{"id":1333,"date":"2018-03-03T10:42:06","date_gmt":"2018-03-03T01:42:06","guid":{"rendered":"https:\/\/plaza.umin.ac.jp\/~OIO\/?p=1333"},"modified":"2018-03-03T11:38:14","modified_gmt":"2018-03-03T02:38:14","slug":"learnbayes-r-%e3%83%91%e3%83%83%e3%82%b1%e3%83%bc%e3%82%b8%e3%81%ab%e3%82%88%e3%82%8b%e8%87%a8%e5%ba%8a%e8%a9%a6%e9%a8%93%e3%81%a8%e5%b8%82%e8%b2%a9%e5%be%8c%e3%81%ae%e5%89%af%e4%bd%9c%e7%94%a8","status":"publish","type":"post","link":"https:\/\/plaza.umin.ac.jp\/~OIO\/?p=1333","title":{"rendered":"LearnBayes R \u30d1\u30c3\u30b1\u30fc\u30b8\u306b\u3088\u308b\u81e8\u5e8a\u8a66\u9a13\u3068\u5e02\u8ca9\u5f8c\u306e\u526f\u4f5c\u7528\u30c7\u30fc\u30bf\u306e\u89e3\u6790"},"content":{"rendered":"

R\u306eLearnBayes \u30d1\u30c3\u30b1\u30fc\u30b8\u3067\u81e8\u5e8a\u8a66\u9a13\u3068\u5e02\u8ca9\u5f8c\u306e\u526f\u4f5c\u7528\u30c7\u30fc\u30bf\u3092\u89e3\u6790\u3057\u3066\u307f\u307e\u3057\u305f<\/h1>\n

\u3053\u3053\u306b\u63d0\u793a\u3055\u308c\u308b\u30c7\u30fc\u30bf\u306f\u3001\u6cbb\u9a13\u30fb\u5e02\u8ca9\u5f8c\u306e\u5b9f\u30c7\u30fc\u30bf\u3092\u5143\u306b\u3057\u3066\u3044\u307e\u3059\u304c\u3001\u5b9f\u969b\u306e\u30c7\u30fc\u30bf\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002LearnBayes\u3068\u3044\u3046R\u306e\u30d1\u30c3\u30b1\u30fc\u30b8\u306f\u30d9\u30a4\u30ba\u63a8\u8a08\u3092\u884c\u3048\u308b\u3088\u3046\u306a\u95a2\u6570\u3092\u63d0\u4f9b\u3057\u3066\u3044\u307e\u3059\u3002\u8aac\u660e\u66f8\u3092\u8aad\u307f\u306a\u304c\u3089\u3001\u3053\u306e\u30d1\u30c3\u30b1\u30fc\u30b8\u306e\u4e00\u90e8\u6a5f\u80fd\u3092\u4f7f\u3063\u3066\u307f\u3066\u307f\u307e\u3057\u305f\u3002<\/p>\n

\n

1\uff0e\u6d77\u5916\u8a66\u9a13\u306e\u7d50\u679c\u304c\u4e8b\u524d\u306b\u3042\u3063\u3066\u3001\u56fd\u5185\u306e\u526f\u4f5c\u7528\u60c5\u5831\u304c\u5f97\u3089\u308c\u305f<\/h2>\n

\u6d77\u5916\u306e\u6cbb\u9a13\u306e\u30c7\u30fc\u30bf\u304c\u3059\u3067\u306b\u3042\u308a\u3001\u305d\u306e\u5f8c\u56fd\u5185\u3067\u8a66\u9a13\u3092\u884c\u3063\u3066\u526f\u4f5c\u7528\u30c7\u30fc\u30bf\u304c\u65b0\u305f\u306b\u5f97\u3089\u308c\u305f\u3002\u3068\u8a00\u3046\u5834\u5408\u3092\u60f3\u5b9a\u3057\u305f\u89e3\u6790\u3092\u3057\u3066\u307f\u305f\u3002<\/p>\n

