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\u6709\u610f\u691c\u5b9a<\/strong><\/p>\n\n\n\n

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    \n
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    \u7d05\u8336\u3068\u6709\u610f\u691c\u5b9a\u306e\u8a71\u306f\u30d5\u30a3\u30c3\u30b7\u30e3\u30fc\u304c1935\u5e74\u306b\u51fa\u7248\u3057\u305f\u300e\u5b9f\u9a13\u306e\u30c7\u30b6\u30a4\u30f3\uff08The Design of Experiments\uff09\u300f\u306e\u7b2c\u4e8c\u7ae0\u306b\u51fa\u3066\u304f\u308b\u3002\u3069\u306e\u3088\u3046\u306b\u3057\u3066\u4eee\u8aac\u3092\u691c\u8a3c\u3059\u308b\u305f\u3081\u306e\u5b9f\u9a13\u3092\u884c\u3046\u304b\u3092\u30d5\u30a3\u30c3\u30b7\u30e3\u30fc\u306f\u8ad6\u3058\u305f\u306e\u3060\u3002\u3057\u304b\u3057\u6709\u610f\u691c\u5b9a\u306e\u4e00\u3064\u306e\u554f\u984c\u306f\u307e\u3055\u306b\u5b9f\u9a13\u30c7\u30b6\u30a4\u30f3\u306b\u95a2\u308f\u308b\u554f\u984c\u3067\u3042\u308b\uff08\u3053\u306e\u6307\u6458\u306f\u30cf\u30ed\u30eb\u30c9\u30fb\u30b8\u30a7\u30d5\u30ea\u30fc\u30ba\u3001J.B.S. \u30db\u30fc\u30eb\u30c7\u30f3\u3001\u30c7\u30cb\u30b9\u30fb\u30ea\u30f3\u30c9\u30ea\u30fc\u3042\u305f\u308a\u304b\u3089\u304d\u3066\u3044\u308b\uff09\u3002\u3044\u3064\u3069\u306e\u3088\u3046\u306b\u5b9f\u9a13\u3092\u7d42\u3048\u308b\u306e\u304b\u3068\u3044\u3046\u30eb\u30fc\u30eb\u306e\u3053\u3068\u3092\u30b9\u30c8\u30c3\u30d4\u30f3\u30b0\u30fb\u30eb\u30fc\u30eb<\/a>\u3068\u547c\u3076\u3002\u554f\u984c\u306f\u3069\u306e\u3088\u3046\u306a\u30b9\u30c8\u30c3\u30d4\u30f3\u30b0\u30fb\u30eb\u30fc\u30eb\u3092\u63a1\u7528\u3059\u308b\u304b\u3067\u6709\u610f\u304b\u6709\u610f\u3067\u306a\u3044\u304b\u306e\u7d50\u679c\u304c180\u5ea6\u5909\u308f\u3063\u3066\u304d\u3066\u3057\u307e\u3046\u3002<\/p>\n\n\n\n

    I\u30fbJ\u30fb\u30b0\u30c3\u30c9\u304c\u30d9\u30a4\u30ba\u30d5\u30a1\u30af\u30bf\u30fc\u3068\u540d\u4ed8\u3051\u305f\u30d9\u30a4\u30ba\u7684\u624b\u6cd5\u3092\u7528\u3044\u308b\u3068\u30b9\u30c8\u30c3\u30d4\u30f3\u30b0\u30fb\u30eb\u30fc\u30eb\u306e\u554f\u984c\u306f\u56de\u907f\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u3053\u306e\u8fba\u308a\u306e\u8a71\u306f\u300e\u672c\u5f53\u306e\u58f0\u3092\u6c42\u3081\u3066\uff1a\u91ce\u86ee\u306a\u5e38\u8b58\u3092\u7591\u3048\u300f<\/a>\u306b\u66f8\u3044\u3066\u3044\u308b\u3002\u3082\u3061\u308d\u3093\u3053\u308c\u306f\u30d9\u30a4\u30ba\u30d5\u30a1\u30af\u30bf\u30fc\u304c\u4e07\u80fd\u3067\u3042\u308b\u3068\u3044\u3046\u3053\u3068\u3067\u306f\u306a\u3044\u3002\u4e07\u80fd\u306a\u9053\u5177\u306a\u3069\u306a\u3044\u3002\u8981\u306f\u9053\u5177\u3092\u72b6\u6cc1\u306b\u5fdc\u3058\u3066\u4f7f\u3044\u5206\u3051\u308b\u80fd\u529b\u304c\u5fc5\u8981\u306a\u306e\u3060\u3002<\/p>\n\n\n\n

