{"id":5290,"date":"2022-09-05T16:00:00","date_gmt":"2022-09-05T08:00:00","guid":{"rendered":"https:\/\/www.btccccc.cc\/?p=5290"},"modified":"2022-09-05T16:00:00","modified_gmt":"2022-09-05T08:00:00","slug":"%e7%bb%9f%e8%ae%a1%e5%ad%a6%e9%87%8c%e9%a2%91%e7%8e%87%e5%ad%a6%e6%b4%befrequentist%e4%b8%8e%e8%b4%9d%e5%8f%b6%e6%96%afbayesian%e5%ad%a6%e6%b4%be%e7%9a%84%e5%8c%ba%e5%88%ab%e5%92%8c%e5%9c%a8","status":"publish","type":"post","link":"https:\/\/www.invbus.com\/blog\/?p=5290","title":{"rendered":"\u7edf\u8ba1\u5b66\u91cc\u9891\u7387\u5b66\u6d3e(Frequentist)\u4e0e\u8d1d\u53f6\u65af(Bayesian)\u5b66\u6d3e\u7684\u533a\u522b\u548c\u5728\u673a\u5668\u5b66\u4e60\u4e2d\u7684\u5e94\u7528"},"content":{"rendered":"\n<h3 class=\"wp-block-heading\">\u4e0e\u673a\u5668\u5b66\u4e60\u4e2dMLE\u548cMAP\u4e24\u5927\u5b66\u6d3e\u7684\u5bf9\u5e94\u5173\u7cfb<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u9891\u7387\u5b66\u6d3e &#8211; Frequentist &#8211; Maximum Likelihood Estimation (MLE\uff0c\u6700\u5927\u4f3c\u7136\u4f30\u8ba1)<\/li>\n\n\n\n<li>\u8d1d\u53f6\u65af\u5b66\u6d3e &#8211; Bayesian &#8211; Maximum A Posteriori (MAP\uff0c\u6700\u5927\u540e\u9a8c\u4f30\u8ba1)<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>\u9891\u7387\u8bba\u548c\u8d1d\u53f6\u65af\u65b9\u6cd5<\/strong><\/h3>\n\n\n\n<p>\u5bf9\u4e8e\u4e0d\u786e\u5b9a\u6027\u7684\u5ea6\u91cf\u7edf\u8ba1\u5b66\u91cc\u81f3\u5c11\u6709\u4e24\u79cd\u4e0d\u540c\u7684\u8003\u8651\u65b9\u5f0f\uff0c\u8fd9\u5bfc\u81f4\u4e86\u4e24\u79cd\u4e0d\u540c\u7c7b\u578b\u7684\u63a8\u7406\/\u51b3\u7b56\u65b9\u6cd5\uff0c\u6211\u4eec\u79f0\u4e4b\u4e3a<strong>\u9891\u7387\u8bba\uff08frequentist\uff09<\/strong>\u548c<strong>\u8d1d\u53f6\u65af\u65b9\u6cd5(Bayesian methods)<\/strong>\u3002<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><th>Frequentist<\/th><th>Bayesian<\/th><\/tr><tr><td>\u9891\u7387\u8bba\u65b9\u6cd5\u901a\u8fc7\u5927\u91cf\u72ec\u7acb\u5b9e\u9a8c\u5c06\u6982\u7387\u89e3\u91ca\u4e3a\u7edf\u8ba1\u5747\u503c\uff08\u5927\u6570\u5b9a\u5f8b\uff09<\/td><td>\u8d1d\u53f6\u65af\u65b9\u6cd5\u5219\u5c06\u6982\u7387\u89e3\u91ca\u4e3a\u4fe1\u5ff5\u5ea6\uff08degree of belief\uff09\uff08\u4e0d\u9700\u8981\u5927\u91cf\u7684\u5b9e\u9a8c\uff09<\/td><\/tr><tr><td>\u9891\u7387\u5b66\u6d3e\u628a\u672a\u77e5\u53c2\u6570\u770b\u4f5c\u666e\u901a\u53d8\u91cf\uff08\u56fa\u5b9a\u503c\uff09\uff0c\u628a\u6837\u672c\u770b\u4f5c\u968f\u673a\u53d8\u91cf<\/td><td>\u8d1d\u53f6\u65af\u5b66\u6d3e\u628a\u4e00\u5207\u53d8\u91cf\u770b\u4f5c\u968f\u673a\u53d8\u91cf<\/td><\/tr><tr><td>\u9891\u7387\u8bba\u4ec5\u4ec5\u5229\u7528\u62bd\u6837\u6570\u636e<\/td><td>\u8d1d\u53f6\u65af\u8bba\u5584\u4e8e\u5229\u7528\u8fc7\u53bb\u7684\u77e5\u8bc6\u548c\u62bd\u6837\u6570\u636e<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">\u9891\u7387\u5b66\u6d3e\u4e0e\u8d1d\u53f6\u65af\u5b66\u6d3e\u7684\u6700\u4e3b\u8981\u533a\u522b\uff1a\u662f\u5426\u5141\u8bb8\u5148\u9a8c\u6982\u7387\u5206\u5e03\u7684\u4f7f\u7528<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u9891\u7387\u5b66\u6d3e\u4e0d\u5047\u8bbe\u4efb\u4f55\u7684\u5148\u9a8c\u77e5\u8bc6\uff0c\u4e0d\u53c2\u7167\u8fc7\u53bb\u7684\u7ecf\u9a8c\uff0c\u53ea\u6309\u7167\u5f53\u524d\u5df2\u6709\u7684\u6570\u636e\u8fdb\u884c\u6982\u7387\u63a8\u65ad<\/li>\n\n\n\n<li>\u8d1d\u53f6\u65af\u5b66\u6d3e\u4f1a\u5047\u8bbe\u5148\u9a8c\u77e5\u8bc6\u7684\u5b58\u5728\uff0c\u7136\u540e\u518d\u7528\u91c7\u6837\u9010\u6e10\u4fee\u6539\u5148\u9a8c\u77e5\u8bc6\u5e76\u903c\u8fd1\u771f\u5b9e\u77e5\u8bc6<\/li>\n<\/ul>\n\n\n\n<p>\u56e0\u6b64\u8d1d\u53f6\u65af\u63a8\u8bba\u4e2d\u524d\u4e00\