\u6d77\u5916\u81e8\u5e8a\u8a66\u9a13\u3067\u306f\u3001\u88ab\u9a13\u8005135\u4f8b\u4e2d50\u4f8b\u306b\u526f\u4f5c\u7528\u304c\u5831\u544a\u3055\u308c\u305f\u3002\u666e\u901a\u306e\u983b\u5ea6\u306e\u89e3\u6790\u306b\u3088\u308b\u3068\u526f\u4f5c\u7528\u304c\u5831\u544a\u3055\u308c\u308b\u5272\u5408\u306f\u3001\u672c\u5264\u4f7f\u7528\u8005\u306e37.0% (95%CI; 28.9 – 45.8)\u3068\u306a\u308b\u3002<\/p>\n

> binom.test(50, 135)<\/p>\n

Exact binomial test<\/p>\n

data: 50 and 135
\nnumber of successes = 50, number of trials = 135, p-value = 0.00328
\nalternative hypothesis: true probability of success is not equal to 0.5
\n95 percent confidence interval:
\n0.2888945 0.4576672
\nsample estimates:
\nprobability of success
\n0.3703704<\/p><\/blockquote>\n

\u3053\u306e\u8a08\u7b97\u7d50\u679c\u3092\u3082\u3068\u306b\u3001\u03b2\u5206\u5e03\u3092\u63a8\u5b9a\u3059\u308b\u300295%\u4fe1\u983c\u533a\u9593\u306e\u4e0a\u9650(p=0.975)\u3092\u4e0e\u3048\u308bx\u306e\u5024\u306f0.4576672\u3067\u3042\u308a\u3001\u6700\u5c24\u5024(p=0.5)\u3092\u4e0e\u3048\u308b\uff58\u306e\u5024\u306f0.3703704\u3002\u3053\u306e2\u70b9\u3092\u4e0e\u3048\u308c\u3070\u4e8b\u524d\u78ba\u7387\u306e\u03b2\u5206\u5e03\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u304c\u63a8\u5b9a\u3067\u304d\u308b\u3002<\/p>\n

quantile2 <- list(p=.975, x=.458)
\nquantile1 <- list(p=0.5, x=.370)
\nbeta_parm <- beta.select(quantile1, quantile2)
\na <- beta_parm[1]
\nb <- beta_parm[2]<\/p><\/blockquote>\n

\u56fd\u5185\u81e8\u5e8a\u8a66\u9a13\u3067\u306f\u6d77\u5916\u3088\u308a\u88ab\u9a13\u8005\u304c\u5c11\u306a\u304f\u300123\u4f8b\u304c\u5b89\u5168\u6027\u89e3\u6790\u5bfe\u8c61\u75c7\u4f8b\u3068\u306a\u3063\u305f\u300223\u4f8b\u4e2d11\u4f8b\u3067\u526f\u4f5c\u7528\u304c\u5831\u544a\u3055\u308c\u305f\u3002\u3053\u306e\u7d50\u679c\u3068\u4e8b\u524d\u63a8\u5b9a\u3055\u308c\u3066\u3044\u308b\u03b2\u5206\u5e03\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u5143\u306b\u524d\u5f8c\u306e\u5206\u5e03\u3092\u56f3\u793a\u3059\u308b\u3002<\/p>\n

# \u4e8b\u5f8c\u5206\u5e03
\ncurve(dbeta(x,a+s,b+f), from=0, to=1, xlab=”p”,ylab=”Density”,lty=1,lwd=4)
\n# \u5b9f\u9a13\u7d50\u679c\u304b\u3089\u51fa\u3066\u304f\u308b\u30a4\u30d9\u30f3\u30c8\u767a\u751f\u983b\u5ea6\u306e\u5c24\u5ea6
\ncurve(dbeta(x,s+1,f+1),add=TRUE,lty=2,lwd=4)
\n# \u4e8b\u524d\u5206\u5e03
\ncurve(dbeta(x,a,b),add=TRUE,lty=3,lwd=4)
\nlegend(.7,9,c(“Prior”,”Likelihood”,”Posterior”), lty=c(3,2,1),lwd=c(3,3,3))<\/p><\/blockquote>\n