    \uff08\u70b9\uff09\u63a8\u5b9a<\/strong><\/p>\n\n\n\n

    \u56e0\u307f\u306b\u3053\u306e\u3088\u3046\u306a\u6b63\u89e3\u304b\u9593\u9055\u3044\u304b\u3001\u8868\u304b\u88cf\u304b\u3001\u3068\u3044\u3063\u305f\u3088\u3046\u306a\u5206\u5e03\u306f\u4e8c\u9805\u5206\u5e03\u3068\u547c\u3070\u308c\u308b\u304c\u3001\u300c\u30b3\u30a4\u30f3\u306f\u516c\u6b63\u3067\u3042\u308b\uff08\u8868=\u88cf=\u00bd\uff09\u300d\u3068\u304b\u300c\u30df\u30e5\u30ea\u30a8\u30eb\u30fb\u30d6\u30ea\u30b9\u30c8\u30eb\u306f\u9055\u3044\u304c\u308f\u304b\u3089\u306a\u3044\uff08\u5f7c\u5973\u306e\u9078\u629e\u306f\u30e9\u30f3\u30c0\u30e0\u3067\u3042\u308b\uff09\uff08\u6b63\u89e3=\u9593\u9055\u3044=\u00bd\uff09\u300d\u306a\u3069\u3068\u4eee\u8aac\u3092\u8a2d\u5b9a\u3057\u305f\u6642\u306e\u5c24\u5ea6P(O|H)\u3092\u6700\u5927\u5316\u3055\u305b\u308b\u3053\u3068\u306f\u6700\u5927\u5024\uff08\u3082\u3057\u304f\u306f\u6700\u5c0f\u5024\uff09\u3092\u63a2\u3059\u3053\u3068\u306b\u7b49\u3057\u3044\u3002\u3053\u306e\u3088\u3046\u306a\u5358\u7d14\u306a\u5834\u5408\u306f\u56f3\u3092\u307f\u308c\u3070\u4e00\u76ee\u77ad\u7136\u306a\u306e\u3060\u304c\u3001\u7406\u8ad6\u7684\u306b\u306f\u5206\u5e03\u56f3\u306b\u63a5\u3059\u308b\u7dda\u306e\u50be\u304d\u30920\u306b\u3059\u308b\u4f5c\u696d\u3067\u3042\u308b\uff08\u4e0b\u8a18\u56f3\uff09\u3002\u66f2\u7dda\u306b\u5bfe\u3059\u308b\u63a5\u7dda\u306f\u66f2\u7dda\u306e\u5fae\u5206\u3092\u53d6\u308c\u3070\u826f\u3044\u306e\u3067\u3001\u5fae\u5206\uff1d0\u306b\u306a\u308b\u30dd\u30a4\u30f3\u30c8\u3092\u63a2\u3059\u3053\u3068\u306b\u306a\u308b\u3002\u3053\u308c\u304c\u30d5\u30a3\u30c3\u30b7\u30e3\u30fc\u306e\u8003\u3048\u305f\uff08\u70b9\uff09\u63a8\u5b9a\u3067\u3042\u308a\u3001\u305d\u308c\u306f\u5c24\u5ea6P(O|H)\u3092\u6700\u5927\u5316\u3055\u305b\u308b\u6700\u5927\u5c24\u5ea6\uff08\u4e00\u70b9\uff09\u3092\u6c42\u3081\u308b\u3053\u3068\u306b\u7b49\u3057\u3044\uff08\u3053\u306e\u3088\u3046\u306a\u5358\u7d14\u306a\u5834\u5408\u306b\u306f\u3001\u5fae\u5206\u304c\u4f7f\u3048\u308b\u304c\u3001\u66f2\u7dda\u304c\u8907\u96d1\u306a\u5834\u5408\u306b\u306f\u5c40\u6240\u7684\u306a\u6700\u5927\u5024\u306b\u6355\u307e\u3063\u3066\u3057\u307e\u3046\u3053\u3068\u304c\u3042\u308b\u305f\u3081\u3001\u52fe\u914d\u6cd5\u306a\u3069\u3068\u3044\u3063\u305f\u65b9\u6cd5\u3092\u7528\u3044\u308b\u3002\u3053\u308c\u306f\u5fae\u5206\u306e\u9006\u64cd\u4f5c\u3067\u3042\u308b\u7a4d\u5206\u304c\u96e3\u3057\u3044\u6642\u306b\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u624b\u6cd5\u306a\u3069\u3092\u7528\u3044\u308b\u3053\u3068\u3068\u4f3c\u3066\u3044\u308b\uff09\u3002<\/p>\n\n\n\n

