{"id":1036,"date":"2023-07-27T21:50:46","date_gmt":"2023-07-27T21:50:46","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e7%ae%80%e7%ba%a6%e6%a8%a1%e5%9e%8b\/"},"modified":"2023-07-27T21:50:46","modified_gmt":"2023-07-27T21:50:46","slug":"%e7%ae%80%e7%ba%a6%e6%a8%a1%e5%9e%8b","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e7%ae%80%e7%ba%a6%e6%a8%a1%e5%9e%8b\/","title":{"rendered":"\u4ec0\u4e48\u662f\u7b80\u7ea6\u6a21\u578b\uff1f"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>\u7b80\u7ea6\u6a21\u578b<\/strong>\u662f\u4f7f\u7528\u5c3d\u53ef\u80fd\u5c11\u7684<a href=\"https:\/\/statorials.org\/cn\/\u53d8\u91cf\u89e3\u91ca\u6027\u53cd\u5e94\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u89e3\u91ca\u53d8\u91cf<\/a>\u6765\u8fbe\u5230\u6240\u9700\u62df\u5408\u6c34\u5e73\u7684\u6a21\u578b\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6b64\u7c7b\u6a21\u578b\u80cc\u540e\u7684\u63a8\u7406\u6e90\u4e8e <a href=\"https:\/\/en.wikipedia.org\/wiki\/Occam%27s_razor\" target=\"_blank\" rel=\"noopener noreferrer\">\u5965\u5361\u59c6\u5243\u5200\u7684<\/a>\u601d\u60f3\uff08\u6709\u65f6\u79f0\u4e3a\u201c\u7b80\u7ea6\u539f\u5219\u201d\uff09\uff0c\u8be5\u601d\u60f3\u8ba4\u4e3a\u6700\u7b80\u5355\u7684\u89e3\u91ca\u53ef\u80fd\u662f\u6b63\u786e\u7684\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5e94\u7528\u4e8e\u7edf\u8ba1\u5b66\u65f6\uff0c\u53c2\u6570\u8f83\u5c11\u4f46\u62df\u5408\u7a0b\u5ea6\u4ee4\u4eba\u6ee1\u610f\u7684\u6a21\u578b\u5e94\u8be5\u4f18\u4e8e\u53c2\u6570\u8f83\u591a\u4e14\u62df\u5408\u7a0b\u5ea6\u7a0d\u9ad8\u7684\u6a21\u578b\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6709\u4e24\u4e2a\u539f\u56e0\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1.\u7b80\u7ea6\u6a21\u578b\u66f4\u5bb9\u6613\u89e3\u91ca\u548c\u7406\u89e3\u3002<\/strong>\u53c2\u6570\u8f83\u5c11\u7684\u6a21\u578b\u66f4\u5bb9\u6613\u7406\u89e3\u548c\u89e3\u91ca\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2. \u7b80\u7ea6\u6a21\u578b\u5f80\u5f80\u5177\u6709\u66f4\u5f3a\u7684\u9884\u6d4b\u80fd\u529b\u3002<\/strong>\u53c2\u6570\u8f83\u5c11\u7684\u6a21\u578b\u5728\u5e94\u7528\u4e8e\u65b0\u6570\u636e\u65f6\u5f80\u5f80\u8868\u73b0\u66f4\u597d\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u8003\u8651\u4ee5\u4e0b\u4e24\u4e2a\u4f8b\u5b50\u6765\u8bf4\u660e\u8fd9\u4e9b\u60f3\u6cd5\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u793a\u4f8b 1\uff1a\u7b80\u7ea6\u6a21\u578b = \u6613\u4e8e\u89e3\u91ca<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u5047\u8bbe\u6211\u4eec\u60f3\u8981\u4f7f\u7528\u4e00\u7ec4\u4e0e\u623f\u5730\u4ea7\u76f8\u5173\u7684\u89e3\u91ca\u53d8\u91cf\u6784\u5efa\u4e00\u4e2a\u6a21\u578b\u6765\u9884\u6d4b\u623f\u5730\u4ea7\u4ef7\u683c\u3002\u8003\u8651\u4ee5\u4e0b\u4e24\u4e2a\u6a21\u578b\u53ca\u5176\u8c03\u6574\u540e\u7684 R \u5e73\u65b9\uff1a<br \/><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u578b\u53f71\uff1a<\/strong><\/span><\/p>\n<ul>\n<li><span style=\"color: #000000;\"><strong>\u516c\u5f0f\uff1a<\/strong>\u623f\u4ef7 = 8,830 + 