u6b21\u5f97\u5230\u7684\u540e\u9a8c\u6982\u7387\u5206\u5e03\u53ef\u4ee5\u4f5c\u4e3a\u540e\u4e00\u6b21\u7684\u5148\u9a8c\u6982\u7387\u3002\u4f46\u5b9e\u9645\u4e0a\uff0c\u5728\u6570\u636e\u91cf\u8d8b\u8fd1\u65e0\u7a77\u65f6\uff0c\u9891\u7387\u5b66\u6d3e\u548c\u8d1d\u53f6\u65af\u5b66\u6d3e\u5f97\u5230\u7684\u7ed3\u679c\u662f\u4e00\u6837\u7684\uff0c\u4e5f\u5c31\u662f\u8bf4<strong>\u9891\u7387\u65b9\u6cd5\u662f\u8d1d\u53f6\u65af\u65b9\u6cd5\u7684\u6781\u9650<\/strong>\u3002<\/p>\n\n\n\n<p>\u5f53\u8003\u8651\u7684\u8bd5\u9a8c\u6b21\u6570\u975e\u5e38\u5c11\u7684\u65f6\u5019\uff0c\u8d1d\u53f6\u65af\u65b9\u6cd5\u7684\u89e3\u91ca\u975e\u5e38\u6709\u7528\u3002\u6b64\u5916\uff0c\u8d1d\u53f6\u65af\u7406\u8bba\u5c06\u6211\u4eec\u5bf9\u4e8e\u968f\u673a\u8fc7\u7a0b\u7684\u5148\u9a8c\u77e5\u8bc6\u7eb3\u5165\u8003\u8651\uff0c\u5f53\u6211\u4eec\u83b7\u5f97\u7684\u6570\u636e\u8d8a\u6765\u8d8a\u591a\u7684\u65f6\u5019\uff0c\u8fd9\u4e2a\u5148\u9a8c\u7684\u6982\u7387\u5206\u5e03\u5c31\u4f1a\u88ab\u66f4\u65b0\u5230\u540e\u9a8c\u5206\u5e03\u4e2d\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u9891\u7387\u8bba\u548c\u8d1d\u53f6\u65af\u65b9\u6cd5\u5404\u6709\u5176\u4f18\u52a3<\/h3>\n\n\n\n<p>\u9891\u7387\u6d3e\u7684\u4f18\u70b9\u5219\u662f\u6ca1\u6709\u5047\u8bbe\u4e00\u4e2a\u5148\u9a8c\u5206\u5e03\uff0c\u56e0\u6b64\u66f4\u52a0\u5ba2\u89c2\uff0c\u4e5f\u66f4\u52a0\u65e0\u504f\uff0c\u5728\u4e00\u4e9b\u4fdd\u5b88\u7684\u9886\u57df\u6bd4\u5982\u5236\u836f\u4e1a\u3001\u6cd5\u5f8b\u6bd4\u8d1d\u53f6\u65af\u65b9\u6cd5\u66f4\u53d7\u5230\u4fe1\u4efb\u3002\u5e76\u4e14\u9891\u7387\u8bba\u65b9\u6cd5\u6bd4\u8d1d\u53f6\u65af\u65b9\u6cd5\u66f4\u5bb9\u6613\u5b9e\u65bd\uff0c\u7136\u800c\u5374\u66f4\u96be\u89e3\u91ca\u3002<\/p>\n\n\n\n<p>\u8d1d\u53f6\u65af\u6d3e\u56e0\u4e3a\u6240\u6709\u7684\u53c2\u6570\u90fd\u662f\u968f\u673a\u53d8\u91cf\uff0c\u90fd\u6709\u5206\u5e03\uff0c\u56e0\u6b64\u53ef\u4ee5\u4f7f\u7528\u4e00\u4e9b\u57fa\u4e8e\u91c7\u6837\u7684\u65b9\u6cd5\u5982MCMC\u65b9\u6cd5(Markov Chain Monte Carlo)\uff09\u4f7f\u5f97\u6211\u4eec\u66f4\u5bb9\u6613\u6784\u5efa\u590d\u6742\u6a21\u578b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u4e24\u5927\u5b66\u6d3e\u7684\u4e89\u8bba<\/h3>\n\n\n\n<p>\u62bd\u8c61\u4e00\u70b9\u6765\u8bb2\uff0c\u9891\u7387\u5b66\u6d3e\u548c\u8d1d\u53f6\u65af\u5b66\u6d3e\u5bf9\u4e16\u754c\u7684\u8ba4\u77e5\u6709\u672c\u8d28\u4e0d\u540c\uff1a\u9891\u7387\u5b66\u6d3e\u8ba4\u4e3a\u4e16\u754c\u662f\u786e\u5b9a\u7684\uff0c\u6709\u4e00\u4e2a\u672c\u4f53\uff0c\u8fd9\u4e2a\u672c\u4f53\u7684\u771f\u503c\u662f\u4e0d\u53d8\u7684\uff0c\u6211\u4eec\u7684\u76ee\u6807\u5c31\u662f\u8981\u627e\u5230\u8fd9\u4e2a\u771f\u503c\u6216\u771f\u503c\u6240\u5728\u7684\u8303\u56f4\uff1b\u800c\u8d1d\u53f6\u65af\u5b66\u6d3e\u8ba4\u4e3a\u4e16\u754c\u662f\u4e0d\u786e\u5b9a\u7684\uff0c\u4eba\u4eec\u5bf9\u4e16\u754c\u5148\u6709\u4e00\u4e2a\u9884\u5224\uff0c\u800c\u540e\u901a\u8fc7\u89c2\u6d4b\u6570\u636e\u5bf9\u8fd9\u4e2a\u9884\u5224\u505a\u8c03\u6574\uff0c\u6211\u4eec\u7684\u76ee\u6807\u662f\u8981\u627e\u5230\u6700\u4f18\u7684\u63cf\u8ff0\u8fd9\u4e2a\u4e16\u754c\u7684\u6982\u7387\u5206\u5e03\u3002<\/p>\n\n\n\n<p>\u5728\u5bf9\u4e8b\u7269\u5efa\u6a21\u65f6\uff0c\u7528\u03b8\u8868\u793a\u6a21\u578b\u7684\u53c2\u6570\uff0c<strong>\u8bf7\u6ce8\u610f\uff0c\u89e3\u51b3\u95ee\u9898\u7684\u672c\u8d28\u5c31\u662f\u6c42\u03b8\u3002<\/strong>\u90a3\u4e48\uff1a<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u4e00\u3001\u9891\u7387\u8bba\u65b9\u6cd5\uff1a<strong>\u4f7f\u7528\u7b80\u5355\u7684z-test\u5f00\u59cb\u5047\u8bbe\u68c0\u9a8c<\/strong><\/h3>\n\n\n\n<p>\u7