591f\u6b21\u6570\u7684\u8fed\u4ee3\u540e\uff0c\u6837\u672c\u5c06\u8fd1\u4f3c\u4e8e\u76ee\u6807\u5206\u5e03\u3002<\/p>\n<h2>\u9a6c\u5c14\u53ef\u592b\u94fe\u8499\u7279\u5361\u6d1b\uff08MCMC\uff09\u7684\u5173\u952e\u7279\u5f81\u5206\u6790<\/h2>\n<p>\u4f7f MCMC \u6210\u4e3a\u5404\u4e2a\u9886\u57df\u6709\u4ef7\u503c\u5de5\u5177\u7684\u5173\u952e\u7279\u6027\u5305\u62ec\uff1a<\/p>\n<ol>\n<li>\n<p><strong>\u4ece\u590d\u6742\u5206\u5e03\u4e2d\u62bd\u6837<\/strong>\uff1a\u7531\u4e8e\u5206\u5e03\u7684\u590d\u6742\u6027\u6216\u95ee\u9898\u7684\u9ad8\u7ef4\u6027\uff0c\u4ece\u76ee\u6807\u5206\u5e03\u4e2d\u76f4\u63a5\u91c7\u6837\u5f88\u56f0\u96be\u6216\u4e0d\u53ef\u80fd\uff0c\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0cMCMC \u7279\u522b\u6709\u6548\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u8d1d\u53f6\u65af\u63a8\u7406<\/strong>\uff1aMCMC \u901a\u8fc7\u4f30\u8ba1\u6a21\u578b\u53c2\u6570\u7684\u540e\u9a8c\u5206\u5e03\u5f7b\u5e95\u6539\u53d8\u4e86\u8d1d\u53f6\u65af\u7edf\u8ba1\u5206\u6790\u3002\u5b83\u5141\u8bb8\u7814\u7a76\u4eba\u5458\u7ed3\u5408\u5148\u9a8c\u77e5\u8bc6\u5e76\u6839\u636e\u89c2\u5bdf\u5230\u7684\u6570\u636e\u66f4\u65b0\u4fe1\u5ff5\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u4e0d\u786e\u5b9a\u6027\u91cf\u5316<\/strong>\uff1aMCMC \u63d0\u4f9b\u4e86\u4e00\u79cd\u91cf\u5316\u6a21\u578b\u9884\u6d4b\u548c\u53c2\u6570\u4f30\u8ba1\u4e2d\u7684\u4e0d\u786e\u5b9a\u6027\u7684\u65b9\u6cd5\uff0c\u8fd9\u5bf9\u4e8e\u51b3\u7b56\u8fc7\u7a0b\u81f3\u5173\u91cd\u8981\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u4f18\u5316<\/strong>\uff1aMCMC \u53ef\u7528\u4f5c\u5168\u5c40\u4f18\u5316\u65b9\u6cd5\u6765\u5bfb\u627e\u76ee\u6807\u5206\u5e03\u7684\u6700\u5927\u503c\u6216\u6700\u5c0f\u503c\uff0c\u4ece\u800c\u6709\u52a9\u4e8e\u5728\u590d\u6742\u7684\u4f18\u5316\u95ee\u9898\u4e2d\u5bfb\u627e\u6700\u4f18\u89e3\u3002<\/p>\n<\/li>\n<\/ol>\n<h2>\u9a6c\u5c14\u53ef\u592b\u94fe\u8499\u7279\u5361\u6d1b\uff08MCMC\uff09\u7684\u7c7b\u578b<\/h2>\n<p>MCMC \u5305\u542b\u51e0\u79cd\u65e8\u5728\u63a2\u7d22\u4e0d\u540c\u7c7b\u578b\u6982\u7387\u5206\u5e03\u7684\u7b97\u6cd5\u3002\u4e00\u4e9b\u6d41\u884c\u7684 MCMC \u7b97\u6cd5\u5305\u62ec\uff1a<\/p>\n<ol>\n<li>\n<p><strong>Metropolis-Hastings \u7b97\u6cd5<\/strong>\uff1a\u6700\u65e9\u4e14\u5e7f\u6cdb\u4f7f\u7528\u7684 MCMC \u7b97\u6cd5\u4e4b\u4e00\uff0c\u9002\u7528\u4e8e\u4ece\u975e\u6b63\u5219\u5316\u5206\u5e03\u4e2d\u91c7\u6837\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u5409\u5e03\u65af\u62bd\u6837<\/strong>\uff1a\u4e13\u95e8\u7528\u4e8e\u901a\u8fc7\u4ece\u6761\u4ef6\u5206\u5e03\u4e2d\u8fed\u4ee3\u62bd\u6837\u6765\u4ece\u8054\u5408\u5206\u5e03\u4e2d\u8fdb\u884c\u62bd\u6837\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u54c8\u5bc6\u987f\u8499\u7279\u5361\u7f57 (HMC)<\/strong>\uff1a\u4e00\u79cd\u66f4\u590d\u6742\u7684 MCMC \u7b97\u6cd5\uff0c\u5229\u7528\u6c49\u5bc6\u5c14\u987f\u52a8\u529b\u5b66\u539f\u7406\u6765\u5b9e\u73b0\u66f4\u9ad8\u6548\u3001\u66f4\u5c11\u76f8\u5173\u7684\u6837\u672c\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u65e0\u6389\u5934\u91c7\u6837\u5668 (NUTS)<\/strong>\uff1aHMC \u7684\u6269\u5c55\uff0c\u53ef\u81ea\u52a8\u786e\u5b9a\u6700\u4f73\u8f68\u8ff9\u957f\u5ea6\uff0c\u4ece\u800c\u63d0\u9ad8 HMC \u7684\u6027\u80fd\u3002<\/p>\n<\/li>\n<\/ol>\n<h2>\u9a6c\u5c14\u53ef\u592b\u94fe\u8499\u7279\u5361\u7f57 (MCMC) \u7684\u4f7f\u7528\u65b9\u6cd5\u3001\u95ee\u9898\u53ca\u5176\u76f8\u5173\u89e3\u51b3\u65b9\u6848<\/h2>\n<p>MCMC \u53ef\u5e94\u7528\u4e8e\u5404\u4e2a\u9886\u57df\uff0c\u4e00\u4e9b\u5e38\u89c1\u7684\u7528\u4f8b\u5305\u62ec\uff1a<\/p>\n<ol>\n<li>\n<p><strong>\u8d1d\u53f6\u65af\u63a8\u7406<\/strong>\uff1aMCMC \u5141\u8bb8\u7814\u7a76\u4eba\u5458\u4f30\u8ba1\u8d1d\u53f6\u65af\u7edf\u8ba1\u5206\u6790\u4e2d\u6a21\u578b\u53c2\u6570\u7684\u540e\u9a8c\u5206\u5e03\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u4ece\u590d\u6742\u5206\u5e03\u4e2d\u62bd\u6837<\/strong>\uff1a\u5728\u5904\u7406\u590d\u6742\u6216\u9ad8\u7ef4\u5206\u5e03\u65f6\uff0cMCMC \u63d0\u4f9b\u4e86\u4e00\u79cd\u63d0\u53d6\u4ee3\u8868\u6027\u6837\u672c\u7684\u6709\u6548\u65b9\u6cd5\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u4f18\u5316<\/strong>\uff1aMCMC \u53ef\u7528\u4e8e\u89e3\u51b3\u5168\u5c40\u4f18\u5316\u95ee\u9898\uff0c\u5176\u4e2d\u5bfb\u627e\u5168\u5c40\u6700\u5927\u503c\u6216\u6700\u5c0f\u503c\u5177\u6709\u6311\u6218\u6027\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u673a\u5668\u5b66\u4e60<\/strong>\uff1aMCMC \u7528\u4e8e\u8d1d\u53f6\u65af\u673a\u5668\u5b66\u4e60\uff0c\u4ee5\u4f30\u8ba1\u6a21\u578b\u53c2\u6570\u7684\u540e\u9a8c\u5206\u5e03\u5e76\u505a\u51fa\u4e0d\u786e\u5b9a\u7684\u9884\u6d4b\u3002<\/p>\n<\/li>\n<\/ol>\n<h3>\u6311\u6218\u548c\u89e3\u51b3\u65b9\u6848\uff1a<\/h3>\n<ol>\n<li>\n<p><strong>\u6536\u655b<\/strong>\uff1aMCMC \u94fe\u9700\u8981\u6536\u655b\u5230\u76ee\u6807\u5206\u5e03\u624d\u80fd\u63d0\u4f9b\u51c6\u786e\u7684\u4f30\u8ba1\u3002\u8bca\u65ad\u548c\u6539\u8fdb\u6536\u655b\u53ef\u80fd\u662f\u4e00\u4e2a\u6311\u6218\u3002<\/p>\n<ul>\n<li>\u89e3\u51b3\u65b9\u6848\uff1a\u8f68\u8ff9\u56fe\u3001\u81ea\u76f8\u5173\u56fe\u548c\u6536\u655b\u6807\u51c6\uff08\u4f8b\u5982 Gelman-Rubin \u7edf\u8ba1\u91cf\uff09\u7b49\u8bca\u65ad\u6709\u52a9\u4e8e\u786e\u4fdd\u6536\u655b\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p><strong>\u63d0\u6848\u5206\u5e03\u7684\u9009\u62e9<\/strong>\uff1aMCMC \u7684\u6548\u7387\u5f88\u5927\u7a0b\u5ea6\u4e0a\u53d6\u51b3\u4e8e\u63d0\u8bae\u5206\u5e03\u7684\u9009\u62e9\u3002<\/p>\n<ul>\n<li>\u89e3\u51b3\u65b9\u6848\uff1a\u81ea\u9002\u5e94 MCMC \u65b9\u6cd5\u5728\u91c7\u6837\u8fc7\u7a0b\u4e2d\u52a8\u6001\u8c03\u6574\u63d0\u8bae\u5206\u5e03\u4ee5\u83b7\u5f97\u66f4\u597d\u7684\u6027\u80fd\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p><strong>\u9ad8\u7ef4<\/strong>\uff1a\u5728\u9ad8\u7ef4\u7a7a\u95f4\u4e2d\uff0c\u72b6\u6001\u7a7a\u95f4\u7684\u63a2\u7d22\u53d8\u5f97\u66f4\u5177\u6311\u6218\u6027\u3002<\/p>\n<ul>\n<li>\u89e3\u51b3\u65b9\u6848\uff1aHMC \u548c NUTS \u7b49\u9ad8\u7ea7\u7b97\u6cd5\u5728\u9ad8\u7ef4\u7a7a\u95f4\u4e2d\u66f4\u6709\u6548\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<h2>\u4e3b\u8981\u7279\u70b9\u53ca\u4e0e\u540c\u7c7b\u672f\u8bed\u7684\u5176\u4ed6\u6bd4\u8f83<\/h2>\n<table>\n<thead>\n<tr>\n<th><strong>\u7279\u5f81<\/strong><\/th>\n<th><strong>\u9a6c\u5c14\u53ef\u592b\u94fe\u8499\u7279\u5361\u6d1b\uff08MCMC\uff09<\/strong><\/th>\n<th><strong>\u8499\u7279\u5361\u7f57\u6a21\u62df<\/strong><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><strong>\u65b9\u6cd5\u7c7b\u578b<\/strong><\/td>\n<td>\u57fa\u4e8e\u91c7\u6837<\/td>\n<td>\u57fa\u4e8e\u4eff\u771f<\/td>\n<\/tr>\n<tr>\n<td><strong>\u76ee\u6807<\/strong><\/td>\n<td>\u5927\u81f4\u76ee\u6807\u5206\u5e03<\/td>\n<td>\u4f30\u8ba1\u6982\u7387<\/td>\n<\/tr>\n<tr>\n<td><strong>\u7528\u4f8b<\/strong><\/td>\n<td>\u8d1d\u53f6\u65af\u63a8\u7406\u3001\u4f18\u5316\u3001\u62bd\u6837<\/td>\n<td>\u79ef\u5206\u3001\u4f30\u8ba1<\/td>\n<\/tr>\n<tr>\n<td><strong>\u5bf9\u6837\u672c\u7684\u4f9d\u8d56<\/strong><\/td>\n<td>\u987a\u5e8f\u3001\u9a6c\u5c14\u53ef\u592b\u94fe\u884c\u4e3a<\/td>\n<td>\u72ec\u7acb\u3001\u968f\u673a\u6837\u672c<\/td>\n<\/tr>\n<tr>\n<td><strong>\u9ad8\u7ef4\u5ea6\u6548\u7387<\/strong><\/td>\n<td>\u4e2d\u7b49\u81f3\u826f\u597d<\/td>\n<td>\u6548\u7387\u4f4e\u4e0b<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>\u4e0e\u9a6c\u5c14\u53ef\u592b\u94fe\u8499\u7279\u5361\u6d1b (MCMC) \u76f8\u5173\u7684\u672a\u6765\u89c2\u70b9\u548c\u6280\u672f<\/h2>\n<p>\u968f\u7740\u6280\u672f\u7684\u8fdb\u6b65\uff0cMCMC \u53ef\u80fd\u4f1a\u671d\u4ee5\u4e0b\u51e0\u4e2a\u65b9\u5411\u53d1\u5c55\uff1a<\/p>\n<ol>\n<li>\n<p><strong>\u5e76\u884c\u548c\u5206\u5e03\u5f0f MCMC<\/strong>\uff1a\u5229\u7528\u5e76\u884c\u548c\u5206\u5e03\u5f0f\u8ba1\u7b97\u8d44\u6e90\u52a0\u901f\u5927\u89c4\u6a21\u95ee\u9898\u7684 MCMC \u8ba1\u7b97\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u53d8\u5206\u63a8\u7406<\/strong>\uff1a\u5c06 