{"id":589,"date":"2023-07-29T09:51:50","date_gmt":"2023-07-29T09:51:50","guid":{"rendered":"https:\/\/statorials.org\/ja\/%e3%83%98%e3%82%99%e3%83%b3%e3%82%b7%e3%82%99%e3%83%a3%e3%83%9f%e3%83%8b%e3%83%bb%e3%83%9b%e3%83%83%e3%83%9b%e3%83%98%e3%82%99%e3%83%ab%e3%82%af%e3%82%99%e6%89%8b%e8%a1%93\/"},"modified":"2023-07-29T09:51:50","modified_gmt":"2023-07-29T09:51:50","slug":"%e3%83%98%e3%82%99%e3%83%b3%e3%82%b7%e3%82%99%e3%83%a3%e3%83%9f%e3%83%8b%e3%83%bb%e3%83%9b%e3%83%83%e3%83%9b%e3%83%98%e3%82%99%e3%83%ab%e3%82%af%e3%82%99%e6%89%8b%e8%a1%93","status":"publish","type":"post","link":"https:\/\/statorials.org\/ja\/%e3%83%98%e3%82%99%e3%83%b3%e3%82%b7%e3%82%99%e3%83%a3%e3%83%9f%e3%83%8b%e3%83%bb%e3%83%9b%e3%83%83%e3%83%9b%e3%83%98%e3%82%99%e3%83%ab%e3%82%af%e3%82%99%e6%89%8b%e8%a1%93\/","title":{"rendered":"Benjamini-hochberg \u624b\u9806\u306e\u30ac\u30a4\u30c9"},"content":{"rendered":"

<\/p>\n

\n

\u7d71\u8a08\u691c\u5b9a\u3092\u5b9f\u884c\u3059\u308b\u3068\u3001\u305f\u3068\u3048\u5e30\u7121\u4eee\u8aac\u304c\u6b63\u3057\u3044\u5834\u5408\u3067\u3082\u3001\u307e\u3063\u305f\u304f\u306e\u5076\u7136\u3067 0.05 \u672a\u6e80\u306e p \u5024\u304c\u5f97\u3089\u308c\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002<\/span><\/p>\n

\u305f\u3068\u3048\u3070\u3001\u7279\u5b9a\u306e\u690d\u7269\u306e\u5e73\u5747\u9ad8\u3055\u304c 10 \u30a4\u30f3\u30c1\u3092\u8d85\u3048\u308b\u304b\u3069\u3046\u304b\u3092\u77e5\u308a\u305f\u3044\u3068\u3057\u307e\u3059\u3002\u30c6\u30b9\u30c8\u7528\u306e\u5e30\u7121\u4eee\u8aac\u3068\u5bfe\u7acb\u4eee\u8aac\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/span><\/p>\n

H 0<\/sub> :<\/strong> \u03bc = 10 \u30a4\u30f3\u30c1<\/span><\/p>\n

H A<\/sub> :<\/strong> \u03bc > 10 \u30a4\u30f3\u30c1<\/span><\/p>\n

\u3053\u306e\u4eee\u8aac\u3092\u691c\u8a3c\u3059\u308b\u306b\u306f\u3001\u5916\u51fa\u3057\u3066 20 \u500b\u306e\u690d\u7269\u306e \u7121\u4f5c\u70ba\u30b5\u30f3\u30d7\u30eb\u3092<\/a>\u53ce\u96c6\u3057\u3066\u6e2c\u5b9a\u3057\u307e\u3059\u3002\u3053\u306e\u690d\u7269\u7a2e\u306e\u5b9f\u969b\u306e\u5e73\u5747\u9ad8\u3055\u306f 10 \u30a4\u30f3\u30c1\u3067\u3059\u304c\u300120 \u500b\u306e\u7570\u5e38\u306b\u9ad8\u3044\u690d\u7269\u306e\u30b5\u30f3\u30d7\u30eb\u3092\u9078\u629e\u3057\u305f\u305f\u3081\u3001\u5e30\u7121\u4eee\u8aac\u304c\u68c4\u5374\u3055\u308c\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002<\/span><\/p>\n

\u305f\u3068\u3048\u5e30\u7121\u4eee\u8aac\u304c\u771f\u5b9f\u3060\u3063\u305f\u3068\u3057\u3066\u3082 (\u3053\u306e\u690d\u7269\u306e\u5e73\u5747\u9ad8\u3055\u306f\u5b9f\u969b\u306b\u306f 10 \u30a4\u30f3\u30c1\u3067\u3057\u305f)\u3001\u3042\u306a\u305f\u306f\u305d\u308c\u3092\u68c4\u5374\u3057\u307e\u3057\u305f\u3002\u7d71\u8a08\u3067\u306f\u3001\u3053\u308c\u3092\u300c\u8aa4\u3063\u305f\u767a\u898b\u300d\u3068\u547c\u3073\u307e\u3059\u3002\u3042\u306a\u305f\u306f\u300c\u91cd\u5927\u306a\u7d50\u679c\u300d\u3092\u767a\u898b\u3057\u305f\u3068\u4e3b\u5f35\u3057\u3066\u3044\u307e\u3059\u304c\u3001\u3053\u308c\u306f\u5b9f\u969b\u306b\u306f\u8aa4\u308a\u3067\u3059\u3002<\/span><\/p>\n