edf\u8ba1\u5047\u8bbe\u68c0\u9a8c\u5141\u8bb8\u6211\u4eec\u5728\u6570\u636e\u4e0d\u5b8c\u6574\u7684\u60c5\u51b5\u4e0b\u505a\u51fa\u51b3\u7b56\uff0c\u5f53\u7136\u4ece\u5b9a\u4e49\u4e0a\u8bf4\uff0c\u8fd9\u4e9b\u51b3\u7b56\u662f\u4e0d\u786e\u5b9a\u7684\u3002\u7edf\u8ba1\u5b66\u5bb6\u5df2\u7ecf\u5236\u5b9a\u4e86\u4e25\u683c\u7684\u65b9\u6cd5\u6765\u8bc4\u4f30\u8fd9\u79cd\u98ce\u9669\u3002\u7136\u800c\uff0c\u5728\u8fdb\u884c\u51b3\u7b56\u7684\u8fc7\u7a0b\u4e2d\u603b\u4f1a\u6d89\u53ca\u4e00\u4e9b\u4e3b\u89c2\u6027\u3002\u7406\u8bba\u53ea\u662f\u5728\u4e0d\u786e\u5b9a\u7684\u4e16\u754c\u4e2d\u5e2e\u52a9\u6211\u4eec\u8fdb\u884c\u51b3\u7b56\u7684\u4e00\u79cd\u5de5\u5177\u3002<\/p>\n\n\n\n<p><strong>\u5728\u8fdb\u884c\u5047\u8bbe\u68c0\u9a8c\u65f6\u8bb8\u591a\u9891\u7387\u8bba\u7684\u65b9\u6cd5\u5927\u81f4\u4e0a\u5305\u542b\u4ee5\u4e0b\u6b65\u9aa4\uff1a<\/strong><\/p>\n\n\n\n<p>1\u3001 \u5199\u51fa\u5047\u8bbe\uff0c\u5c24\u5176\u662f\u96f6\u5047\u8bbe\uff08Null hypothesis\uff09\uff0c\u5b83\u4e0e\u6211\u4eec\u8981\uff08\u4ee5\u4e00\u5b9a\u7684\u7f6e\u4fe1\u5ea6\uff09\u8bc1\u660e\u7684\u5047\u8bbe\u76f8\u53cd\u3002<\/p>\n\n\n\n<p>2\u3001 \u8ba1\u7b97\u68c0\u9a8c\u7edf\u8ba1\u91cf\uff0c\u8fd9\u662f\u4e00\u4e2a\u6570\u5b66\u516c\u5f0f\uff0c\u53d6\u51b3\u4e8e\u68c0\u9a8c\u7684\u7c7b\u578b\uff0c\u6a21\u578b\uff0c\u5047\u8bbe\u548c\u6570\u636e\u3002<\/p>\n\n\n\n<p>3\u3001 \u4f7f\u7528\u8ba1\u7b97\u51fa\u7684\u503c\u63a5\u53d7\u5047\u8bbe\uff0c\u6216\u8005\u62d2\u7edd\u5047\u8bbe\uff0c\u6216\u8005\u672a\u80fd\u5f97\u51fa\u7ed3\u8bba\u3002<\/p>\n\n\n\n<p><strong>\u9891\u7387\u5b66\u6d3e<\/strong>\uff1a\u5b58\u5728\u552f\u4e00\u771f\u503c\u03b8\u3002\u4e3e\u4e00\u4e2a\u7b80\u5355\u76f4\u89c2\u7684\u4f8b\u5b50\u2014\u629b\u786c\u5e01\uff0c\u6211\u4eec\u7528P(head)\u6765\u8868\u793a\u786c\u5e01\u7684bias\u3002\u629b\u4e00\u679a\u786c\u5e01100\u6b21\uff0c\u670920\u6b21\u6b63\u9762\u671d\u4e0a\uff0c\u8981\u4f30\u8ba1\u629b\u786c\u5e01\u6b63\u9762\u671d\u4e0a\u7684bias P(head)=\u03b8\u3002\u5728\u9891\u7387\u5b66\u6d3e\u6765\u770b\uff0c\u03b8= 20 \/ 100 = 0.2\uff0c\u5f88\u76f4\u89c2\u3002<\/p>\n\n\n\n<p>\u5f53\u6570\u636e\u91cf\u8d8b\u4e8e\u65e0\u7a77\u65f6\uff0c\u8fd9\u79cd\u65b9\u6cd5\u80fd\u7ed9\u51fa\u7cbe\u51c6\u7684\u4f30\u8ba1\uff1b\u7136\u800c\u7f3a\u4e4f\u6570\u636e\u65f6\u5219\u53ef\u80fd\u4ea7\u751f\u4e25\u91cd\u7684\u504f\u5dee\u3002\u4f8b\u5982\uff0c\u5bf9\u4e8e\u4e00\u679a\u5747\u5300\u786c\u5e01\uff0c\u5373\u03b8= 0.5\uff0c\u629b\u63b75\u6b21\uff0c\u51fa\u73b05\u6b21\u6b63\u9762 (\u8fd9\u79cd\u60c5\u51b5\u51fa\u73b0\u7684\u6982\u7387\u662f1\/2^5=3.125%)\uff0c\u9891\u7387\u5b66\u6d3e\u4f1a\u76f4\u63a5\u4f30\u8ba1\u8fd9\u679a\u786c\u5e01\u03b8= 1\uff0c\u51fa\u73b0\u4e25\u91cd\u9519\u8bef\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>\u4e8c\u3001\u4f7f\u7528\u8d1d\u53f6\u65af\u65b9\u6cd5<\/strong><\/h3>\n\n\n\n<p>\u57fa\u4e8e\u8d1d\u53f6\u65af\u7406\u8bba\u7684\u65b9\u6cd5\u4e3b\u8981\u601d\u60f3\u662f\u5c06\u672a\u77e5\u53c2\u6570\u5f53\u4f5c\u662f\u968f\u673a\u53d8\u91cf\uff0c\u5c31\u50cf\u63cf\u8ff0\u8bd5\u9a8c\u65f6\u4f7f\u7528\u7684\u53d8\u91cf\u4e00\u6837\u3002\u5173\u4e8e\u53c2\u6570\u7684\u5148\u9a8c\u77e5\u8bc6\u88ab\u96c6\u6210\u5230\u6a21\u578b\u4e2d\uff0c\u968f\u7740\u89c2\u5bdf\u5230\u7684\u6570\u636e\u8d8a\u6765\u8d8a\u591a\uff0c\u8fd9\u4e9b\u77e5\u8bc6\u4f1a\u88ab\u4e00\u76f4\u66f4\u65b0\u3002<\/p>\n\n\n\n<p>\u9891\u7387\u8bba\u65b9\u6cd5\u548c\u8d1d\u53f6\u65af\u65b9\u6cd5\u5bf9\u4e8e\u6982\u7387\u7684\u89e3\u91ca\u4e0d\u592a\u4e00\u6837\u3002\u9891\u7387\u8bba\u8ba4\u4e3a\u6982\u7387\u662f\u5f53\u6837