MCMC \u4e0e\u53d8\u5206\u63a8\u7406\u6280\u672f\u76f8\u7ed3\u5408\uff0c\u4ee5\u63d0\u9ad8\u8d1d\u53f6\u65af\u8ba1\u7b97\u7684\u6548\u7387\u548c\u53ef\u6269\u5c55\u6027\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u6df7\u5408\u65b9\u6cd5<\/strong>\uff1a\u5c06 MCMC \u4e0e\u4f18\u5316\u6216\u53d8\u5206\u65b9\u6cd5\u76f8\u7ed3\u5408\uff0c\u4ee5\u53d1\u6325\u5b83\u4eec\u5404\u81ea\u7684\u4f18\u52bf\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u786c\u4ef6\u52a0\u901f<\/strong>\uff1a\u5229\u7528 GPU \u548c TPU \u7b49\u4e13\u7528\u786c\u4ef6\u8fdb\u4e00\u6b65\u52a0\u901f MCMC \u8ba1\u7b97\u3002<\/p>\n<\/li>\n<\/ol>\n<h2>\u4ee3\u7406\u670d\u52a1\u5668\u5982\u4f55\u4e0e\u9a6c\u5c14\u53ef\u592b\u94fe\u8499\u7279\u5361\u6d1b (MCMC) \u4e00\u8d77\u4f7f\u7528\u6216\u5173\u8054<\/h2>\n<p>\u4ee3\u7406\u670d\u52a1\u5668\u5728\u52a0\u901f MCMC \u8ba1\u7b97\u65b9\u9762\u53d1\u6325\u7740\u91cd\u8981\u4f5c\u7528\uff0c\u5c24\u5176\u662f\u5728\u6240\u9700\u8ba1\u7b97\u8d44\u6e90\u5927\u91cf\u7684\u60c5\u51b5\u4e0b\u3002\u901a\u8fc7\u4f7f\u7528\u591a\u4e2a\u4ee3\u7406\u670d\u52a1\u5668\uff0c\u53ef\u4ee5\u5c06\u8ba1\u7b97\u5206\u5e03\u5230\u5404\u4e2a\u8282\u70b9\uff0c\u4ece\u800c\u51cf\u5c11\u751f\u6210 MCMC \u6837\u672c\u6240\u9700\u7684\u65f6\u95f4\u3002\u6b64\u5916\uff0c\u53ef\u4ee5\u4f7f\u7528\u4ee3\u7406\u670d\u52a1\u5668\u8bbf\u95ee\u8fdc\u7a0b\u6570\u636e\u96c6\uff0c\u4ece\u800c\u5b9e\u73b0\u66f4\u5e7f\u6cdb\u3001\u66f4\u591a\u6837\u5316\u7684\u6570\u636e\u4f9b\u5206\u6790\u3002<\/p>\n<p>\u4ee3\u7406\u670d\u52a1\u5668\u8fd8\u53ef\u4ee5\u5728 MCMC \u6a21\u62df\u8fc7\u7a0b\u4e2d\u589e\u5f3a\u5b89\u5168\u6027\u548c\u9690\u79c1\u6027\u3002\u901a\u8fc7\u63a9\u76d6\u7528\u6237\u7684\u5b9e\u9645\u4f4d\u7f6e\u548c\u8eab\u4efd\uff0c\u4ee3\u7406\u670d\u52a1\u5668\u53ef\u4ee5\u4fdd\u62a4\u654f\u611f\u6570\u636e\u5e76\u4fdd\u6301\u533f\u540d\u6027\uff0c\u8fd9\u5728\u5904\u7406\u79c1\u4eba\u4fe1\u606f\u7684\u8d1d\u53f6\u65af\u63a8\u7406\u4e2d\u5c24\u4e3a\u91cd\u8981\u3002<\/p>\n<h2>\u76f8\u5173\u94fe\u63a5<\/h2>\n<p>\u6709\u5173\u9a6c\u5c14\u53ef\u592b\u94fe\u8499\u7279\u5361\u6d1b\uff08MCMC\uff09\u7684\u66f4\u591a\u4fe1\u606f\uff0c\u60a8\u53ef\u4ee5\u63a2\u7d22\u4ee5\u4e0b\u8d44\u6e90\uff1a<\/p>\n<ol>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Metropolis%E2%80%93Hastings_algorithm\" target=\"_new\" rel=\"noopener nofollow\">Metropolis-Hastings \u7b97\u6cd5<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Gibbs_sampling\" target=\"_new\" rel=\"noopener nofollow\">\u5409\u5e03\u65af\u62bd\u6837<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Hamiltonian_Monte_Carlo\" target=\"_new\" rel=\"noopener