\"\"<\/p>\n

\u56fd\u5185\u8a66\u9a13\u306e\u30c7\u30fc\u30bf\u306e\u5206\u5e03\uff08\u8352\u3044\u7834\u7dda\uff09\u306e\u30c7\u30fc\u30bf\u304c\u5f97\u3089\u308c\u305f\u5f8c\u3082\u3001\u4e8b\u5f8c\u306e\u5206\u5e03\uff08\u5b9f\u7dda\uff09\u306f\u4e8b\u524d\u5206\u5e03\uff08\u7d30\u304b\u3044\u7834\u7dda\uff09\u3068\u5927\u304d\u304f\u5909\u308f\u3089\u306a\u3044\u3088\u3046\u3060\u3002<\/p>\n

# \u4e8b\u5f8c\u306e\u5206\u5e03\u306b\u3088\u308b\u63a8\u5b9a<\/p>\n

> # 90%\u4fe1\u983c\u533a\u9593
\n> qbeta(c(0.05, 0.95), a+s, b+f)
\n[1] 0.3222927 0.4550214
\n> # \u70b9\u63a8\u5b9a
\n> qbeta(0.5, a+s, b+f)
\n[1] 0.3872558<\/p><\/blockquote>\n

\u4e8b\u5f8c\u306e\u78ba\u7387\u306f0.39 (90%CI; 0.32 – 0.46)\u3067\u3001\u56fd\u5185\u306e\u30c7\u30fc\u30bf0.48 (90%CI; 0.30 – 0.66)\u3068\u305a\u3044\u3076\u3093\u305a\u308c\u3066\u3044\u308b\u3088\u3046\u306b\u898b\u3048\u308b\u3002<\/p>\n

# \u56fd\u5185\u30c7\u30fc\u30bf\u306e\u307f\u306b\u3088\u308b\u63a8\u5b9a<\/p>\n

> binom.test(11, 23, conf.level=.9)<\/p>\n

Exact binomial test<\/p>\n

data: 11 and 23
\nnumber of successes = 11, number of trials = 23, p-value = 1
\nalternative hypothesis: true probability of success is not equal to 0.5
\n90 percent confidence interval:
\n0.2960934 0.6648524
\nsample estimates:
\nprobability of success
\n0.4782609<\/p><\/blockquote>\n

2. \u6cbb\u9a13\u306e\u7d50\u679c\u3092\u3082\u3068\u306b\u88fd\u9020\u8ca9\u58f2\u304c\u627f\u8a8d\u3055\u308c\u3001\u5e02\u8ca9\u5f8c\u306b\u533b\u85ac\u54c1\u304c\u4f7f\u308f\u308c\u3066\u5b89\u5168\u6027\u30c7\u30fc\u30bf\u304c\u96c6\u7a4d\u3057\u305f<\/h2>\n

\u4e0a\u8a18\u306e\u81e8\u5e8a\u8a66\u9a13\u306e\u7d50\u679c\u3092\u5143\u306b\u627f\u8a8d\u7533\u8acb\u304c\u306a\u3055\u308c\u3001\u88fd\u9020\u8ca9\u58f2\u306e\u627f\u8a8d\u3092\u5f97\u305f\u3002\u5e02\u8ca9\u5f8c\u306f\u3053\u306e\u533b\u85ac\u54c1\u306f\u6cbb\u9a13\u306b\u53c2\u52a0\u3057\u305f\u88ab\u9a13\u8005\u306e\u6570\u3088\u308a\u306f\u308b\u304b\u306b\u591a\u3044\u60a3\u8005\u3055\u3093\u306b\u4f7f\u7528\u3055\u308c\u3066\u591a\u304f\u306e\u5b89\u5168\u6027\u30c7\u30fc\u30bf\u3092\u5f97\u305f\u3002\u6cbb\u9a13\u306e\u7d50\u679c\u3092\u4e8b\u524d\u5206\u5e03\u3001\u5e02\u8ca9\u5f8c\u306e\u30c7\u30fc\u30bf\u3092\u52a0\u3048\u3066\u4e8b\u5f8c\u306e\u5206\u5e03\u3092\u96c6\u8a08\u3057\u3066\u307f\u308b\u3002<\/p>\n

