{"id":3368,"date":"2022-02-27T15:26:52","date_gmt":"2022-02-27T07:26:52","guid":{"rendered":"https:\/\/egonlin.com\/?p=3368"},"modified":"2022-02-27T15:26:52","modified_gmt":"2022-02-27T07:26:52","slug":"%e7%ac%ac%e4%b8%89%e7%af%87%ef%bc%9a%e6%a6%82%e7%8e%87%e8%ae%ba-%e6%9e%81%e5%a4%a7%e4%bc%bc%e7%84%b6%e4%bc%b0%e8%ae%a1","status":"publish","type":"post","link":"https:\/\/egonlin.com\/?p=3368","title":{"rendered":"\u7b2c\u4e09\u7bc7\uff1a\u6982\u7387\u8bba-\u6781\u5927\u4f3c\u7136\u4f30\u8ba1"},"content":{"rendered":"

\u6781\u5927\u4f3c\u7136\u4f30\u8ba1<\/h1>\n

\u6700\u5927\u4f3c\u7136\u539f\u7406<\/h1>\n

\"\"<\/div><\/p>\n

\u6781\u5927\u4f3c\u7136\u4f30\u8ba1<\/h1>\n

  \u6781\u5927\u4f3c\u7136\u4f30\u8ba1\u662f\u5efa\u7acb\u5728\u6700\u5927\u4f3c\u7136\u539f\u7406\u7684\u57fa\u7840\u4e0a\u7684\u4e00\u4e2a\u7edf\u8ba1\u65b9\u6cd5\u3002\u6781\u5927\u4f3c\u7136\u4f30\u8ba1\u63d0\u4f9b\u4e86\u4e00\u79cd\u7ed9\u5b9a\u89c2\u5bdf\u6570\u636e\u6765\u8bc4\u4f30\u6a21\u578b\u53c2\u6570\u7684\u65b9\u6cd5\uff0c\u5373\u201c\u6a21\u578b\u5df2\u5b9a\uff0c\u53c2\u6570\u672a\u77e5\u201d\u3002\u901a\u8fc7\u89c2\u5bdf\u82e5\u5e72\u6b21\u5b9e\u9a8c\u7684\u7ed3\u679c\uff0c\u5229\u7528\u5b9e\u9a8c\u7ed3\u679c\u5f97\u5230\u67d0\u4e2a\u53c2\u6570\u503c\u80fd\u591f\u4f7f\u6837\u672c\u51fa\u73b0\u7684\u6982\u7387\u6700\u5927\uff0c\u5219\u79f0\u4e3a\u6781\u5927\u4f3c\u7136\u4f30\u8ba1\u3002<\/p>\n

  \u7b80\u800c\u8a00\u4e4b\uff0c\u6781\u5927\u4f3c\u7136\u4f30\u8ba1\u7684\u76ee\u7684\u662f\u5229\u7528\u5df2\u77e5\u7684\u6837\u672c\u7ed3\u679c\uff0c\u53cd\u63a8\u6700\u6709\u53ef\u80fd\u5bfc\u81f4\u8fd9\u6837\u7ed3\u679c\u7684\u53c2\u6570\u503c\u3002<\/p>\n

\u4f3c\u7136\u51fd\u6570<\/h1>\n

  \u5047\u8bbe\u4e00\u4e2a\u6837\u672c\u96c6$D$\u7684$n$\u4e2a\u6837\u672c\u90fd\u662f\u72ec\u7acb\u540c\u5206\u5e03\u7684\uff0c\u5e76\u4e14\u8be5\u6837\u672c\u96c6\u4e3a
\n$$
\nD={x_1,x_2,\\ldots,x_n}
\n$$
\n  \u4f3c\u7136\u51fd\u6570\uff08likelihood function\uff09\uff1a\u8054\u5408\u6982\u7387\u5bc6\u5ea6\u51fd\u6570$p(D|\\theta)$\u79f0\u4e3a\u76f8\u5bf9\u4e8e${x_1,x_2,\\ldots,x_n}$\u7684$\\theta$\u7684\u4f3c\u7136\u51fd\u6570\u3002
\n$$
\nl(\\theta) = p(D|\\theta) = p(x_1,x_2,\\ldots,xn|\\theta) = \\prod<\/em>{i=1}^n p(x_i|\\theta)
\n$$<\/p>\n