\u3053\u3053\u3067\u3001100 \u500b\u306e\u7d71\u8a08\u30c6\u30b9\u30c8\u3092\u4e00\u5ea6\u306b\u5b9f\u884c\u3059\u308b\u3053\u3068\u3092\u60f3\u50cf\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u30a2\u30eb\u30d5\u30a1 \u30ec\u30d9\u30eb<\/a>0.05 \u3092\u4f7f\u7528\u3059\u308b\u3068\u3001\u500b\u3005\u306e\u30c6\u30b9\u30c8\u3067\u8aa4\u3063\u305f\u691c\u51fa\u304c\u884c\u308f\u308c\u308b\u53ef\u80fd\u6027\u306f 5% \u306e\u307f\u3067\u3059\u304c\u3001\u975e\u5e38\u306b\u591a\u304f\u306e\u30c6\u30b9\u30c8\u3092\u5b9f\u884c\u3057\u3066\u3044\u308b\u305f\u3081\u3001\u8aa4\u3063\u305f\u691c\u51fa\u306b\u3064\u306a\u304c\u308b\u306e\u306f 100 \u4ef6\u4e2d 5 \u4ef6\u306e\u307f\u3067\u3042\u308b\u3068\u4e88\u60f3\u3055\u308c\u307e\u3059\u3002<\/span><\/p>\n

\u73fe\u4ee3\u4e16\u754c\u3067\u306f\u3001\u6280\u8853\u306e\u9032\u6b69\u306b\u3088\u308a\u3001\u7814\u7a76\u8005\u306f\u4e00\u5ea6\u306b\u4f55\u767e\u3001\u5834\u5408\u306b\u3088\u3063\u3066\u306f\u4f55\u5343\u3082\u306e\u7d71\u8a08\u7684\u30c6\u30b9\u30c8\u3092\u5b9f\u884c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u3063\u305f\u305f\u3081\u3001\u8aa4\u3063\u305f\u767a\u898b\u304c\u4e00\u822c\u7684\u306a\u554f\u984c\u3068\u306a\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002<\/span><\/p>\n

\u305f\u3068\u3048\u3070\u3001\u533b\u5b66\u7814\u7a76\u8005\u306f\u3001\u4e00\u5ea6\u306b\u6570\u4e07\u306e\u907a\u4f1d\u5b50\u306b\u5bfe\u3057\u3066\u7d71\u8a08\u7684\u691c\u67fb\u3092\u5b9f\u884c\u3067\u304d\u307e\u3059\u3002\u8aa4\u691c\u51fa\u7387\u304c\u308f\u305a\u304b 5% \u3067\u3042\u3063\u3066\u3082\u3001\u4f55\u767e\u56de\u3082\u306e\u30c6\u30b9\u30c8\u3067\u8aa4\u691c\u51fa\u304c\u751f\u3058\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002<\/span><\/p>\n

\u8aa4\u691c\u51fa\u7387\u3092\u5236\u5fa1\u3059\u308b 1 \u3064\u306e\u65b9\u6cd5\u306f\u3001\u3044\u308f\u3086\u308bBenjamini-Hochberg \u624b\u9806\u3092\u4f7f\u7528\u3059\u308b\u3053\u3068\u3067\u3059\u3002<\/strong><\/span><\/p>\n

\u30d9\u30f3\u30b8\u30e3\u30df\u30cb\u30fb\u30db\u30c3\u30db\u30d9\u30eb\u30b0\u6cd5<\/strong><\/span><\/h2>\n

Benjamini-Hochberg \u624b\u9806\u306f<\/strong>\u6b21\u306e\u3088\u3046\u306b\u6a5f\u80fd\u3057\u307e\u3059\u3002<\/span><\/p>\n

\u30b9\u30c6\u30c3\u30d7 1:<\/strong>\u3059\u3079\u3066\u306e\u7d71\u8a08\u691c\u5b9a\u3092\u5b9f\u884c\u3057\u3001\u5404\u691c\u5b9a\u306e p \u5024\u3092\u898b\u3064\u3051\u307e\u3059\u3002<\/span><\/p>\n

