{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "'Sun Oct 02 20:58:13 2016'" ], "text/latex": [ "'Sun Oct 02 20:58:13 2016'" ], "text/markdown": [ "'Sun Oct 02 20:58:13 2016'" ], "text/plain": [ "[1] \"Sun Oct 02 20:58:13 2016\"" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "date()" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Loading required package: pipeR\n", "Loading required package: ggplot2\n", "Loading required package: dplyr\n", "Warning message:\n", ": package 'dplyr' was built under R version 3.3.1\n", "Attaching package: 'dplyr'\n", "\n", "The following objects are masked from 'package:stats':\n", "\n", " filter, lag\n", "\n", "The following objects are masked from 'package:base':\n", "\n", " intersect, setdiff, setequal, union\n", "\n", "Loading required package: tidyr\n", "Warning message:\n", ": package 'tidyr' was built under R version 3.3.1Loading required package: readr\n", "Warning message:\n", ": package 'readr' was built under R version 3.3.1" ] }, { "data": { "text/html": [ "
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Median Mean 3rd Qu. Max. \n", " 0.00 2.00 3.00 3.56 4.75 7.00 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "summary(data)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "度数分布" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "data\n", " 0 1 2 3 4 5 6 7 \n", " 1 3 11 12 10 5 4 4 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "table(data)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "ヒストグラムを描く\n", "\n", "* ひと山の分布" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "data_frame(data = data) %>>% \n", " ggplot(aes(x = data)) + \n", " geom_histogram(binwidth = 1, colour = \"black\", fill = gray(0.6)) + \n", " scale_y_continuous(breaks = seq(0, 12, 2)) + \n", " scale_x_continuous(breaks = seq(0, 8, 2), limits = c(-0.5, 8.1)) + \n", " labs(title = \"Histogram of data\") + \n", " ylab(\"Frequency\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "標本分散" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "2.98612244897959" ], "text/latex": [ "2.98612244897959" ], "text/markdown": [ "2.98612244897959" ], "text/plain": [ "[1] 2.986122" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "var(data)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "標本標準偏差" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "1.72804006000428" ], "text/latex": [ "1.72804006000428" ], "text/markdown": [ "1.72804006000428" ], "text/plain": [ "[1] 1.72804" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sd(data)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "1.72804006000428" ], "text/latex": [ "1.72804006000428" ], "text/markdown": [ "1.72804006000428" ], "text/plain": [ "[1] 