\u672c\u7684\u6570\u91cf\u8d8b\u8fd1\u4e8e\u65e0\u7a77\u65f6\uff08\u6837\u672c\u51fa\u73b0\uff09\u9891\u7387\u7684\u6781\u9650\u3002\u8d1d\u53f6\u65af\u65b9\u6cd5\u5c06\u5176\u89e3\u91ca\u4e3a\u4e00\u79cd\u4fe1\u5ff5\uff08belief\uff09\uff0c\u5b83\u5c06\u4f1a\u968f\u7740\u89c2\u6d4b\u6570\u636e\u7684\u589e\u52a0\u800c\u4e0d\u65ad\u88ab\u66f4\u65b0\u3002<\/p>\n\n\n\n<p>\u8fd9\u91cc\uff0c\u6211\u4eec\u5c06\u4f7f\u7528\u8d1d\u53f6\u65af\u65b9\u6cd5\u91cd\u65b0\u8fdb\u884c\u4e4b\u524d\u7684\u786c\u5e01\u629b\u63b7\u5b9e\u9a8c\u3002<\/p>\n\n\n\n<p>\u5177\u4f53\u505a\u6cd5\uff1a\u6211\u4eec\u5c06P(head)\u5b9a\u4e49\u4e3a\u89c2\u5bdf\u5230\u786c\u5e01\u6b63\u9762\u7684\u6982\u7387\u3002\u5728\u4e0a\u4e00\u8282\u4e2dP(head)\u53ea\u662f\u4e00\u4e2a\u56fa\u5b9a\u7684\u6570\u5b57\uff0c\u7136\u800c\u6b64\u5904\u6211\u4eec\u5c06\u5176\u770b\u4f5c\u662f\u4e00\u4e2a\u968f\u673a\u53d8\u91cf\u3002\u6700\u521d\uff0c\u8fd9\u4e2a\u53d8\u91cf\u9075\u5faa\u4e00\u79cd\u79f0\u4e4b\u4e3a\u5148\u9a8c\u5206\u5e03\uff08prior distribution\uff09\u7684\u5206\u5e03\uff0c\u5b83\u4ee3\u8868\u4e86\u5728\u5f00\u59cb\u8fdb\u884c\u629b\u63b7\u786c\u5e01\u4e4b\u524d\u6211\u4eec\u5bf9\u4e8eP(head)\u7684\u77e5\u8bc6\u3002\u6211\u4eec\u5c06\u4f1a\u5728\u6bcf\u6b21\u8bd5\u9a8c\u4e4b\u540e\u66f4\u65b0\u8fd9\u4e2a\u5206\u5e03\uff08\u540e\u9a8c\u5206\u5e03\uff0cposterior distribution\uff09\u3002<\/p>\n\n\n\n<p><strong>\u8d1d\u53f6\u65af\u5b66\u6d3e<\/strong>\uff1a \u03b8\u662f\u4e00\u4e2a\u968f\u673a\u53d8\u91cf\uff0c\u7b26\u5408\u4e00\u5b9a\u7684\u6982\u7387\u5206\u5e03\u3002\u5728\u8d1d\u53f6\u65af\u5b66\u6d3e\u91cc\u6709\u4e24\u5927\u8f93\u5165\u548c\u4e00\u5927\u8f93\u51fa\uff0c\u8f93\u5165\u662f\u5148\u9a8c (prior)\u548c\u4f3c\u7136 (likelihood)\uff0c\u8f93\u51fa\u662f\u540e\u9a8c (posterior)\u3002<\/p>\n\n\n\n<p>\u5148\u9a8c\uff0c\u5373P(\u03b8)\uff0c\u6307\u7684\u662f\u5728\u6ca1\u6709\u89c2\u6d4b\u5230\u4efb\u4f55\u6570\u636e\u65f6\u5bf9\u03b8\u7684\u9884\u5148\u5224\u65ad\uff0c\u4f8b\u5982\u7ed9\u6211\u4e00\u4e2a\u786c\u5e01\uff0c\u4e00\u79cd\u53ef\u884c\u7684\u5148\u9a8c\u662f\u8ba4\u4e3a\u8fd9\u4e2a\u786c\u5e01\u6709\u5f88\u5927\u7684\u6982\u7387\u662f\u5747\u5300\u7684\uff0c\u6709\u8f83\u5c0f\u7684\u6982\u7387\u662f\u662f\u4e0d\u5747\u5300\u7684\uff1b\u4f3c\u7136\uff0c\u5373P(X|\u03b8)\uff0c\u662f\u5047\u8bbe\u03b8\u5df2\u77e5\u540e\u6211\u4eec\u89c2\u5bdf\u5230\u7684\u6570\u636e\u5e94\u8be5\u662f\u4ec0\u4e48\u6837\u5b50\u7684\uff1b\u540e\u9a8c\uff0c\u5373P(\u03b8|X)\uff0c\u662f\u6700\u7ec8\u7684\u53c2\u6570\u5206\u5e03\u3002<\/p>\n\n\n\n<p>\u8d1d\u53f6\u65af\u4f30\u8ba1\u7684\u57fa\u7840\u662f\u8d1d\u53f6\u65af\u516c\u5f0f\uff0c\u5982\u4e0b\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/pic4.zhimg.com\/80\/v2-04b28f7c68bd4c6bcec2c938b86ffc5b_720w.webp'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/pic4.zhimg.com\/80\/v2-04b28f7c68bd4c6bcec2c938b86ffc5b_720w.webp\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<p>\u540c\u6837\u662f\u629b\u786c\u5e01\u7684\u4f8b\u5b50\uff0c\u5bf9\u4e00\u679a\u5747\u5300\u786c\u5e01\u629b5\u6b21\u5f97\u52305\u6b21\u6b63\u9762\uff0c\u5982\u679c\u5148\u9a8c\u8ba4\u4e3a\u5927\u6982\u7387\u4e0b\u8fd9\u4e2a\u786c\u5e01\u662f\u5747\u5300\u7684 (\u4f8b\u5982\u6700\u5927\u503c\u53d6\u57280.5\u5904\u7684Beta\u5206\u5e03)\uff0c\u90a3\u4e48P(head)\uff0c\u5373P(\u03b8|X)\uff0c\u662f\u4e00\u4e2adistribution\uff0c\u6700\u5927\u503c\u4f1a\u4ecb\u4e8e0.5~1\u4e4b\u95f4\uff0c\u800c\u4e0d\u662f\u6b66\u65ad\u7684\u03b8= 1\u3002<\/p>\n\n\n\n<p>\u8fd9\u91cc\u6709\u4e24\u70b9\u503c\u5f97\u6ce8\u610f\u7684\u5730\u65b9\uff1a<\/p>\n\n\n\n<p>1\u3001 \u968f\u7740\u6570\u636e\u91cf\u7684\u589e\u52a0\uff0c\u53c2\u6570\u5206\u5e03\u4f1a\u8d8a\u6765\u8d8a\u5411\u6570\u636e\u9760\u62e2\uff0c\u5148\u9a8c\u7684\u5f71\u54cd\u529b\u4f1a\u8d8a\u6765\u8d8a\u5c0f<\/p>\n\n\n\n<p>2\u3001 \u5982\u679c\u5148\u9a8c\u662funiform distribution\uff0c\u5219\u8d1d\u53f6\u65af\u65b9\u6cd5\u7b49\u4ef7\u4e8e\u9891\u7387\u65b9\u6cd5\u3002\u56e0\u4e3a\u76f4\u89c2\u4e0a\u6765\u8bb2\uff0c\u5148\u9a8c\u662funiform distribution\u672c\u8d28\u4e0a\u8868\u793a\u5bf9\u4e8b\u7269\u6ca1\u6709\u4efb\u4f55\u9884\u5224\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u8d1d\u53f6\u65af<strong>\u5de5\u4f5c\u539f\u7406<\/strong><\/h3>\n\n\n\n<p>\u8d1d\u53f6\u65af\u5b9a\u7406\uff1a\u4f7f\u7528\u4e00\u4e2a\u6570\u5b66\u6a21\u578b\u6765\u5bf9\u6570\u636e\u8fdb\u884c\u89e3\u91ca\u662f\u6570\u636e\u79d1\u5b66\u4e2d\u975e\u5e38\u901a\u7528\u7684\u4e00\u4e2a\u60f3\u6cd5\uff0c\u8fd9\u88ab\u5b9a\u4e49\u4e3a\u4e00\u4e2a\u5355\u5411\u7684\u8fc7\u7a0b\uff1amodel&nbsp;\u2192&nbsp;data\u3002\u4e00\u65e6\u8fd9\u4e2a\u6a21\u578b\u88ab\u786e\u5b9a\uff0c\u6570\u636e\u79d1\u5b66\u5bb6\u7684\u4efb\u52a1\u5c31\u53d8\u4e3a\u5229\u7528\u6570\u636e\u6062\u590d\u5173\u4e8e\u8be5\u6a21\u578b\u7684\u4fe1\u606f\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u6211\u4eec\u60f3\u5bf9\u539f\u59cb\u7684\u8fc7\u7a0b\u8fdb\u884c\u53cd\u8f6c\uff1adata&nbsp;\u2192&nbsp;model\u3002<\/p>\n\n\n\n<p>\u5728\u4e00\u4e2a\u6982\u7387\u96c6\u5408\u4e2d\uff0c\u4e0a\u8ff0\u6b63\u5411\u7684\u8fc7\u7a0b\u88ab\u8868\u793a\u4e3a\u4e00\u4e2a\u6761\u4ef6\u6982\u7387:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/pic1.zhimg.com\/80\/v2-901566bae20db02bb990e7a5e3ce4b24_720w.webp'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/pic1.zhimg.com\/80\/v2-901566bae20db02bb990e7a5e3ce4b24_720w.webp\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<p>\u8fd9\u662f\u6a21\u578b\u88ab\u5b8c\u5168\u6307\u5b9a\u540e\u89c2\u6d4b\u6570\u636e\u51fa\u73b0\u7684\u6982\u7387\u3002\u4e0e\u6b64\u76f8\u540c\u7684\uff0c\u53cd\u5411\u7684\u8fc7\u7a0b\u4e5f\u53ef\u4ee5\u8868\u793a\u4e3a\u4e00\u4e2a\u6761\u4ef6\u6982\u7387:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/pic4.zhimg.com\/80\/v2-019f12814ea0972b26c6e550cd2890eb_720w.webp'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/pic4.zhimg.com\/80\/v2-019f12814ea0972b26c6e550cd2890eb_720w.webp\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<p>\u8fd9\u5728\u5f97\u5230\u89c2\u6d4b\u6570\u636e\uff08\u6211\u4eec\u8fdb\u884c\u8bd5\u9a8c\u540e\u53ef\u4ee5\u5f97\u5230\u7684\u6570\u636e\uff09\u540e\u63d0\u4f9b\u4e86\u5173\u4e8e\uff08\u6211\u4eec\u6b63\u5728\u5bfb\u627e\u7684\uff09\u6a21\u578b\u7684\u4fe1\u606f\u3002<\/p>\n\n\n\n<p>\u8d1d\u53f6\u65af\u5b9a\u7406\u662f\u5bf9\u6982\u7387\u8fc7\u7a0bmodel&nbsp;\u2192&nbsp;data\u8fdb\u884c\u53cd\u8f6c\u7684\u901a\u7528\u6846\u67b6\u7684\u6838\u5fc3\u3002\u5b83\u53ef\u4ee5\u88ab\u5b9a\u4e49\u4e3a\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/pic1.zhimg.com\/80\/v2-bcc2bc78c4234dcd43a8580aceab23c4_720w.webp'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/pic1.zhimg.com\/80\/v2-bcc2bc78c4234dcd43a8580aceab23c4_720w.webp\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<p>\u5f53\u6211\u4eec\u5f97\u5230\u4e86\u89c2\u6d4b\u6570\u636e\u540e\uff0c\u8fd9\u4e2a\u516c\u5f0f\u63d0\u4f9b\u4e86\u5173\u4e8e\u6a21\u578b\u7684\u4fe1\u606f\u3002\u8d1d\u53f6\u65af\u516c\u5f0f\u88ab\u5e7f\u6cdb\u7684\u5e94\u7528\u4e8e\u4fe1\u53f7\u5904\u7406\uff0c\u7edf\u8ba1\uff0c\u673a\u5668\u5b66\u4e60\uff0c\u53cd\u5411\u95ee\u9898\uff08inverse