\u30b9\u30c6\u30c3\u30d7 2:<\/strong> p \u5024\u3092\u964d\u9806\u3067\u30e9\u30f3\u30af\u4ed8\u3051\u3057\u3001\u305d\u308c\u305e\u308c\u306b\u30e9\u30f3\u30af\u3092\u5272\u308a\u5f53\u3066\u307e\u3059\u3002\u6700\u3082\u5c0f\u3055\u3044\u5024\u306e\u30e9\u30f3\u30af\u306f 1\u3001\u6b21\u306b\u5c0f\u3055\u3044\u5024\u306e\u30e9\u30f3\u30af\u306f 2 \u306a\u3069\u306b\u306a\u308a\u307e\u3059\u3002<\/span><\/p>\n

\u30b9\u30c6\u30c3\u30d7 3:<\/strong>\u5f0f(i\/m)*Q<\/em>\u3092\u4f7f\u7528\u3057\u3066\u3001\u5404 p \u5024\u306e\u81e8\u754c\u30d9\u30f3\u30b8\u30e3\u30df\u30cb\u30fb\u30db\u30c3\u30db\u30d9\u30eb\u30b0\u5024\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/span><\/p>\n

\u91d1\uff1a<\/span><\/p>\n

i<\/em> = p \u5024\u306e\u30e9\u30f3\u30af<\/span><\/p>\n

m<\/em> = \u30c6\u30b9\u30c8\u306e\u7dcf\u6570<\/span><\/p>\n

Q<\/em> = \u9078\u629e\u3057\u305f\u8aa4\u691c\u51fa\u7387<\/span><\/p>\n

\u30b9\u30c6\u30c3\u30d7 4: \u81e8\u754c\u5024\u672a\u6e80\u306e\u6700\u5927\u306e p \u5024\u3092\u898b\u3064\u3051\u307e\u3059\u3002\u3053\u306e p \u5024\u3088\u308a\u5c0f\u3055\u3044\u5404 p \u5024\u3092\u6709\u610f\u306a\u3082\u306e\u3068\u3057\u3066\u6307\u5b9a\u3057\u307e\u3059\u3002<\/strong><\/span><\/p>\n

\u6b21\u306e\u4f8b\u306f\u3001\u5177\u4f53\u7684\u306a\u5024\u3092\u4f7f\u7528\u3057\u3066\u3053\u306e\u624b\u9806\u3092\u5b9f\u884c\u3059\u308b\u65b9\u6cd5\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002<\/span><\/p>\n

\u4f8b<\/strong><\/span><\/h2>\n

\u7814\u7a76\u8005\u304c 20 \u306e\u7570\u306a\u308b\u5909\u6570\u304c\u5fc3\u81d3\u75c5\u306b\u95a2\u9023\u3057\u3066\u3044\u308b\u304b\u3069\u3046\u304b\u3092\u5224\u65ad\u3057\u305f\u3044\u3068\u3057\u307e\u3059\u3002\u4e00\u5ea6\u306b 20 \u500b\u306e\u500b\u5225\u306e\u7d71\u8a08\u691c\u5b9a\u3092\u5b9f\u884c\u3057\u3001\u5404\u691c\u5b9a\u306e p \u5024\u3092\u53d7\u3051\u53d6\u308a\u307e\u3059\u3002\u6b21\u306e\u8868\u306f\u3001\u5404\u30c6\u30b9\u30c8\u306e p \u5024\u3092\u964d\u9806\u306b\u793a\u3057\u3066\u3044\u307e\u3059\u3002<\/span> <\/p>\n

\"Benjamini-Hochberg<\/p>\n

\u7814\u7a76\u8005\u304c\u8aa4\u767a\u898b\u7387 20% \u3092\u559c\u3093\u3067\u53d7\u3051\u5165\u308c\u308b\u3068\u4eee\u5b9a\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u5404 p \u5024\u306e\u81e8\u754c Benjamini-Hochberg \u5024\u3092\u8a08\u7b97\u3059\u308b\u306b\u306f\u3001\u6b21\u306e\u5f0f\u3092\u4f7f\u7528\u3067\u304d\u307e\u3059: (i\/20)*0.2 \u3053\u3053\u3067\u3001 i<\/em> = p \u5024\u306e\u30e9\u30f3\u30af\u3002<\/span><\/p>\n

\u6b21\u306e\u8868\u306f\u3001\u500b\u3005\u306e p \u5024\u306b\u5bfe\u3059\u308b\u81e8\u754c Benjamini-Hochberg \u5024\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002<\/span> <\/p>\n

\"Benjamini-Hochberg<\/p>\n

Benjamini-Hochberg \u81e8\u754c\u5024\u3092\u4e0b\u56de\u308b\u6700\u5927\u306e p \u5024\u3092\u6301\u3064\u691c\u5b9a\u306f\u5909\u6570 #11 \u3067\u3001p \u5024\u306f 0.039\u3001BH \u81e8\u754c\u5024\u306f 0.040 \u3067\u3059\u3002<\/span><\/p>\n