1.72804" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "var(data) %>>% sqrt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2.2 データと確率分布の対応関係をながめる" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* 確率分布: 確率変数の値とそれが出現する確率を対応させたもの\n", " * 確率変数: ある植物個体 $i$ の種子数 $y_i$\n", " * 個体$i$の種子数が$y_i$になる確率はポアソン分布に従う,と考える\n", "* ポアソン分布]\n", " * [ポアソン分布 - Wikipedia](https://ja.wikipedia.org/wiki/%E3%83%9D%E3%82%A2%E3%82%BD%E3%83%B3%E5%88%86%E5%B8%83)\n", " * パラメータ: 分布の平均\n", "\n", "平均 3.56 のポアソン分布は," ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": true }, "outputs": [], "source": [ "y <- 0:9\n", "prob <- dpois(y, lambda = 3.56)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* 種子数が0になる確率は,0.028,1になる確率は0.10\n", "* 一番確立が高いのは種子数が3になる場合で,0.21" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\n", "
yprob
0 0.02843882
1 0.10124222
2 0.18021114
3 0.21385056
4 0.19032700
5 0.13551282
6 0.08040427
7 0.04089132
8 0.01819664
9 0.00719778
\n" ], "text/latex": [ "\\begin{tabular}{ll}\n", " y & prob\\\\\n", "\\hline\n", "\t 0 & 0.02843882\\\\\n", "\t 1 & 0.10124222\\\\\n", "\t 2 & 0.18021114\\\\\n", "\t 3 & 0.21385056\\\\\n", "\t 4 & 0.19032700\\\\\n", "\t 5 & 0.13551282\\\\\n", "\t 6 & 0.08040427\\\\\n", "\t 7 & 0.04089132\\\\\n", "\t 8 & 0.01819664\\\\\n", "\t 9 & 0.00719778\\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "1. 0\n", "2. 1\n", "3. 2\n", "4. 3\n", "5. 4\n", "6. 5\n", "7. 6\n", "8. 7\n", "9. 8\n", "10. 9\n", "11. 0.0284388247141845\n", "12. 0.101242215982497\n", "13. 0.180211144448844\n", "14. 0.213850558079295\n", "15. 0.190326996690573\n", "16. 0.135512821643688\n", "17. 0.0804042741752548\n", "18. 0.0408913165805582\n", "19. 0.0181966358783484\n", "20. 0.00719778041410224\n", "\n", "\n" ], "text/plain": [ " y prob \n", " [1,] 0 0.02843882\n", " [2,] 1 0.10124222\n", " [3,] 2 0.18021114\n", " [4,] 3 0.21385056\n", " [5,] 4 0.19032700\n", " [6,] 5 0.13551282\n", " [7,] 6 0.08040427\n", " [8,] 7 0.04089132\n", " [9,] 8 0.01819664\n", "[10,] 9 0.00719778" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cbind(y, prob)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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P7GoUOHMAEpWAMF2p1UVVXt27dv27ZtX3/9NessYI85c+YoFIqxY8eiQIM1cBaH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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "data_frame(y, prob) %>>% \n", " ggplot(aes(y, prob)) + \n", " geom_line(linetype = 2) +\n", " geom_point() + \n", " scale_x_continuous(breaks = seq(0, 8, 2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "観測データのヒストグラムと確率分布を重ねる(確率分布 $\\times$ 