81*(\u5e73\u65b9\u82f1\u5c3a)<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>\u8c03\u6574\u540e\u7684<sup>R2<\/sup> \uff1a<\/strong> 0.7734<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\"><strong>\u578b\u53f72\uff1a<\/strong><\/span><\/p>\n<ul>\n<li><span style=\"color: #000000;\"><strong>\u516c\u5f0f\uff1a<\/strong>\u623f\u4ef7 = 8,921 + 77*\uff08\u5e73\u65b9\u82f1\u5c3a\uff09+ 7*\uff08\u5e73\u65b9\u82f1\u5c3a\uff09 <sup>2<\/sup> \u2013 9*\uff08\u5e74\u9f84\uff09+ 600*\uff08\u5367\u5ba4\uff09+ 38*\uff08\u6d74\u5ba4\uff09<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>\u8c03\u6574\u540e\u7684<sup>R2<\/sup> \uff1a<\/strong> 0.7823<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u7b2c\u4e00\u4e2a\u6a21\u578b\u53ea\u6709\u4e00\u4e2a\u89e3\u91ca\u53d8\u91cf\uff0c\u8c03\u6574\u540e\u7684<sup>R2<\/sup>\u4e3a 0.7734\uff0c\u800c\u7b2c\u4e8c\u4e2a\u6a21\u578b\u6709\u4e94\u4e2a\u89e3\u91ca\u53d8\u91cf\uff0c\u8c03\u6574\u540e\u7684<sup>R2<\/sup>\u7565\u9ad8\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u57fa\u4e8e\u7b80\u7ea6\u539f\u5219\uff0c\u6211\u4eec\u66f4\u503e\u5411\u4e8e\u4f7f\u7528\u7b2c\u4e00\u4e2a\u6a21\u578b\uff0c\u56e0\u4e3a\u6bcf\u4e2a\u6a21\u578b\u5bf9\u623f\u4ef7\u53d8\u5316\u7684\u89e3\u91ca\u80fd\u529b\u5927\u81f4\u76f8\u540c\uff0c\u4f46\u7b2c\u4e00\u4e2a\u6a21\u578b<em>\u66f4<\/em>\u5bb9\u6613\u7406\u89e3\u548c\u89e3\u91ca\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4f8b\u5982\uff0c\u5728\u7b2c\u4e00\u4e2a\u6a21\u578b\u4e2d\uff0c\u6211\u4eec\u77e5\u9053\u623f\u5c4b\u9762\u79ef\u589e\u52a0\u4e00\u4e2a\u5355\u4f4d\u4e0e\u5e73\u5747\u623f\u4ef7\u4e0a\u6da8 81 \u7f8e\u5143\u76f8\u5173\u3002\u5f88\u5bb9\u6613\u7406\u89e3\u548c\u89e3\u91ca\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u7136\u800c\uff0c\u5728\u7b2c\u4e8c\u4e2a\u793a\u4f8b\u4e2d\uff0c\u7cfb\u6570\u4f30\u8ba1\u503c\u66f4\u96be\u4ee5\u89e3\u91ca\u3002\u4f8b\u5982\uff0c\u5047\u8bbe\u9762\u79ef\u3001\u623f\u5c4b\u5e74\u9f84\u548c\u6d74\u5ba4\u6570\u91cf\u4fdd\u6301\u4e0d\u53d8\uff0c\u623f\u5c4b\u4e2d\u589e\u52a0\u4e00\u4e2a\u623f\u95f4\u4e0e\u623f\u4ef7\u5e73\u5747\u4e0a\u6da8 600 \u7f8e\u5143\u76f8\u5173\u3002\u7406\u89e3\u548c\u89e3\u91ca\u8981\u56f0\u96be\u5f97\u591a\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u793a\u4f8b 2\uff1a\u7b80\u7ea6\u6a21\u578b = \u66f4\u597d\u7684\u9884\u6d4b<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u7b80\u7ea6\u6a21\u578b\u8fd8\u503e\u5411\u4e8e\u5bf9\u65b0\u6570\u636e\u96c6\u505a\u51fa\u66f4\u51c6\u786e\u7684\u9884\u6d4b\uff0c\u56e0\u4e3a\u5b83\u4eec\u4e0d\u592a\u53ef\u80fd<em><a href=\"https:\/\/statorials.org\/cn\/\u673a\u5668\u5b66\u4e60\u8fc7\u5ea6\u62df\u5408\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u8fc7\u5ea6\u62df\u5408<\/a><\/em>\u539f\u59cb\u6570\u636e\u96c6\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4e00\u822c\u6765\u8bf4\uff0c\u53c2\u6570\u8f83\u591a\u7684\u6a21\u578b\u4f1a\u6bd4\u53c2\u6570\u8f83\u5c11\u7684\u6a21\u578b\u4ea7\u751f\u66f4\u7d27\u7684\u62df\u5408\u548c\u66f4\u9ad8\u7684 R <sup>2<\/sup>\u503c\u3002\u4e0d\u5e78\u7684\u662f\uff0c\u5728\u6a21\u578b\u4e2d\u5305\u542b\u592a\u591a\u53c2\u6570\u53ef\u80fd\u4f1a\u5bfc\u81f4\u6a21\u578b\u6839\u636e\u6570\u636e\u7684\u566a\u58f0\uff08\u6216\u201c\u968f\u673a\u6027\u201d\uff09\u8fdb\u884c\u8c03\u6574\uff0c\u800c\u4e0d\u662f\u89e3\u91ca\u53d8\u91cf\u4e4b\u95f4\u771f\u6b63\u7684\u6f5c\u5728\u5173\u7cfb\u3002\u548c\u54cd\u5e94\u53d8\u91cf\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u8fd9\u610f\u5473\u7740\u4e0e\u53c2\u6570\u8f83\u5c11\u7684\u7b80\u5355\u6a21\u578b\u76f8\u6bd4\uff0c\u5177\u6709\u8bb8\u591a\u53c2\u6570\u7684\u975e\u5e38\u590d\u6742\u7684\u6a21\u578b\u53ef\u80fd\u5728\u4ee5\u524d\u4ece\u672a\u89c1\u8fc7\u7684\u65b0\u6570\u636e\u96c6\u4e0a\u8868\u73b0\u4e0d\u4f73\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u5982\u4f55\u9009\u62e9\u7b80\u7ea6\u578b\u53f7<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u53ef\u80fd\u6709\u4e00\u6574\u95e8\u8bfe\u7a0b\u4e13\u95e8\u8ba8\u8bba<strong>\u6a21\u578b\u9009\u62e9<\/strong>\u7684\u4e3b\u9898\uff0c\u4f46\u672c\u8d28\u4e0a\uff0c\u9009\u62e9\u7b80\u7ea6\u6a21\u578b\u610f\u5473\u7740\u9009\u62e9\u6839\u636e\u6307\u6807\u8868\u73b0\u6700\u4f73\u7684\u6a21\u578b\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6839\u636e\u6a21\u578b\u5728\u8bad\u7ec3\u6570\u636e\u96c6\u4e0a\u7684\u6027\u80fd<em>\u53ca\u5176<\/em>\u53c2\u6570\u6570\u91cf\u6765\u8bc4\u4f30\u6a21\u578b\u7684\u5e38\u7528\u6307\u6807\u5305\u62ec\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. \u8d64\u6c60\u4fe1\u606f\u51c6\u5219\uff08AIC\uff09<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u6a21\u578b\u7684 AIC \u53ef\u4ee5\u8ba1\u7b97\u5982\u4e0b\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>AIC = -2\/n * LL + 2 * k\/n<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u91d1\u5b50\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>n\uff1a<\/strong>\u8bad\u7ec3\u6570\u636e\u96c6\u4e2d\u7684\u89c2\u6d4b\u503c\u6570\u91cf\u3002<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>LL\uff1a<\/strong>\u8bad\u7ec3\u6570\u636e\u96c6\u4e0a\u6a21\u578b\u7684\u5bf9\u6570\u4f3c\u7136\u3002<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>k\uff1a<\/strong>\u6a21\u578b\u4e2d\u53c2\u6570\u7684\u6570\u91cf\u3002<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u4f7f\u7528\u8fd9\u79cd\u65b9\u6cd5\uff0c\u60a8\u53ef\u4ee5\u8ba1\u7b97\u6bcf\u4e2a\u6a21\u578b\u7684AIC\uff0c\u7136\u540e\u9009\u62e9AIC\u503c\u6700\u4f4e\u7684\u6a21\u578b\u4f5c\u4e3a\u6700\u4f73\u6a21\u578b\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4e0e\u4e0b\u4e00\u79cd\u65b9\u6cd5 BIC \u76f8\u6bd4\uff0c\u8fd9\u79cd\u65b9\u6cd5\u503e\u5411\u4e8e\u66f4\u590d\u6742\u7684\u6a21\u578b\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2.