problems\uff09\u548c\u8bb8\u591a\u5176\u4ed6\u7684\u79d1\u5b66\u5e94\u7528\u3002<\/p>\n\n\n\n<p>\u5728\u8d1d\u53f6\u65af\u516c\u5f0f\u4e2d\uff0cP(model)\u53cd\u6620\u4e86\u6211\u4eec\u5bf9\u4e8e\u6a21\u578b\u7684\u5148\u9a8c\u77e5\u8bc6\u3002<\/p>\n\n\n\n<p>P(data)\u662f\u6570\u636e\u7684\u5206\u5e03\uff0c\u5b83\u901a\u5e38\u88ab\u63cf\u8ff0\u4e3a\u5bf9\u4e0b\u5217\u5f0f\u5b50\u7684\u79ef\u5206\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/pic3.zhimg.com\/80\/v2-f5ae820babc709185450950eb94cc2f2_720w.webp'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/pic3.zhimg.com\/80\/v2-f5ae820babc709185450950eb94cc2f2_720w.webp\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<p>\u603b\u4e4b\u6765\u8bf4\uff0c\u8d1d\u53f6\u65af\u516c\u5f0f\u4e3a\u6211\u4eec\u63d0\u4f9b\u4e86\u4e00\u4e2a\u5173\u4e8e\u6570\u636e\u63a8\u65ad\u7684\u901a\u7528\u8def\u7ebf\u56fe\uff1a<\/p>\n\n\n\n<p>1\u3001 \u4e3a\u6b63\u5411\u8fc7\u7a0b\uff08\u6570\u636e\u63a8\u7406\u8fc7\u7a0b\uff09\u6307\u5b9a\u4e00\u4e2a\u6570\u5b66\u6a21\u578bmodel&nbsp;\u2192&nbsp;data\uff1b<\/p>\n\n\n\n<p>2\u3001 \u4e3a\u6a21\u578b\u6307\u5b9a\u5148\u9a8c\u77e5\u8bc6P(model)\uff1b<\/p>\n\n\n\n<p>3\u3001 \u4e3a\u6c42\u89e3\u516c\u5f0f\u8fdb\u884c\u5206\u6790\u6216\u8005\u6570\u503c\u8fd0\u7b97\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>\u8ba1\u7b97\u540e\u9a8c\u5206\u5e03<\/strong><\/h3>\n\n\n\n<p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u8d1d\u53f6\u65af\u5b9a\u7406\u5f97\u5230\u540e\u9a8c\u5206\u5e03\u670d\u4ece\u4e0b\u9762\u7684\u516c\u5f0f\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/pic4.zhimg.com\/80\/v2-b516441382e9693bac8c897cfc84f29b_720w.webp'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/pic4.zhimg.com\/80\/v2-b516441382e9693bac8c897cfc84f29b_720w.webp\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<p>\u7531\u4e8e&nbsp;\ufffd\ufffd&nbsp;\u662f\u76f8\u4e92\u72ec\u7acb\u7684\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\uff08h\u662f\u6b63\u9762\u5411\u4e0a\u7684\u6b21\u6570\uff09\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/pic3.zhimg.com\/80\/v2-3f73cefcb2d03c76a4ea5a17984cc2d2_720w.webp'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/pic3.zhimg.com\/80\/v2-3f73cefcb2d03c76a4ea5a17984cc2d2_720w.webp\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<p>\u6b64\u5916\uff0c\u6211\u4eec\u53ef\u4ee5\u5206\u6790\u8ba1\u7b97\u5982\u4e0b\u79ef\u5206\uff08\u4f7f\u7528\u5206\u90e8\u79ef\u5206\u63a8\u5bfc\uff09\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/pic2.zhimg.com\/80\/v2-58bf1e7d9607743dd0cd1ab140b45865_720w.webp'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/pic2.zhimg.com\/80\/v2-58bf1e7d9607743dd0cd1ab140b45865_720w.webp\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<p>\u6700\u7ec8\uff0c\u6211\u4eec\u5c06\u5f97\u5230\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/pic4.zhimg.com\/80\/v2-eccdebeda1dd89409b080e34d8aa11e7_720w.webp'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/pic4.zhimg.com\/80\/v2-eccdebeda1dd89409b080e34d8aa11e7_720w.webp\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>\u5bf9\u540e\u9a8c\u6982\u7387\u8fdb\u884c\u6700\u5927\u4f30\u8ba1<\/strong><\/h3>\n\n\n\n<p>\u6211\u4eec\u53ef\u4ee5\u4ece\u540e\u9a8c\u5206\u5e03\u4e2d\u8fdb\u884c\u70b9\u4f30\u8ba1\u3002\u4f8b\u5982\uff0c\u5bf9\u4e8e\u8fd9\u4e2a\u5206\u5e03\u4e2d\u7684&nbsp;\ufffd&nbsp;\u4f5c\u6700\u5927\u540e\u9a8c\u4f30\u8ba1\uff08maximum a