nofollow\">\u54c8\u5bc6\u987f\u8499\u7279\u5361\u7f57 (HMC)<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/No-U-Turn_Sampler\" target=\"_new\" rel=\"noopener nofollow\">\u65e0\u6389\u5934\u91c7\u6837\u5668 (NUTS)<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Adaptive_Metropolis%E2%80%93Hastings_algorithm\" target=\"_new\" rel=\"noopener nofollow\">\u81ea\u9002\u5e94 MCMC<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Variational_Bayesian_methods\" target=\"_new\" rel=\"noopener nofollow\">\u53d8\u5206\u63a8\u7406<\/a><\/li>\n<\/ol>\n<p>\u603b\u4e4b\uff0c\u9a6c\u5c14\u53ef\u592b\u94fe\u8499\u7279\u5361\u7f57 (MCMC) \u662f\u4e00\u79cd\u591a\u529f\u80fd\u4e14\u529f\u80fd\u5f3a\u5927\u7684\u6280\u672f\uff0c\u5b83\u5f7b\u5e95\u6539\u53d8\u4e86\u8d1d\u53f6\u65af\u7edf\u8ba1\u3001\u673a\u5668\u5b66\u4e60\u548c\u4f18\u5316\u7b49\u5404\u4e2a\u9886\u57df\u3002\u5b83\u7ee7\u7eed\u5904\u4e8e\u7814\u7a76\u7684\u524d\u6cbf\uff0c\u65e0\u7591\u5c06\u5728\u5851\u9020\u672a\u6765\u6280\u672f\u548c\u5e94\u7528\u4e2d\u53d1\u6325\u91cd\u8981\u4f5c\u7528\u3002<\/p>","protected":false},"featured_media":468867,"menu_order":0,"template":"","meta":{"_acf_changed":false,"content-type":"","inline_featured_image":false,"footnotes":""},"class_list":["post-477963","wiki","type-wiki","status-publish","has-post-thumbnail","hentry"],"acf":{"faq_title":"Frequently Asked Questions about <mark>Markov Chain Monte Carlo (MCMC): Exploring Probabilistic Landscapes<\/mark>","faq_items":[{"question":"What is Markov Chain Monte Carlo (MCMC)?","answer":"<p>Markov Chain Monte Carlo (MCMC) is a powerful computational technique used to explore complex probability distributions and perform numerical integration. It allows for sampling from a target distribution, even when its analytical form is unknown or difficult to compute. MCMC is widely employed in Bayesian inference, statistical modeling, and optimization problems.<\/p>"},{"question":"How did Markov Chain Monte Carlo (MCMC) originate?","answer":"<p>The origins of MCMC can be traced back to the mid-20th century, with its foundations laid in the field of statistical mechanics by Stanislaw Ulam and John von Neumann. The term \"Markov Chain Monte Carlo\" was coined in the 1950s when physicists introduced the Metropolis-Hastings algorithm to efficiently sample the Boltzmann distribution in simulations.<\/p>"},{"question":"How does Markov Chain Monte Carlo (MCMC) work?","answer":"<p>MCMC constructs a Markov chain whose stationary distribution is the target probability distribution. The process involves proposing new states, accepting or rejecting them based on their probabilities, and updating the chain iteratively. After a sufficient number of iterations, the samples approximate the target distribution.