\u8d1d\u53f6\u65af\u4fe1\u606f\u51c6\u5219\uff08BIC\uff09<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u6a21\u578b\u7684 BIC \u53ef\u4ee5\u8ba1\u7b97\u5982\u4e0b\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>BIC = -2 * LL + log(n) * k<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u91d1\u5b50\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>n\uff1a<\/strong>\u8bad\u7ec3\u6570\u636e\u96c6\u4e2d\u7684\u89c2\u6d4b\u503c\u6570\u91cf\u3002<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>log\uff1a<\/strong>\u81ea\u7136\u5bf9\u6570\uff08\u4ee5 e \u4e3a\u5e95\uff09<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>LL\uff1a<\/strong>\u8bad\u7ec3\u6570\u636e\u96c6\u4e0a\u6a21\u578b\u7684\u5bf9\u6570\u4f3c\u7136\u3002<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>k\uff1a<\/strong>\u6a21\u578b\u4e2d\u53c2\u6570\u7684\u6570\u91cf\u3002<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u4f7f\u7528\u6b64\u65b9\u6cd5\uff0c\u60a8\u53ef\u4ee5\u8ba1\u7b97\u6bcf\u4e2a\u6a21\u578b\u7684 BIC\uff0c\u7136\u540e\u9009\u62e9 BIC \u503c\u6700\u4f4e\u7684\u6a21\u578b\u4f5c\u4e3a\u6700\u4f73\u6a21\u578b\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4e0e AIC \u65b9\u6cd5\u76f8\u6bd4\uff0c\u8fd9\u79cd\u65b9\u6cd5\u503e\u5411\u4e8e\u4f7f\u7528\u53c2\u6570\u8f83\u5c11\u7684\u6a21\u578b\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>3. \u6700\u5c0f\u63cf\u8ff0\u957f\u5ea6\uff08MDL\uff09<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">MDL \u662f\u4e00\u79cd\u8bc4\u4f30\u4fe1\u606f\u8bba\u9886\u57df\u6a21\u578b\u7684\u65b9\u6cd5\u3002\u53ef\u4ee5\u6309\u4e0b\u5f0f\u8ba1\u7b97\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>MDL = L(h) + L(D | h)<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u91d1\u5b50\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>h\uff1a<\/strong>\u6a21\u578b\u3002<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>D\uff1a<\/strong>\u6a21\u578b\u505a\u51fa\u7684\u9884\u6d4b\u3002<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>L(h)\uff1a<\/strong>\u8868\u793a\u6a21\u578b\u6240\u9700\u7684\u4f4d\u6570\u3002<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>L(D | h)\uff1a<\/strong>\u8868\u793a\u6a21\u578b\u5bf9\u8bad\u7ec3\u6570\u636e\u7684\u9884\u6d4b\u6240\u9700\u7684\u4f4d\u6570\u3002<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u4f7f\u7528\u8fd9\u79cd\u65b9\u6cd5\uff0c\u60a8\u53ef\u4ee5\u8ba1\u7b97\u6bcf\u4e2a\u6a21\u578b\u7684MDL\uff0c\u7136\u540e\u9009\u62e9MDL\u503c\u6700\u4f4e\u7684\u6a21\u578b\u4f5c\u4e3a\u6700\u4f73\u6a21\u578b\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6839\u636e\u60a8\u6b63\u5728\u5904\u7406\u7684\u95ee\u9898\u7c7b\u578b\uff0c\u5728\u9009\u62e9\u7b80\u7ea6\u6a21\u578b\u65f6\uff0c\u53ef\u80fd\u4f1a\u4f18\u5148\u9009\u62e9\u5176\u4e2d\u4e00\u79cd\u65b9\u6cd5\uff08AIC\u3001BIC \u6216 MDL\uff09\u3002<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u7b80\u7ea6\u6a21\u578b\u662f\u4f7f\u7528\u5c3d\u53ef\u80fd\u5c11\u7684\u89e3\u91ca\u53d8\u91cf\u6765\u8fbe\u5230\u6240\u9700\u62df\u5408\u6c34\u5e73\u7684\u6a21\u578b\u3002 \u6b64\u7c7b\u6a21\u578b\u80cc\u540e\u7684\u63a8\u7406\u6e90\u4e8e \u5965\u5361\u59c6\u5243\u5200\u7684\u601d\u60f3\uff08\u6709\u65f6\u79f0\u4e3a [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-1036","post","type-post","status-publish","format-standard","hentry","category-11"],"yoast_head":"<!-- This site is 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