posteriori(MAP) estimation\uff09\u3002<\/p>\n\n\n\n<p>\u8fd9\u91cc\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u5bf9\u540e\u9a8c\u6982\u7387\u4e2d\u7684&nbsp;\ufffd&nbsp;\u6c42\u5bfc\u8fdb\u884c\u4f30\u8ba1\uff0c\u5047\u5b9a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/pic1.zhimg.com\/80\/v2-7e8b6feb5e7a695630e6e9fda8a441b0_720w.webp'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/pic1.zhimg.com\/80\/v2-7e8b6feb5e7a695630e6e9fda8a441b0_720w.webp\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<p>\u53ef\u4ee5\u5f97\u5230\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/pic1.zhimg.com\/80\/v2-3ff185cfde8443f87e417d9c91efa210_720w.webp'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/pic1.zhimg.com\/80\/v2-3ff185cfde8443f87e417d9c91efa210_720w.webp\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<p>\u5f53&nbsp;\ufffd=\u210e\ufffd&nbsp;\u65f6\uff0c\u8be5\u8868\u8fbe\u5f0f\u7b49\u4e8e0\uff0c\u8fd9\u5c31\u662f\u5bf9\u4e8e\u53c2\u6570&nbsp;\ufffd&nbsp;\u7684\u6700\u5927\u540e\u9a8c\u4f30\u8ba1\u3002\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u8fd9\u4e2a\u503c\u6070\u597d\u662f\u5b9e\u9a8c\u4e2d\u6b63\u9762\u5411\u4e0a\u51fa\u73b0\u7684\u6bd4\u4f8b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u673a\u5668\u5b66\u4e60\u4e2d\u7684\u5e94\u7528<\/h3>\n\n\n\n<h3 class=\"wp-block-heading\">\u4e00\u3001MLE &#8211; \u6700\u5927\u4f3c\u7136\u4f30\u8ba1<\/h3>\n\n\n\n<p>Maximum Likelihood Estimation, \u662f\u9891\u7387\u5b66\u6d3e\u5e38\u7528\u7684\u4f30\u8ba1\u65b9\u6cd5\u3002<\/p>\n\n\n\n<p>\u5047\u8bbe\u6570\u636eX1\uff0cX2\uff0c\u2026\uff0cXn\u662fi.i.d.\u7684\u4e00\u7ec4\u62bd\u6837\uff0cX=(X1\uff0cX2\uff0c\u2026\uff0cXn)\u3002(\u5176\u4e2di.i.d.\u8868\u793aIndependent and identical distribution\uff0c\u72ec\u7acb\u540c\u5206\u5e03)\u3002\u90a3\u4e48MLE\u5bf9\u03b8\u7684\u4f30\u8ba1\u65b9\u6cd5\u53ef\u4ee5\u5982\u4e0b\u63a8\u5bfc\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/pic3.zhimg.com\/80\/v2-32951e8e47b546c10bf7276343e58d8a_720w.webp'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/pic3.zhimg.com\/80\/v2-32951e8e47b546c10bf7276343e58d8a_720w.webp\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<p>\u6700\u540e\u8fd9\u4e00\u884c\u6240\u4f18\u5316\u7684\u51fd\u6570\u88ab\u79f0\u4e3aNegative Log Likelihood (NLL)\u3002<\/p>\n\n\n\n<p>\u6211\u4eec\u7ecf\u5e38\u5728\u4e0d\u7ecf\u610f\u95f4\u4f7f\u7528MLE\uff0c\u4f8b\u5982\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u5173\u4e8e\u9891\u7387\u5b66\u6d3e\u6c42\u786c\u5e01\u6982\u7387\u7684\u4f8b\u5b50\uff0c\u5176\u65b9\u6cd5\u5176\u5b9e\u672c\u8d28\u662f\u7531\u4f18\u5316NLL\u5f97\u51fa\u3002<\/li>\n\n\n\n<li>\u7ed9\u5b9a\u4e00\u4e9b\u6570\u636e\uff0c\u6c42\u5bf9\u5e94\u7684\u9ad8\u65af\u5206\u5e03\u65f6\uff0c\u6211\u4eec\u7ecf\u5e38\u4f1a\u7b97\u8fd9\u4e9b\u6570\u636e\u70b9\u7684\u5747\u503c\u548c\u65b9\u5dee\u7136\u540e\u5e26\u5165\u5230\u9ad8\u65af\u5206\u5e03\u7684\u516c\u5f0f\uff0c\u5176\u7406\u8bba\u4f9d\u636e\u662f\u4f18\u5316NLL\u3002<\/li>\n\n\n\n<li>\u6df1\u5ea6\u5b66\u4e60\u505a\u5206\u7c7b\u4efb\u52a1\u65f6\u6240\u7528\u7684cross entropy loss\uff0c\u5176\u672c\u8d28\u4e5f\u662fMLE\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">\u4e8c\u3001MAP &#8211; \u6700\u5927\u540e\u9a8c\u4f30\u8ba1<\/h3>\n\n\n\n<p>Maximum A Posteriori, MAP\u662f\u8d1d\u53f6\u65af\u5b66\u6d3e\u5e38\u7528\u7684\u4f30\u8ba1\u65b9\u6cd5\u3002<\/p>\n\n\n\n<p>\u540c\u6837\u7684\uff0c\u5047\u8bbe\u6570\u636eX1\uff0cX2\uff0c\u2026\uff0cXn\u662fi.i.d.