\u3057\u305f\u304c\u3063\u3066\u3001\u3053\u306e\u691c\u5b9a\u3068\u3001p \u5024\u304c\u5c0f\u3055\u3044\u3059\u3079\u3066\u306e\u691c\u5b9a\u306f\u6709\u610f\u3067\u3042\u308b\u3068\u307f\u306a\u3055\u308c\u307e\u3059\u3002<\/span> <\/p>\n

\"Bejamini-Hochberg<\/p>\n

\u5909\u6570 #17 \u3068 #3 \u306e p \u5024\u306f BH \u81e8\u754c\u5024\u3088\u308a\u3082\u5c0f\u3055\u304f\u3042\u308a\u307e\u305b\u3093\u3067\u3057\u305f\u304c\u3001\u5909\u6570 #11 \u3088\u308a\u3082 p \u5024\u304c\u5c0f\u3055\u3044\u305f\u3081\u3001\u4f9d\u7136\u3068\u3057\u3066\u6709\u610f\u3067\u3042\u308b\u3068\u307f\u306a\u3055\u308c\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/span><\/p>\n

\u8aa4\u691c\u51fa\u7387\u306e\u9078\u3073\u65b9<\/strong><\/span><\/h3>\n

Benjamini-Hochberg \u624b\u9806\u3067\u6700\u3082\u91cd\u8981\u306a\u624b\u9806\u306e 1 \u3064\u306f\u3001\u8aa4\u691c\u51fa\u7387\u3092\u9078\u629e\u3059\u308b\u3053\u3068\u3067\u3059\u3002\u30c7\u30fc\u30bf\u3092\u53ce\u96c6\u3057\u305f\u308a\u7d71\u8a08\u30c6\u30b9\u30c8\u3092\u5b9f\u884c\u3057\u305f\u308a\u3059\u308b\u524d\u306b\u3001\u8aa4\u691c\u51fa\u7387\u3092\u9078\u629e\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/span><\/p>\n

\u901a\u5e38\u3001\u5206\u6790\u306e\u63a2\u7d22\u6bb5\u968e\u3067\u306f\u591a\u6570\u306e\u7d71\u8a08\u30c6\u30b9\u30c8\u3092\u5b9f\u884c\u3057\u3001\u305d\u306e\u5f8c\u3001\u4ed6\u306e\u30c6\u30b9\u30c8\u3092\u5b9f\u884c\u3057\u3066\u7d50\u679c\u3092\u3055\u3089\u306b\u8abf\u67fb\u3057\u307e\u3059\u3002<\/span><\/p>\n

\u30d5\u30a9\u30ed\u30fc\u30a2\u30c3\u30d7 \u30c6\u30b9\u30c8\u306e\u30b3\u30b9\u30c8\u304c\u4f4e\u3044\u5834\u5408\u306f\u3001\u8aa4\u691c\u51fa\u7387\u3092\u9ad8\u304f\u8a2d\u5b9a\u3059\u308b\u3053\u3068\u3092\u691c\u8a0e\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u305f\u3068\u3048\u5c11\u6570\u306e\u8aa4\u691c\u51fa\u304c\u3042\u3063\u305f\u3068\u3057\u3066\u3082\u3001\u305d\u306e\u5f8c\u306e\u30c6\u30b9\u30c8\u3067\u305d\u308c\u3089\u306e\u8aa4\u691c\u51fa\u304c\u691c\u51fa\u3055\u308c\u308b\u53ef\u80fd\u6027\u304c\u9ad8\u3044\u304b\u3089\u3067\u3059\u3002<\/span><\/p>\n

\u3055\u3089\u306b\u3001\u91cd\u8981\u306a\u767a\u898b\u3092\u898b\u9003\u3059\u30b3\u30b9\u30c8\u304c\u9ad8\u3044\u5834\u5408\u306f\u3001\u91cd\u8981\u306a\u3082\u306e\u3092\u898b\u9003\u3055\u306a\u3044\u3088\u3046\u306b\u8aa4\u767a\u898b\u7387\u3092\u9ad8\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/span><\/p>\n

\u7814\u7a76\u306e\u30b3\u30b9\u30c8\u3068\u3001\u91cd\u8981\u306a\u767a\u898b\u3092\u898b\u9003\u3055\u306a\u3044\u3053\u3068\u306e\u91cd\u8981\u6027\u306b\u5fdc\u3058\u3066\u3001\u8aa4\u691c\u51fa\u7387\u306f\u72b6\u6cc1\u306b\u3088\u3063\u3066\u7570\u306a\u308a\u307e\u3059\u3002<\/span><\/p>\n

\u8ffd\u52a0\u30ea\u30bd\u30fc\u30b9<\/strong><\/span><\/h3>\n

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