\u4e0a\u8a18\u306e\u5206\u5e03\u3092\u4e8b\u524d\u5206\u5e03\u306e\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u63a8\u8a08\u306b\u7528\u3044\u308b<\/p>\n

# 90%\u4fe1\u983c\u533a\u9593\u306e\u4e0a\u9650 0.95\u306ex\u5024\u306f0.455
\nquantile4 <- list(p=.95, x=.455)
\nquantile4$x <- qbeta(0.95, a+s, b+f)
\n# \u4e8b\u524d\u78ba\u7387\uff08\u70b9\u63a8\u5b9a; p=0.5\uff09\u306f0.387\u3067\u3042\u3063\u305f
\nquantile3 <- list(p=0.5, x=.387)
\nquantile3$x <- qbeta(0.5, a+s, b+f)
\nbeta_parm <- beta.select(quantile3, quantile4)
\na <- beta_parm[1]
\nb <- beta_parm[2]<\/p><\/blockquote>\n

\u56fd\u5185\u306e\u5e02\u8ca9\u5f8c\u306e\u8abf\u67fb\u306b\u767b\u9332\u3055\u308c\u5b89\u5168\u6027\u89e3\u6790\u5bfe\u8c61\u3068\u3055\u308c\u305f\u60a3\u8005\u306f2072\u4f8b\u3067\u3042\u308a\u3001\u305d\u306e\u3046\u3061964\u4f8b\u306b\u526f\u4f5c\u7528\u304c\u5831\u544a\u3055\u308c\u305f\u3002\u3053\u306e\u7d50\u679c\u3068\u4e8b\u524d\u63a8\u5b9a\u3055\u308c\u3066\u3044\u308b\u03b2\u5206\u5e03\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u5143\u306b\u524d\u5f8c\u306e\u5206\u5e03\u3092\u56f3\u793a\u3059\u308b\u3002<\/p>\n

s <- 964
\nf <- 2072-s
\n# \u5206\u5e03\u3092\u898b\u3066\u307f\u3088\u3046
\n# \u4e8b\u5f8c\u5206\u5e03
\ncurve(dbeta(x,a+s,b+f), from=0, to=1, xlab=”p”,ylab=”Density”,lty=1,lwd=4)
\n# \u5b9f\u9a13\u7d50\u679c\u304b\u3089\u51fa\u3066\u304f\u308b\u30a4\u30d9\u30f3\u30c8\u767a\u751f\u983b\u5ea6\u306e\u5c24\u5ea6
\ncurve(dbeta(x,s+1,f+1),add=TRUE,lty=2,lwd=4)
\n# \u4e8b\u524d\u5206\u5e03
\ncurve(dbeta(x,a,b),add=TRUE,lty=3,lwd=4)
\nlegend(.7,35,c(“Prior”,”Likelihood”,”Posterior”), lty=c(3,2,1),lwd=c(3,3,3))<\/p><\/blockquote>\n

 <\/p>\n

\"\"<\/p>\n

\u5e02\u8ca9\u5f8c\u306e\u8abf\u67fb\u306e\u30c7\u30fc\u30bf\u306e\u5206\u5e03\uff08\u8352\u3044\u7834\u7dda\uff09\u306e\u30c7\u30fc\u30bf\u304c\u5f97\u3089\u308c\u305f\u5f8c\u3001\u4e8b\u5f8c\u306e\u5206\u5e03\uff08\u5b9f\u7dda\uff09\u306f\u4e8b\u524d\u5206\u5e03\uff08\u7d30\u304b\u3044\u7834\u7dda\uff09\u304b\u3089\u5927\u304d\u304f\u53f3\u3078\u30b7\u30d5\u30c8\u3057\u305f\u3002<\/p>\n

# 90%\u4fe1\u983c\u533a\u9593
\n> qbeta(c(0.05, 0.95), a+s, b+f)
\n[1] 0.4427958 0.4776115
\n> # \u70b9\u63a8\u5b9a
\n> qbeta(0.5, a+s, b+f)
\n[1] 0.4601712<\/p><\/blockquote>\n