    \"\"<\/figure>\n\n\n\n

    \u56f3\u3092\u898b\u308c\u3070\u3001\u3069\u3053\u3067\u63a5\u7dda\u306e\u50be\u304d\u304c0\u306b\u306a\u308b\u304b\u308f\u304b\u308b\u3002<\/p>\n\n\n\n

    \u4ecan\u56de\u30b3\u30a4\u30f3\u3092\u6295\u3052\u3066k\u56de\u8868\u304c\u51fa\u308b\uff08\u3082\u3057\u304f\u306fn\u56de\u7d05\u8336\u306e\u30c6\u30a4\u30b9\u30c6\u30a3\u30f3\u30b0\u3092\u3057\u3066k\u56de\u6b63\u89e3\u304c\u51fa\u308b\uff09\u78ba\u7387\u306f<\/p>\n\n\n\n

    \\(\\binom{n}{k} p^k (1-p)^{n-k}\\)<\/p>\n\n\n\n

    \u3068\u5b9a\u7fa9\u3067\u304d\u308b\u3002\u5bfe\u6570\uff08log\uff09\u3092\u53d6\u308b\u3068\u639b\u3051\u7b97\u306f\u8db3\u3057\u7b97\u306b\u3001\u301c\u4e57\u306e\u90e8\u5206\u306f\u4fc2\u6570\u3068\u3057\u3066\u524d\u306b\u51fa\u308b\u306e\u3067\u3001<\/p>\n\n\n\n

    \\(\\log \\binom{n}{k} + k \\log p + (n-k) \\log (1-p)\\)<\/p>\n\n\n\n

    \u304c\u5f97\u3089\u308c\u308b\u3002\u3053\u308c\u3092\u5fae\u5206\u3059\u308b\uff08\u5fae\u5206\u306b\u3064\u3044\u3066\u3082\u6642\u9593\u304c\u3042\u308c\u3070\u7c21\u5358\u306a\u89e3\u8aac\u3092\u66f8\u304d\u305f\u3044\uff09\u3002\\(\\binom{n}{k} \\)\u306f\\(\\frac{n!}{k!(n-k)!} \\)\u306a\u306e\u3067\u5b9a\u6570\u3067\u3042\u308a\u3001\u5b9a\u6570\u306f\u5fae\u5206\u3059\u308b\u3068\u6d88\u3048\u308b\u306e\u3067\u6700\u7d42\u7684\u306b\u3001<\/p>\n\n\n\n

    \\( \\frac{d}{dp} \\left[ k \\log p + (n-k) \\log (1-p) \\right]\\)<\/p>\n\n\n\n

    \u3068\u306a\u308b\u3002\u5bfe\u6570\u3092\u5fae\u5206\u3059\u308b\u3068\u3001\u4f55\u5206\u306e1\u3068\u3044\u3046\u5f62\u306b\u306a\u308b\u306e\u3067\u3001<\/p>\n\n\n\n