\u6781\u5927\u4f3c\u7136\u51fd\u6570\u4f30\u8ba1\u503c<\/h1>\n

  \u5982\u679c$\\hat{\\theta}$\u662f$\\theta$\u53c2\u6570\u7a7a\u95f4\u4e2d\u80fd\u4f7f\u4f3c\u7136\u51fd\u6570$l(\\theta)$\u6700\u5927\u7684$\\theta$\u503c\uff0c\u5219$\\hat{\\theta}$\u662f\u6700\u53ef\u80fd\u7684\u53c2\u6570\u503c\uff0c\u90a3\u4e48$\\hat{\\theta}$\u662f$\\theta$\u7684\u6700\u5927\u4f3c\u7136\u4f30\u8ba1\u91cf\uff0c\u8bb0\u4f5c
\n$$
\n\\hat{\\theta} = d(x_1,x_2,\\ldots,x_n) = d(D)
\n$$
\n\u5e76\u4e14$\\hat{\\theta}(x_1,x_2,\\ldots,x_n)$\u79f0\u4f5c\u6781\u5927\u4f3c\u7136\u51fd\u6570\u4f30\u8ba1\u503c\u3002<\/p>\n

\u6c42\u89e3\u6781\u5927\u4f3c\u7136\u51fd\u6570<\/h1>\n

  \u7ed9\u51fa\u6c42\u89e3\u6700\u5927$\\theta$\u503c\u7684\u516c\u5f0f
\n$$
\n\\hat{\\theta} = arg \\underbrace{max}\\theta l(\\theta) = arg \\underbrace{max}<\/em>\\theta \\prod_{i=1}^n p(xi|\\theta)
\n$$
\n  \u4e3a\u4e86\u65b9\u4fbf\u8ba1\u7b97\uff0c\u5b9a\u4e49\u5bf9\u6570\u4f3c\u7136\u51fd\u6570$H(\\theta)$\uff0c\u5373\u5bf9\u4f3c\u7136\u51fd\u6570\u6c42\u5bf9\u6570
\n$$
\nH(\\theta) = \\ln{l(\\theta)}
\n$$
\n  \u56e0\u6b64\u6c42\u6700\u5927$\\theta$\u503c\u7684\u516c\u5f0f\u53d8\u6210\u4e86
\n$$
\n\\hat{\\theta} = arg \\underbrace{max}<\/em>\\theta H(\\theta) = arg \\underbrace{max}\\theta \\ln{l(\\theta)} = arg \\underbrace{max}<\/em>\\theta \\prod_{i=1}^n \\ln{p(x_i|\\theta)}
\n$$
\n\u5e76\u4e14\u53ef\u4ee5\u53d1\u73b0\u516c\u5f0f\u4e2d\u53ea\u6709\u4e00\u4e2a\u53d8\u91cf$\\theta$<\/p>\n

\u672a\u77e5\u53c2\u6570\u53ea\u6709\u4e00\u4e2a<\/h2>\n

  \u5982\u679c$\\theta$\u4e3a\u6807\u91cf\uff0c\u5728\u4f3c\u7136\u51fd\u6570\u6ee1\u8db3\u8fde\u7eed\u3001\u53ef\u5fae\u7684\u60c5\u51b5\u4e0b\uff0c\u5219\u6781\u5927\u4f3c\u7136\u4f30\u8ba1\u91cf\u662f\u4e0b\u9762\u5fae\u5206\u65b9\u7a0b\u7684\u89e3
\n$$
\n{\\frac{dH(\\theta)}{d\\theta}} = {\\frac{d\\ln{l(\\theta)}}{d\\theta}} = 0
\n$$<\/p>\n

\u4f4d\u7f6e\u53c2\u6570\u6709\u591a\u4e2a<\/h2>\n

<\/p>

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\u67e5\u770b\u66f4\u591a<\/h2>

\u8054\u7cfb\u7ba1\u7406\u5458\u5fae\u4fe1tutu19192010\uff0c\u6ce8\u518c\u8d26\u53f7<\/p>\n<\/div>

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\u6781\u5927\u4f3c\u7136\u4f30\u8ba1 \u6700\u5927\u4f3c\u7136\u539f\u7406 \u6781\u5927\u4f3c\u7136\u4f30\u8ba1   \u6781\u5927\u4f3c\u7136\u4f30\u8ba1\u662f\u5efa\u7acb\u5728\u6700\u5927\u4f3c\u7136\u539f\u7406\u7684\u57fa\u7840\u4e0a\u7684\u4e00 […]<\/p>\n","protected":false},"author":3,"featured_media":3360,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[276,303,305],"tags":[],"_links":{"self":[{"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/posts\/3368"}],"collection":[{"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3368"}],"version-history":[{"count":0,"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/posts\/3368\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/media\/3360"}],"wp:attachment":[{"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3368"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3368"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3368"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}