{"id":3357,"date":"2022-02-27T15:20:27","date_gmt":"2022-02-27T07:20:27","guid":{"rendered":"https:\/\/egonlin.com\/?p=3357"},"modified":"2022-02-27T15:27:28","modified_gmt":"2022-02-27T07:27:28","slug":"%e7%ac%ac%e4%b8%80%e7%af%87%ef%bc%9a%e8%b4%9d%e5%8f%b6%e6%96%af%e5%86%b3%e7%ad%96","status":"publish","type":"post","link":"https:\/\/egonlin.com\/?p=3357","title":{"rendered":"\u7b2c\u4e00\u7bc7\uff1a\u8d1d\u53f6\u65af\u51b3\u7b56"},"content":{"rendered":"

\u8d1d\u53f6\u65af\u51b3\u7b56<\/h1>\n

\u8d1d\u53f6\u65af\u51b3\u7b56\u7406\u8bba<\/h1>\n

  \u8d1d\u53f6\u65af\u51b3\u7b56\u7406\u8bba\uff1a\u5728\u4e0d\u5b8c\u5168\u60c5\u62a5\u4e0b\uff0c\u5bf9\u90e8\u5206\u672a\u77e5\u7684\u72b6\u6001\u7528\u4e3b\u89c2\u6982\u7387\u4f30\u8ba1\u3002<\/p>\n

\u8d1d\u53f6\u65af\u516c\u5f0f<\/h1>\n

\u4ece\u6761\u4ef6\u6982\u7387\u516c\u5f0f\u63a8\u5bfc\u8d1d\u53f6\u65af\u516c\u5f0f<\/h2>\n

\u82e5\u679c$A$\u548c$B$\u76f8\u4e92\u72ec\u7acb\uff0c\u5219\u6709$p(A,B) = p(A)p(B)$\uff0c\u5e76\u6709\u6761\u4ef6\u6982\u7387\u516c\u5f0f
\n$$
\np(A|B) = {\\frac{p(A,B)}{p(B)}} \\
\np(B|A) = {\\frac{p(A,B)}{p(A)}} \\
\n$$
\n\u901a\u8fc7\u6761\u4ef6\u6982\u7387\u53ef\u5f97
\n$$
\np(A,B) = p(B|A)p(A) \\
\np(A|B) = {\\frac{p(B|A)p(A)}{p(B)}} \\quad \\text{\u7b80\u5199\u7684\u8d1d\u53f6\u65af\u516c\u5f0f}
\n$$
\n  $p(A|B)$\uff1a\u540e\u9a8c\u6982\u7387\uff0cB\u53d1\u751f\u7684\u60c5\u51b5\u4e0b\u53d1\u751fA\u7684\u6982\u7387\uff0c\u9700\u8981\u8ba1\u7b97\u7684\u6982\u7387<\/p>\n

  $p(B|A)$\uff1a\u4f3c\u7136\u5ea6\uff0cA\u5047\u8bbe\u6761\u4ef6\u6210\u7acb\u7684\u60c5\u51b5\u53d1\u751fB\u7684\u6982\u7387<\/p>\n

  $p(A)$\uff1aA\u7684\u5148\u9a8c\u6982\u7387\uff0c\u4e5f\u53ef\u4ee5\u7406\u89e3\u6210\u4e00\u822c\u60c5\u51b5\u4e0bA\u53d1\u751f\u7684\u6982\u7387<\/p>\n

  $p(B)$\uff1a\u6807\u51c6\u5316\u5e38\u91cf\uff0c\u4e5f\u53ef\u4ee5\u7406\u89e3\u6210\u4e00\u822c\u60c5\u51b5\u4e0bB\u53d1\u751f\u7684\u6982\u7387<\/p>\n

\u4ece\u5168\u6982\u7387\u516c\u5f0f\u63a8\u5bfc\u8d1d\u53f6\u65af\u516c\u5f0f<\/h2>\n

[rml_readmore]\uff1a
\n\u5168\u6982\u7387\u516c\u5f0f
\n$$
\np(B) = \\sum<\/em>{i=1}^n{p(B|A=A_i)p(Ai)} \\quad \\text{\u5176\u4e2d}\\sum<\/em>{i=1}^n{p(Ai)=1}
\n$$
\n\u901a\u8fc7\u5168\u6982\u7387\u516c\u5f0f\u53ef\u5f97
\n$$
\np(A|B) = {\\frac{p(B|A)p(A)}{\\sum<\/em>{i=1}^n{p(B|A=A_i)p(A_i)}}} \\quad \\text{\u5b8c\u6574\u7684\u8d1d\u53f6\u65af\u516c\u5f0f}
\n$$<\/p>\n