<\/p>"},{"question":"What are the key features of Markov Chain Monte Carlo (MCMC)?","answer":"<p>MCMC is renowned for its ability to sample from complex distributions, perform Bayesian inference, quantify uncertainty in predictions, and tackle optimization problems. It provides a robust approach to dealing with high-dimensional spaces and exploring intricate probability landscapes.<\/p>"},{"question":"What types of Markov Chain Monte Carlo (MCMC) exist?","answer":"<p>There are several MCMC algorithms, including the Metropolis-Hastings Algorithm, Gibbs Sampling, Hamiltonian Monte Carlo (HMC), and No-U-Turn Sampler (NUTS). Each algorithm is tailored to explore different types of probability distributions.<\/p>"},{"question":"How can Markov Chain Monte Carlo (MCMC) be used, and what are some common challenges?","answer":"<p>MCMC finds applications in Bayesian inference, optimization, and sampling from complex distributions. Common challenges include ensuring convergence, selecting suitable proposal distributions, and addressing high-dimensional problems. Adaptive methods and diagnostics help address these challenges.<\/p>"},{"question":"What does the future hold for Markov Chain Monte Carlo (MCMC)?","answer":"<p>The future of MCMC involves parallel and distributed computing, hybrid methods with other inference techniques, and hardware acceleration. These advancements will lead to more efficient and scalable MCMC computations for complex problems.<\/p>"},{"question":"How are proxy servers associated with Markov Chain Monte Carlo (MCMC)?","answer":"<p>Proxy servers can enhance MCMC computations by distributing the workload across multiple nodes, reducing computation time. Additionally, they offer added security and privacy during simulations by anonymizing users' identities and locations.<\/p>"}]},"_links":{"self":[{"href":"https:\/\/oneproxy.pro\/cn\/wp-json\/wp\/v2\/wiki\/477963","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/oneproxy.pro\/cn\/wp-json\/wp\/v2\/wiki"}],"about":[{"href":"https:\/\/oneproxy.pro\/cn\/wp-json\/wp\/v2\/types\/wiki"}],"version-history":[{"count":0,"href":"https:\/\/oneproxy.pro\/cn\/wp-json\/wp\/v2\/wiki\/477963\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/oneproxy.pro\/cn\/wp-json\/wp\/v2\/media\/468867"}],"wp:attachment":[{"href":"https:\/\/oneproxy.pro\/cn\/wp-json\/wp\/v2\/media?parent=477963"}],"curies":[{"name":"\u53ef\u6e7f\u6027\u7c89\u5242","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}