\u56f3\u304b\u3089\u53d7\u3051\u308b\u5370\u8c61\u306e\u901a\u308a\u3001\u4e8b\u5f8c\u306e\u78ba\u7387\u306f0.\uff14\uff16 (90%CI; 0.\uff14\uff14 – 0.48)\u306f\u3001\u4e8b\u524d\u306e\u30c7\u30fc\u30bf0.\uff13\uff19 (90%CI; 0.32 – 0.46)\u3068\u305a\u308c\u3066\u3044\u308b\u3088\u3046\u306b\u898b\u3048\u308b\u3002\u5b9f\u306f\u3001\u4e8b\u5f8c\u306e\u78ba\u7387\u306f\u3001\u56fd\u5185\u6cbb\u9a13\u306e\u30c7\u30fc\u30bf0.48 (90%CI; 0.30 – 0.66)\u3092\u7cbe\u5bc6\u306b\u3057\u305f\u3088\u3046\u306b\u898b\u3048\u308b\u3002<\/p>\n

3. \u307e\u3068\u3081<\/h2>\n

\u3053\u3053\u307e\u3067\u3084\u3063\u3066\u307f\u305f\u611f\u60f3<\/p>\n

    \n
  1. \u4e8b\u524d\u306e\u8a66\u9a13\u30fb\u8abf\u67fb\u3068\u4e8b\u5f8c\u3068\u3067\u5927\u304d\u304f\u898f\u6a21\uff08\u88ab\u9a13\u8005\u6570\uff09\u304c\u9055\u3046\u5834\u5408\u3001\u88ab\u9a13\u8005\u6570\u306e\u5927\u304d\u306a\u65b9\u306e\u8a66\u9a13\u30fb\u8abf\u67fb\u306e\u7d50\u679c\u304c\u4e8b\u5f8c\u306e\u5206\u5e03\u306b\u53cd\u6620\u3057\u3066\u3044\u308b\u3060\u3051\u3067\u306f\u306a\u3044\u304b<\/li>\n
  2. \u305d\u308c\u306a\u3089\u5358\u306b\u898f\u6a21\u306e\u5927\u304d\u306a\u8a66\u9a13\u30fb\u8abf\u67fb\u306e\u7d50\u679c\u306e\u5206\u5e03\u3092\u96c6\u8a08\u3057\u3066\u3082\u540c\u3058\u3067\u306f\u306a\u3044\u304b\u3001\u3042\u308b\u3044\u306f\u3001\u5358\u7d14\u306b\u8db3\u3057\u305f\u3088\u3046\u306a\u4f75\u5408\u89e3\u6790\u3067\u3082\u7d50\u679c\u306f\u4f3c\u305f\u3088\u3046\u306a\u3082\u306e\u306b\u306a\u308b\u306e\u3067\u306f\u306a\u3044\u304b<\/li>\n
  3. \u3053\u306e\u69d8\u306a\u4f8b\u3067\u306f\u3001\u56fd\u5185\u5916\u3067\u526f\u4f5c\u7528\u306e\u5831\u544a\u983b\u5ea6\u304c\u7570\u306a\u308b\u3068\u3044\u3046\u4eee\u8aac\u3092\u5c0e\u304d\u305f\u3044<\/li>\n
  4. \u7d50\u5c40\u4e8b\u5f8c\u5206\u5e03\u3063\u3066\u4f55\u3092\u793a\u3057\u3066\u3044\u308b\u3082\u306e\u306a\u3093\u3060\u308d\u3046\u304b\uff1f<\/li>\n
  5. \u306a\u305c\u3001\u03b2\u5206\u5e03\u3092\u60f3\u5b9a\u3059\u308b\u306e\u3060\u308d\u3046\u304b\uff1f<\/li>\n<\/ol>\n

    \u7591\u554f\u304c\u3088\u308a\u5177\u4f53\u5316\u3057\u305f\u306e\u3067\u826f\u3057\u3068\u3057\u3088\u3046\u3002<\/p>\n

     <\/p>\n","protected":false},"excerpt":{"rendered":"

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