\u8d1d\u53f6\u65af\u516c\u5f0f\u5e94\u7528<\/h1>\n

  \u5728\u6570\u5b57\u901a\u4fe1\u4e2d\uff0c\u7531\u4e8e\u968f\u673a\u5e72\u6270\uff0c\u56e0\u6b64\u63a5\u53d7\u7684\u4fe1\u53f7\u4e0e\u53d1\u51fa\u7684\u4fe1\u53f7\u53ef\u80fd\u4e0d\u540c\uff0c\u4e3a\u4e86\u786e\u5b9a\u53d1\u51fa\u7684\u4fe1\u53f7\uff0c\u901a\u5e38\u9700\u8981\u8ba1\u7b97\u5404\u79cd\u6982\u7387\u3002<\/p>\n

    \u5982\u679c\u53d1\u62a5\u673a\u4ee50.6\u548c0.4\u7684\u6982\u7387\u53d1\u51fa\u4fe1\u53f70\u548c1\uff1b<\/p>\n

    \u5f53\u53d1\u51fa\u4fe1\u53f70\u65f6\uff0c\u4ee50.7\u548c0.2\u7684\u6982\u7387\u6536\u5230\u4fe1\u53f70\u548c1\uff1b<\/p>\n

    \u5f53\u53d1\u51fa\u4fe1\u53f71\u65f6\uff0c\u63a5\u6536\u673a\u4ee50.8\u548c0.2\u6536\u5230\u4fe1\u53f71\u548c0\u3002<\/p>\n

    \u8ba1\u7b97\u5f53\u63a5\u53d7\u673a\u6536\u5230\u4fe1\u53f70\u65f6\uff0c\u53d1\u62a5\u673a\u53d1\u51fa\u4fe1\u53f70\u7684\u6982\u7387\u3002<\/p>\n

  \u901a\u8fc7\u4e0a\u8ff0\u7ed9\u51fa\u7684\u6570\u636e\u53ef\u4ee5\u5f97\u5230\u4ee5\u4e0b\u63a8\u5bfc<\/p>\n

    $p(A_0) = 0.6$\uff1a\u53d1\u62a5\u673a\u53d1\u51fa\u4fe1\u53f70\u7684\u6982\u7387<\/p>\n

    $p(A_1) = 0.4$\uff1a\u53d1\u62a5\u673a\u53d1\u51fa\u4fe1\u53f71\u7684\u6982\u7387<\/p>\n

    $p(B)=p(A_0)p(B|A_0) + p(A_1)p(B|A_1)$\uff1a\u53d1\u62a5\u673a\u63a5\u6536\u5230\u4fe1\u53f70\u7684\u6982\u7387<\/p>\n

    $p(B|A_0) = 0.7$\uff1a\u53d1\u62a5\u673a\u53d1\u51fa\u4fe1\u53f70\u63a5\u6536\u5230\u4fe1\u53f70\u7684\u6982\u7387<\/p>\n

    $p(B|A_1) = 0.2$\uff1a\u53d1\u62a5\u673a\u53d1\u51fa\u4fe1\u53f71\u63a5\u6536\u5230\u4fe1\u53f70\u7684\u6982\u7387<\/p>\n

$$
\n\\begin{align}
\np(A_0|B) & = {\\frac{p(B|A_0)p(A_0)}{p(A_0)p(B|A_0) + p(A_1)p(B|A_1)}} \\
\n& ={\\frac{0.60.7}{0.6<\/em>0.7 + 0.4*0.2}} \\
\n& ={\\frac{0.42}{0.50}} \\
\n& =0.84
\n\\end{align}
\n$$<\/p>\n","protected":false},"excerpt":{"rendered":"

\u8d1d\u53f6\u65af\u51b3\u7b56 \u8d1d\u53f6\u65af\u51b3\u7b56\u7406\u8bba   \u8d1d\u53f6\u65af\u51b3\u7b56\u7406\u8bba\uff1a\u5728\u4e0d\u5b8c\u5168\u60c5\u62a5\u4e0b\uff0c\u5bf9\u90e8\u5206\u672a\u77e5\u7684\u72b6\u6001\u7528\u4e3b\u89c2\u6982\u7387 […]<\/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\/3357"}],"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=3357"}],"version-history":[{"count":0,"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/posts\/3357\/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=3357"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3357"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3357"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}