    \\(\\frac{k}{p} – \\frac{n-k}{1-p} \\cdot (-1)\\)<\/p>\n\n\n\n

    \u304c\u5f97\u3089\u308c\u308b\uff08\u6700\u5f8c\u306b\\(-1\\)\u304c\u51fa\u73fe\u3059\u308b\u306e\u306f\u3001\u9023\u9396\u5f8b\uff08chain rule\uff09\u3068\u547c\u3070\u308c\u308b\u3082\u306e\u306e\u7d50\u679c\u3067\u3001\\(f(x)\\)\u3068\\(g(x)\\)\u3092\u305d\u308c\u305e\u308c\u95a2\u6570\u3068\u3057\u3066\u3001\\(f(x)\\)\u306e\u4e2d\u306b\\(g(x)\\)\u304c\u5165\u3063\u3066\u3044\u308b\uff08\u3053\u306e\u5165\u3063\u3066\u3044\u308b\u3068\u3044\u3046\u306e\u3092nested\u3068\u8a00\u3046\uff09\u3002\\(f(g(x))\\)\u306e\u3088\u3046\u306a\u95a2\u6570\u306e\u3053\u3068\u3092\u5408\u6210\u95a2\u6570\uff08composite function\uff09\u3068\u547c\u3076\u304c\u3001\u5408\u6210\u95a2\u6570\u3092\u5fae\u5206\u3059\u308b\u3068\u304d\u306b\u306f\u9023\u9396\u7387\u304c\u9069\u7528\u3055\u308c\u308b\u3002\u3053\u306e\u5834\u5408\\(f(x)\\)\u304c\\(log\\)\u3067\u3042\u308a\\(g(x)\\)\u304c\\(1-p\\)\u306a\u306e\u3067\u3001\\( log(1-p)\\)\u306e\u5f62\u306b\u306a\u3063\u3066\u3044\u308b\u3002\u3053\u3046\u3044\u3063\u305f\u5834\u5408\u3001\u307e\u305a\\(f(x)\\)\u3092\u5fae\u5206\u3057\u3066\u3001\u6b21\u306b\\(g(x)\\)\u3092\u5fae\u5206\u3057\u3066\u305d\u308c\u3089\u3092\u639b\u3051\u5408\u308f\u305b\u308b\u3002\\(log(1-p)\\)\u306e\u5fae\u5206\u306f\\(\\frac{1}{1-p}\\)\u3067\u3001\\( 1-p\\)\u306e\u5fae\u5206\u306f\\(-1\\)\u3067\u3042\u308b\uff09\u3002\u3053\u308c\u3092\u89e3\u304f\u3068<\/p>\n\n\n\n

    \\(\\frac{k}{p} + \\frac{n-k}{1-p}\\)<\/p>\n\n\n\n

    \u304c\u3048\u3089\u308c\u3001\u3053\u308c\u30920\u306b\u8a2d\u5b9a\u3057\u3066\u89e3\u304f\u3068\u3001<\/p>\n\n\n\n

    \\(\\frac{k}{p} + \\frac{n-k}{1-p} = 0\\)<\/p>\n\n\n\n

    \\(\\frac{k}{p} = -\\frac{n-k}{1-p}\\)<\/p>\n\n\n\n

    \\(k(1-p) = -p(n-k)\\)<\/p>\n\n\n\n

    \\(k – kp = -pn + pk\\)<\/p>\n\n\n\n

    \\(k = pn\\)<\/p>\n\n\n\n

    \\(p = \\frac{k}{n}\\)<\/p>\n\n\n\n

    \u304c\u5f97\u3089\u308c\u308b\u3002\u3053\u308c\u306f\u4e0a\u8a18\u306e\u56f3\u306e\u9802\u70b9\u306e\u90e8\u5206\u3001\u63a5\u7dda\u306e\u50be\u304d\u304c0\u306e\u3068\u3053\u308d\u3067\u3042\u308b\u3002\u5f53\u7136\u3001\u300c\u30b3\u30a4\u30f3\u306f\u516c\u6b63\u3067\u3042\u308b\uff08\u8868=\u88cf=\u00bd\uff09\u300d\u3068\u304b\u300c\u30df\u30e5\u30ea\u30a8\u30eb\u30fb\u30d6\u30ea\u30b9\u30c8\u30eb\u306f\u9055\u3044\u304c\u308f\u304b\u3089\u306a\u3044\uff08\u5f7c\u5973\u306e\u9078\u629e\u306f\u30e9\u30f3\u30c0\u30e0\u3067\u3042\u308b\uff09\uff08\u6b63\u89e3=\u9593\u9055\u3044=\u00bd\uff09\u300d\u306a\u3069\u3068\u4eee\u8aac\u3092\u8a2d\u5b9a\u3057\u305f\u6642\u306e\u6700\u5927\u5c24\u5ea6\u306f1\/2\u3068\u306a\u308b\u3002\u30d5\u30a3\u30c3\u30b7\u30e3\u30fc\u306f\u5c24\u5ea6\u306b\u57fa\u3065\u3044\u3066\u3001\u4eee\u8aac\u691c\u5b9a\uff08\u6709\u610f\u691c\u5b9a\uff09\u3068\uff08\u70b9\uff09\u63a8\u5b9a\u3068\u3044\u3046\u533a\u5225\u3092\u4f5c\u3063\u305f\u304c\u3001\u3053\u308c\u3089\u306f\u4e21\u65b9\u5c24\u5ea6<\/a>\u306b\u57fa\u3065\u3044\u3066\u3044\u308b\u3002<\/p>\n\n\n\n

    \"\"<\/figure>\n\n\n\n

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