\u7684\u4e00\u7ec4\u62bd\u6837\uff0cX=(X1\uff0cX2\uff0c\u2026\uff0cXn) \u3002\u90a3\u4e48MAP\u5bf9\u03b8\u7684\u4f30\u8ba1\u65b9\u6cd5\u53ef\u4ee5\u5982\u4e0b\u63a8\u5bfc\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/pic1.zhimg.com\/80\/v2-98bb1bd5b55287902d569d6f96b7d49c_720w.webp'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/pic1.zhimg.com\/80\/v2-98bb1bd5b55287902d569d6f96b7d49c_720w.webp\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<p>\u5176\u4e2d\uff0c\u7b2c\u4e8c\u884c\u5230\u7b2c\u4e09\u884c\u4f7f\u7528\u4e86\u8d1d\u53f6\u65af\u5b9a\u7406\uff0c\u7b2c\u4e09\u884c\u5230\u7b2c\u56db\u884cP(X)\u53ef\u4ee5\u4e22\u6389\u56e0\u4e3a\u4e0e\u03b8\u65e0\u5173\u3002<\/p>\n\n\n\n<p><strong>\u6ce8\u610f-log P(X|\u03b8)\u5176\u5b9e\u5c31\u662fNLL\uff0c\u6240\u4ee5MLE\u548cMAP\u5728\u4f18\u5316\u65f6\u7684\u4e0d\u540c\u5c31\u662f\u5728\u4e8e\u5148\u9a8c\u9879-log P(\u03b8)<\/strong>\u3002\u90a3\u73b0\u5728\u6211\u4eec\u6765\u7814\u7a76\u4e00\u4e0b\u8fd9\u4e2a\u5148\u9a8c\u9879\uff0c\u5047\u5b9a\u5148\u9a8c\u662f\u4e00\u4e2a\u9ad8\u65af\u5206\u5e03\uff0c\u5373<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/pic1.zhimg.com\/80\/v2-1db1818ef4c7f49d836769439e345630_720w.webp'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/pic1.zhimg.com\/80\/v2-1db1818ef4c7f49d836769439e345630_720w.webp\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<p>\u90a3\u4e48\uff0c<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/pic2.zhimg.com\/80\/v2-fb1717ff658820c90a43980ac1fd073d_720w.webp'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/pic2.zhimg.com\/80\/v2-fb1717ff658820c90a43980ac1fd073d_720w.webp\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<p>\u81f3\u6b64\uff0c\u4e00\u4ef6\u795e\u5947\u7684\u4e8b\u60c5\u53d1\u751f\u4e86 \u2014 \u5728MAP\u4e2d\u4f7f\u7528\u4e00\u4e2a\u9ad8\u65af\u5206\u5e03\u7684\u5148\u9a8c\u7b49\u4ef7\u4e8e\u5728MLE\u4e2d\u91c7\u7528L2\u7684regularization\u3002<\/p>\n\n\n\n<p><em>\u53c2\u8003\u8d44\u6599\uff1a<\/em><\/p>\n\n\n\n<p>https:\/\/www.cnblogs.com\/chaosimple\/p\/4154009.html<\/p>\n\n\n\n<p>https:\/\/www.sohu.com\/a\/215176689_610300<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><a href=\"https:\/\/zhuanlan.zhihu.com\/p\/337637096\">https:\/\/zhuanlan.zhihu.com\/p\/337637096<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u4e0e\u673a\u5668\u5b66\u4e60\u4e2dMLE\u548cMAP\u4e24\u5927\u5b66\u6d3e\u7684\u5bf9\u5e94\u5173\u7cfb \u9891\u7387\u8bba\u548c\u8d1d\u53f6\u65af\u65b9\u6cd5 \u5bf9\u4e8e\u4e0d\u786e\u5b9a\u6027\u7684\u5ea6\u91cf\u7edf\u8ba1\u5b66\u91cc\u81f3\u5c11\u6709\u4e24\u79cd\u4e0d\u540c\u7684\u8003 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[59],"class_list":["post-5290","post","type-post","status-publish","format-standard","hentry","category-investment","tag-59"],"_links":{"self":[{"href":"https:\/\/www.invbus.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/5290","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.invbus.com\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.invbus.com\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.invbus.com\/blog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.invbus.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5290"}],"version-history":[{"count":0,"href":"https:\/\/www.invbus.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/5290\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.invbus.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5290"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.invbus.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5290"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.invbus.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5290"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}