個体数)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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PZEB8zp9fqAgIDnnnvOtrXrY2NjZTLZ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\nFy9eZB0ImHLKNmgB0ul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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ggplot() + \n", " geom_histogram(data = data_frame(x = data), aes(x = x), \n", " colour = \"black\", fill = gray(0.6), binwidth = 1) + \n", " geom_line(data = data_frame(y, prob = prob * 50), aes(x = y, y = prob), linetype = 2) + \n", " geom_point(data = data_frame(y, prob = prob * 50), aes(x = y, y = prob), \n", " shape = 21, fill = \"white\") + \n", " labs(title = \"Histogram of data\") + \n", " ylab(\"Frequency\") + \n", " xlab(\"data\") + \n", " scale_x_continuous(breaks = seq(0, 8, 2)) + \n", " scale_y_continuous(breaks = seq(0, 12, 2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2.3 ポアソン分布とは何か?\n", "\n", "定義は,\n", "\n", "$$p(y | \\lambda) = \\frac{\\lambda^y \\exp(-\\lambda)}{y!} $$\n", "\n", "性質は,\n", "\n", "* $\\sum\\limits^{\\infty}_{y = 0}p(y | \\lambda) = 1$\n", "* 平均は $\\lambda$\n", "* 分散と平均は等しい\n", "\n", "種子数のデータを表現するのにポアソン分布を選んだのは,\n", "\n", "* 値が非負の整数\n", "* $y_i$ に下限(0)はあるが上限はわからない\n", "* 平均(3.56)と分散(2.99)がだいたい等しい\n", "\n", "パラメータ $\\lambda$ を変化させると," ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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BAQ4FkJnC/Xdi1rwC8N/fv3xzL8qoHN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\nNzc3ALhz586xY8eINqdlsEC3ARLoZ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3\n798XwXJuJ0+eRA1TduzYoaqqKpyLonaFKSkpHh4epqamWVlZwrku5sfIzc1F3UVQ/18ymezj\n4/Ply5cDBw4I5Pyd9YvdcaAVQhD5GXRqairKpul08RtNQV7Xqqqqp0+fEm3Lf2AwGB4eHgAw\nduzY762M2B5MTEzExMQAwMHB4evXr+bm5pmZmUK7OuZ7QaGWTeV40qRJ8+bNCwkJEch/HBbo\n5qDnSiqV2rdvX6Jt4QXyb/Ts2XPSpElE2/LjjBo1CsUXi5SXg8PhrFmzprKyUlJSMiAgQGgP\nKGVlZRYWFiwWKzg42N/f/+7du/X19aampm/evBGOAZjvIiUl5fLly+Li4nZ2dkZNyMjIYDKZ\nqCJmO8EC3Rw0g1ZRUUHrVyILKkk8ffp0EbeTN1QqdeLEiSBiAh0ZGYmcG5s3bxZajwgmk7l4\n8eKXL18ePHgQRe/p6upGR0fX1dXNmzePW+scIzqw2eyRI0f269evuLj4y5cvZWVlZWVlxcXF\nJBJpxIgRSkpK7b8EjoNuDhLoAQMGEG0IL9LT09FMvxMVSGqNIUOGXL9+PSUlxcTERFdXd926\ndcLP3mwKg8H4448/AGDMmDHc+r/CuW5KSoqqqurixYu5G/X09KZPn37hwoVHjx4J7acCwydj\nx47lxttwq9nxmQPMJ3gG3ZxOEWN36dIlAJCVlUVLE52Xc+fOHTp0iEql6ujo1NTUHD16dNy4\ncQ8fPiTQJBcXl8rKSjqd7uPjI8zVV3V19aNHjxYWFk6aNAk19GGz2StXrrxw4YKTkxP//VYw\nXQks0M1BM2gRF2jUu8DIyIjYvkftJC8vb+PGjTo6Om/fvn327Nnr168fPnwoKytrY2NDVLpz\nbGwsmhOtX7++aTl24WBqahoYGJiZmWlsbFxUVLRo0aKTJ0/q6+ujGT2mG4IF+j+UlJSgAEZR\nFug3b95kZ2dDJ4/fAIDo6Oj6+voTJ05wHUpjxozZv38/g8EgxCX95csXZ2dnANDW1nZychK+\nAQDw66+/enp6vnz5cujQoWfPngWAlJQUbodMTHcDC/R/QMIHoi3QKH5DUlKys/s3cnJyaDRa\nszYiqI4BITkaf/75Z2lpKYVC8fX1JfDRZMmSJV5eXqWlpfPmzaPT6V+/fhVsnUJMJwIL9H/g\n5gWoq6sTawkPUOFsAwMDCQkJom1pFzIyMiwWq1lh2OLiYgCQlZUVsjFxcXHnzp0DAFtbW5Tf\nSCDLli179+7dkSNHHBwcACAqKkpks+ExHQoW6P+AYsuVlJQ6uov7D5OZmYmiYjtp/Y2moB6p\n+/bt425hs9n79u2jUCio34rQqKiocHFxAYABAwb8/vvvwrx0a/To0QMANm3ahOYKLi4u9fX1\nRBuFETZYoP8DmkGLrH8jICBg5syZACAmJjZ9+nSizWkvU6dONTEx2bdv38yZMwMDA318fMaO\nHXvp0iUHBwehpVYjPDw8Pn36RCKRDh48KC4uLsxL80ZcXNzLywsAPnz44OvrS7Q5GGGD46D/\nAxJo0azC4efnt3PnTtTdXUdHR2Tn+PxDIpGOHj168ODBI0eOoILLZDIZVZwRphl3794NDQ0F\ngKVLl6KsGZFCX1/fzMwsJibG19f3t99+Q10OMN0EPIP+DyI7g/b09Ny5c+fs2bMzMjJUVVWf\nP38uUql3P4yYmNiWLVuys7OTkpJiY2OpVGpDQ4Mwe6fW1NRs3LiRw+H06dNn+/btQrvud7F3\n715ZWVkmk+ns7Nwle9RhWgML9P+prq5G8UyiJtC7du3y8vKaPXt2VFTUoEGDEhMT+/Tps3jx\n4hs3bhBtmmCgUqmamprjx4+fO3cuAISGhn758kU4l963bx/Kot6/fz+366Co0atXL1dXVwBI\nTk6+cOEC0eZghAcW6P/z4cMHND0RKYG+cuXKoUOH9PT0IiMjUeyXmpra9evXe/TosXr16g7t\nKCx8NmzYQKFQampqQkJCOvRCNTU1APDkyZPAwEAAmDt3rojHLK5cuXLIkCEA4O7uLsCG4hgR\nBwv0/+HG2IlUIQ5VVVVJSckPHz4UFhZyN75586asrKxPnz5dwBPdlH79+qHolJCQkI6ToY0b\nN+rq6ubn569fv57NZispKQmnHn97oFKp3t7eZDKZwWCIrCsGI3CwQP8fJNAyMjIKCgpE2/J/\ndHR0YmJiqqqqJk6c+Pr1awA4e/bsnDlzBg0aFBsbKyUlRbSBAsbJyYlEIlVWVp48ebIjzp+S\nkhIeHl5SUrJ06VLUC3HPnj3y8vIdcS3BMmbMGNQF8fDhw48fPybaHIwwwAL9D2w2+9mzZyBi\n/g3EiBEjXFxcvnz5YmxsHBwcvHz5cg0NjXPnzonUD4mgGDp06LRp0wAgMDBQ4BU5OBzO1q1b\nZWRkZs+enZ6eDgCzZs0yNzcX7FU6Djc3N2VlZTab7eTk1NDQQLQ5mA4HCzQwmUw/P7/+/fuf\nOnUKADIzM0+ePCnAvrwCIS4ujs1mMxgMW1vbfv36RUdH9+rVi2ijOoqNGzcCQHFxcXh4uGDP\nfPr06dTU1B07dhw7dkxaWppGo+3du1ewl+hQZGRkdu7cCQCvXr06fvw40eZgOhws0ODg4LBz\n504dHR1vb++//vpLU1PTxcXlzz//JNqu//Pw4cN79+4BgJ2d3fz58y9evCiQWuAiy+jRo1E8\n8uHDh1F/SIFQWVnp4eExdOjQtWvX9urVa+vWrSwWCxXm70SYm5ujZKW9e/einmeYLkx3F+jH\njx9funRpzZo1iYmJmzZtcnV1TU1NnTt37tGjR7nNCQkHdTxTUVFxc3Pz9/fv2uqMQMXkCgoK\nBBhVdvDgwZKSEi8vLyqVii4xePBgd3f3r1+/CuoSwsHHx0dCQqKqqmrr1q1E24LpWLq7QN++\nfRsAtmzZwt1CJpO3bNnCZrNFJBPk8ePHyMi1a9d26urP34W+vj6qWOTr68tms9t/wqysrODg\n4JkzZ86YMQNtodPpnp6excXFhw4dav/5hYmGhsamTZsAICYmpsvEwmNapLsLdEVFBQA067GE\n/kRvEc7BgwcBQFlZecmSJUTbIlQcHR0BIDMz88qVK+0/2+7du5lMJovFsm3C1atXxcXFg4KC\nCgoK2n8JYcLtJ7BlyxYU043pknT3WhyoVNjTp09RGWJEWloaiEY4x9OnTxMSEgDA0dFRTEyM\naHOEipmZmba29ps3bzw8PNrfmiAvLw8A4uPjv31LTEyssLCwT58+7byEMKHT6d7e3r/++mte\nXp6Pj4+bmxvRFmE6hO4+g549e7aYmJijo2NOTg7a8ubNG2dnZ3l5eQMDA2Jtg3+9zz/99NPy\n5cuJtkXYkEikNWvWAMCLFy/a/yDP7a5rY2NT/F/y8/Ob/jx3FiZMmDB//nwA8Pf3f/v2LdHm\nYDqE7i7Qffr08fT0fPbsmaam5rhx40aPHq2jo5OXl+fr6yv8mvHNePbsWVxcHADY2dl1t+kz\nwsLCAlUWRCU3f5iYmJg9e/YAgKGhIQpT6xrs3LlTXl4eF1HqwnR3gQaAhQsX3rx587fffqup\nqWloaFiwYEFSUpKJiQnRdgGq/6uoqLhixQqibSEGCoVib28PAPfv3//hVt+vX79et24dh8MZ\nMGBAYGAghUIRqI1EIi8vjwI5Hj58GBkZSbQ5GMGDBRoAQFtbOzAw8OXLl8+ePfP19RWFflev\nX79Gi2N2dnaSkpJEm0MYixYtUlZWhn8XS7+XkpKSxYsXV1dXy8nJRUREoDYlXYnFixePHTsW\nALZv315aWpqfn48br3QlsECLKAcOHOBwOAoKCqtXrybaFiKh0+lr164FgFu3bqFcfP5hMpnL\nly/Py8ujUCghISEDBw7sGBuJhEQieXt702i00tJSa2vr0aNH//rrr50ushvTGligRZH09HTU\nGdbW1rY7T58RNjY2qOrI9wYsOzs7P3r0CAC2bt2qr6/fIcaJANra2nZ2dgCQlJSkoqKSlpZm\naWlZVVVFtF0YAdBlw+xQthj/cF2TFAqFRCJ1gEXfYclff/3FZrN79uxpZ2f3vR9EUJDJ//x4\nE2UAF0lJSXt7ew8PjytXrmRmZmppafFzVEhIyJkzZwBgyZIlKC9RIJBIJMJvCABQKJSmZgwe\nPJhEIo0aNSohISEuLm7x4sW//vprdHR0z549O8gA0Rke6JtLuBnohvzA8GhjdZfTFWloaCDa\nhB8nMzMT/R9v3bqVaFtEhS9fvqB2J8uXL+dn/6tXr6Lv7fjx42trazvaPGIJDw+nUCijR48u\nKytDW86cOUOlUkeNGlVaWkqsbZg24S1WJE5XjM5paGgoLy//rkNoNJqcnBwAlJWVEVvKbuPG\njadOnZKWlk5LS+u4GVCbSElJSUhINDY2lpWVEWUDAjUlcHZ29vf3p9Fojx494t3zOzs729jY\nuLy8XEVFJT4+XlBl/3r27EmhUGpra6urqwVywh9GXl6+qqoKlZGqr6/X0NAQExN79+5d04RY\nNze3vXv3btq0qWkZAwFCoVDQ4CwvLye28CmVSu3Ro0dJSQmBNgCAhISElJQUm80uLS393mMV\nFRVbewv7oEWLvLy8s2fPAsCqVasIVGcRxMHBQVxcnMVi+fv789itoqJi0aJF5eXlEhIS4eHh\nXbgoK0JMTGzVqlWVlZWurq7coiVpaWmBgYFKSkqoxyOm84IFWrTYv38/i8WSkZFBlSgwXHr1\n6rVgwQIACA8Pb60TY2Nj4+rVqzMzM0kkkr+///Dhw4VrIzG4u7s7OTmFhoZaWlo2NDQ8fPhw\nypQplZWVu3fv7pKBK90KLNAiRG5u7rlz5wDA0dERT5+/Zc2aNVQqtb6+Pjg4uMUddu3ahSr/\nrV+/HvU27Ca4ublZW1ufP3/ewsJixowZtbW1jY2Nzs7OL168INo0TLvAAi1CHDp0iMViSUtL\no5YimGaoqanNmTMHAI4fP47WGDgcDnfBIDw8HHk/TExMfv/9dwLtFD4kEmnPnj0rVqyIiYmh\nUCiHDx+WkpKqrKycP3/+u3fviLYO8+NggRYV8vLyTp8+DQDW1tZdstmgQFi/fj2ZTK6qqjp6\n9CgArFixYsaMGSwW68GDB66urvBvUig3CKz7QCKR9u3b5+fnFxsbO3fu3FOnTomJiX358mXe\nvHmokh+mM9LtxrHI4u/vz2KxpKSk1q1bR7QtosvgwYNRxf3g4OCLFy9euXLl6dOnBw8eXLVq\nFZPJVFBQiIiI6HqdzvmERCJZWVkNGjQIAPT09I4ePUqj0QoLCy0sLFrz2mNEHCzQIgGDwUAt\na5cuXYqnz7zZtGkTiUQqKyv7/fff+/TpM3LkSB8fn+LiYjqdfvLkSd4ReN0KExOT4OBgCoXy\n4cOHefPm/UD4F4ZwsECLBKg7qri4OKqAjOHB8OHDp06dCgBfvnzx9vY+cuQIisPduXPn+PHj\nCTZOxJg9e7aPjw+JRHrz5s2CBQtw/nenAws08Xz69Ck0NBQAlixZ0uXjdgXCwoULyWSynp6e\nlZXV+PHjFy9ejBKdibZLFLGystq9ezcApKWlzZ8/H/fH6lxggSaegICA+vp6cXHx9evXE21L\n5yA8PBz+rZcNAHv37pWQkLC3t++SabHtZ/Xq1c7OzgDw5MmTZcuWoRRETKcACzTBlJSUnDhx\nAgAWLVrUrHctpkUSExPv3r27cuVK1PYbAPr06fP7779nZWUdP36cWNtEFldXV5T6dOfOHRsb\nG2KTszH8Q3xdrm5OQEBAbW0tt+oxhjccDmfTpk0AwGKxmlaZqKmpIZFInp6eixcv7p7twdpk\n+/btlZWVp06dunLlyoYNG3x9fbthMGKnAws0kXz58gXF8y5YsKBzdZUmikePHuXm5gIA8to3\no6KioqioSE1NTeh2dQJIJJKXl1dVVdXFixfPnj0rLS29d+9eoo3CtAH+CSUMJpMZFBRUU1ND\np9MFWLC4CxMVFTV37lxUEujmzZulTUBtre3s7LA684BCofj7+0+fPh0Ajh49um/fPqItwrQB\nFmgCYDKZS5cu1dTUDAoKAoB58+b17duXaKNEGg6H4+npaW9vX19fLyMjQyaTg4KC5OTkev7L\nsWPHAGDatGlEWyrq0Gi0Y8eOTZo0CQC8vb39/Pzy8vImTJiAAzxEEyzQwobJZK5YseLatWsA\nUFdXR6FQNmzYQLRRIk1tbe3SpUu9vLw4HI6GhkZCQoKNjc25c+cmTZrk6+sbGBg4ffp0T09P\nALh+/TrRxnYCxMXFT58+jVrN7tq1y8jIKCcn5/bt2wsXLsQaLWpggRYqNTU1c+fOvXHjhqen\nZ3p6uqqqKolE+vDhA9F2iS7FxcUzZsw4f/48AEycOPHq1asDBgxwd3fftm3b69evnZyc7O3t\nExMT0SNIYGDgtm3biDa5EyApKXn69GnUKKu2tvbmzZtBQUHJyclz587FDWdFCizQwqO6utrK\nyurBgweenp4uLi7q6up3797t27fv4sWL4+PjibZOFMnIyDAxMUGNXy0tLf/++295eXkAIJPJ\n69ate/369b179xITE9++fZucnKynpwcAgYGBW7duJdjuzsCnT59KS0slJCSuX7+up6dnY2MT\nGBiYkpLy22+/fW83IkzHgQVaeBw+fPjBgwdr1qxxcXFBW9TV1ePi4shksq2tLU4faMb169dN\nTExyc3PJZLKXl9fhw4fpdHrTHcTExLS0tLS1tVF3roiIiMmTJwNAUFAQaudIkOGdA1tb2y9f\nvkRFRf3yyy9oi42Nzc6dO58/f75jxw5CTcP8HyzQwsPAwEBSUvLChQvv379HWzgcjp+fX21t\n7fTp05upT3dj+/btKOIQcejQoWXLllVXVyPl5adECepxxdXobdu2YY3mwYQJEzgczrlz57iN\nsiorKy9fvkwikSZMmECsbRguWKCFx5gxY+zs7D59+jRx4sSXL1+y2Wxra2t/f38rK6sjR44Q\nbR2R3Lhx48iRI3/++efbt29ZLNbGjRt37drV2NjYq1ev6Ohoc3NzPs+DNHrKlCkAEBQU5OLi\ngjW6Nfbs2bN69erjx48vXLiwsbGxtLR08uTJjx8/5nA40dHRuIS0iEDpko8zbDa7rq7uuw6h\nUCji4uIAUFdX10Hf6oiICHd3dzabXV9ff/HixefPn4eGhs6ZM8fPz49CoTS1hE6n19bWdoQN\n/EOn02k0GofD+d47+b2goEMajcZkMt++fRsVFRUTEwMAOjo60dHRgwcPRs8WfLqAaDSamZlZ\nWlpaTk7O8+fPP3/+bGRkRCKR2m+nhIQEmUxuaGhgsVjtP1s7LWEyme3sPU8ikQwMDIqKik6f\nPs1gMA4fPvzkyZO+fftWVlZmZ2eHhYVRKBRdXd3Wsg3JZLKEhAQA1NXVcefghEAmk8XFxQmP\nP6HRaHQ6ncPh/MA3V1JSsrW38AxaSAQFBW3YsIHNZg8YMCAkJKSysjI8PNzCwuLIkSNN1bkb\ncuTIkaysrAMHDri6uqI6GwAwY8aMmJgYZWXlHzihuLg4dx4dGhrq7OyM59EtQiKRvL29ly1b\nFhISkpSUtH///sePH+/evVtKSqq2tnbXrl3Tpk1LS0sj2sxuDalLjt2GhobvXYmm0WhycnIA\nUFZW1s65ybfs37//r7/+AgBtbe2oqCglJaW0tLSkpCRHR8dv1ZlOp0tLSxNeXh2tvDU2NpaV\nlXXcVT59+jR+/PiRI0cmJibW1dUNHjy4sLBw0aJFnp6eVOo/dQikpaUB4HtrGdfV1S1ZsuTO\nnTsAsHTpUm9v73bOo3v27EmhUGpra6urq9tznvYjLy9fVVUlqFVlDofj6+vbr18/rispNzfX\nxcXl1q1bAEAmkxcvXuzu7o7+F7hQKBTU17i8vJzY0ktUKrVHjx4lJSUE2gAAEhISUlJSbDb7\nB765ioqKrb2FZ9Adzq5du5A6jxw58tKlS0pKSgAwatSodevWdfO5MwDs3r27trbW19eXRCJJ\nSEj89ddfbDZbTU2Nq84/jLi4eEREhJGREQCEhYVt2rSpS85F2g+JRHJycmrq6FdTU4uMjAwP\nD1dWVmaz2WFhYRMmTIiNjSXQyG4LFugOhMPh7Nix49ChQwAwevTov//+G006MIhbt25FRkYu\nXbqUW2t/4cKFenp6Pj4+nz59av/5URMsVHri1KlTmzZtItZb2rkwNja+d+/e6tWryWTyp0+f\nVq5cuWjRooKCAu4OYWFhAQEBBFrYHcCLhP8g8EVCNpu9efPmkJAQANDT04uMjJSRkeHTki6/\nSFhaWurl5fX7779zOJz169eXlJRkZ2dnZ2d/+PBBXFz8+vXrX79+NTEx4VoCfC8SNoNCoZia\nmqanp2dlZb148aKwsLCgoCAgIODUqVMZGRmqqqr8/2R2sUVCfhAXFzc0NJwyZUpaWlpJSUlW\nVlZERISEhMTPP/8cFBS0bt26K1euNDY2ciOpCaFrLxJiH/Q/CNYH3dDQsHbtWpSgPHXq1LCw\nMLTkzQ9d2wf9+fPnffv2nT17lrfgUqnUjx8/osrOP+aDbgqqf3Ljxg0ymcxms+Xl5RUUFLKy\nsmg02t69e5csWcLPSbqqD5ofWCxWQECAp6dnfX09AKioqBQWFurr60tLS8fGxrq4uGzevFlo\nxjSja/ugcT1owcNisezt7S9dugQAM2bMOHr0aLdKQjl37tyoUaMGDhzYbHtxcfHBgwcjIiLQ\nZIdOpxsYGBgaGqLs7Wb07t1bgHX36XT6iRMnhg0bVlNTExoaamlpCQAfPnxYsGCBi4vLyJEj\nhw0bJqhrdUloNNq6devMzMxcXFzu3LlTWFg4a9asCxcuUCgUVMeqpqamSz6LEw4WaAHTVJ2N\njIxCQkK6lTrfunXL0dFx8ODBd+7codFoaGN5ebmfn9+xY8fQ3JNKpS5cuNDJyUlVVVVohmVn\nZ5eVlbm7uyN1BoD+/fv//fff/fv3P3PmDGqriuFNv379fv3117t3706dOvXcuXNoYJ84caK6\nutrf379Xr14ODg5E29jVwIuEgoTJZK5cuRKp8+zZs0+ePNmt2i+xWKxt27bRaLR3796dPHkS\nACorK3ft2jVy5MhDhw5VV1ejCdejR4/2798vTHUGgKysLACYOHFi042qqqpqamqZmZnCtKRT\nEx8fz+Fwli9fznWb0un0VatWAcCxY8eys7MJta4LgmfQ7eXUqVOFhYXOzs5MJnPZsmW3b98G\ngLlz5/r5+bU/VqxzERQU9O7du+PHjwcGBu7Zsyc/P//s2bPIJUehUCwsLNavXz948GBCbEOC\n0mxlgs1ml5eXp6enx8XFGRkZ4ajHNvHz8ysqKlq5ciUALF26FACio6PnzZtHJpNzc3PHjRs3\nYsSI3377zdzcvLUWbp8+fcrPzx89erRQ7e604EXCf/ixRUJ/f3/kevvtt98+fPjw7NkzALCx\nsfHw8PjhtIhOukhYVFQ0fvz4IUOGPHz48OHDh5MmTUJDi0QimZqauri4aGlp/Zgl7V8kBICv\nX79qa2v/8ssvcXFx3B/O0NDQ5cuXo9dKSkoLFixYvnx5a1P77rxI2JTKysp58+Y9f/782LFj\ncnJy8+fP7927t66u7s2bN5v+H2lqapqZmVlaWqqrq3M3ZmZm/vbbb0VFRZ6entw730669iIh\nDrP7hx8IswsMDNy+fbuBgcH06dPDw8NR6O7GjRu3b9/enqQ1EQmzq6ur27BhQ9++fXv06MHP\n/q6urs+ePTt//ryqqqqqqur79+/T09N//vnno0ePOjg48BiCbdKeMDsuYmJiFAolNDQ0Li4O\nAHJycg4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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "data_frame(x = c(0:20), y1 = dpois(x, lambda = 3.5), y2 = dpois(x, lambda = 7.7), \n", " y3 = dpois(x, lambda = 15.1)) %>>%\n", " gather(lambda, val, -x) %>>%\n", " ggplot(aes(x = x, y = val, shape = lambda)) + \n", " geom_line() + \n", " geom_point(fill = \"white\") + \n", " ylab(\"prob\") + \n", " xlab(\"y\") + \n", " scale_shape_manual(values = c(21, 23, 24), labels = c(\"3.5\", \"7.7\", \"15.1\")) + \n", " theme(legend.position=c(.9, .85))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2.4 ポアソン分布のパラメータの最尤推定\n", "\n", "* 最尤推定\n", " * 尤度(当てはまりの良さ)を最大にするパラメータ(ここでは$\\lambda$)の値を探す\n", " * 尤度($L(\\lambda)$)はある$\\lambda$ における $p(y_i | \\lambda)$ の積 (同時確率)\n", " \n", "$$ \n", "\\begin{align}\n", "L(\\lambda) &= \\prod\\limits_{i}p(y_i | \\lambda) \\\\\n", " &= \\prod\\limits_{i}\\frac{\\lambda^{y_i} \\exp(-\\lambda)}{y_i!}\n", "\\end{align}\n", "$$\n", "\n", "* 実際には対数尤度関数を使う\n", "\n", "$$\n", "\\log L(y_i) = \\sum\\limits_{i}\\left( y_i \\log\\lambda - \\lambda - \\sum\\limits^{y_i}_{k}\\log k \\right)\n", "$$\n", "\n", "$y_i$,$y_2$,$y_3$についてなら,尤度は," ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "text/html": [ "
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\n" ], "text/latex": [ "\\begin{enumerate*}\n", "\\item 0.180211144448844\n", "\\item 0.180211144448844\n", "\\item 0.190326996690573\n", "\\end{enumerate*}\n" ], "text/markdown": [ "1. 0.180211144448844\n", "2. 0.180211144448844\n", "3. 0.190326996690573\n", "\n", "\n" ], "text/plain": [ "[1] 0.1802111 0.1802111 0.1903270" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dpois(data[1:3], lambda = 3.56)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "0.00618107031390251" ], "text/latex": [ "0.00618107031390251" ], "text/markdown": [ "0.00618107031390251" ], "text/plain": [ "[1] 0.00618107" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dpois(data[1:3], lambda = 3.56) %>>% prod()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "平均 $\\lambda$ を変化させたときにポアソン分布の形状と対数尤度がどのように変化するか\n", "\n", "対数尤度にして計算" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [], "source": [ "logL <- function(m){\n", " dpois(data, m, log = TRUE) %>>% sum\n", "}" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [], "source": [ "gpPois <- function(lambda){\n", " gp <- ggplot() + \n", " geom_histogram(data = data_frame(x = data), aes(x = x), \n", " colour = \"black\", fill = gray(0.6), binwidth = 1) + \n", " geom_line(data = data_frame(y, prob = dpois(y, lambda = lambda) * 50), aes(x = y, y = prob), \n", " linetype = 2) + \n", " geom_point(data = data_frame(y, prob = dpois(y, lambda = lambda) * 50), aes(x = y, y = prob), \n", " shape = 21, fill = \"white\") + \n", " scale_x_continuous(breaks = seq(0, 8, 2)) + \n", " scale_y_continuous(breaks = seq(0, 15, 5), limits = c(0, 15)) + \n", " annotate(x = 6, y = 13, hjust = 0, vjust = 0, geom = \"text\", size = 3, \n", " label = sprintf(\"lambda=%.1f\\nlog L=%.1f\", lambda, logL(lambda))) + \n", " theme(axis.title = element_blank())\n", " return(gp)\n", "}" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": true }, "outputs": [], "source": [ "gps <- seq(2.0, 5.2, 0.4) %>>% lapply(gpPois)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Warning message:\n", ": package 'gridExtra' was built under R version 3.3.1\n", "Attaching package: 'gridExtra'\n", "\n", "The following object is masked from 'package:dplyr':\n", "\n", " combine\n", "\n" ] } ], "source": [ "library(gridExtra)" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": true }, "outputs": [], "source": [ "options(repr.plot.width = 8, repr.plot.height = 8)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\lambda = 3.6$ のとき $\\log L = -97.3$ で最大" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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UlNTU21tbUymYy0oIDSKH4YsLW1DQsLe/LkiaOjI+4sCCGkOWklAIAU+fn5e/fu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+fZvz84Dkn+u4metjDOSruclDfuuF/GoK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\nl4b8Mo+RX03l5OT88MMPCoWiX79+LVu2vHjx4q5duzIzM+fNm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VgszszMxJzt0Dzl5+evXLmyffv2M2fOdHJy4rocbTk5OT148AATiQCo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XmNkZ6eHu4srYXL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\nhAAAAABJRU5ErkJggg==", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "do.call(grid.arrange, c(gps, ncol = 3))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "対数尤度と$\\lambda$の関係\n", "\n", "* 3.5ぐらいで最大" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": true }, "outputs": [], "source": [ "options(repr.plot.width = 4, repr.plot.height = 4)" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false }, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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/bNtq9CgvZ3Npvt9ddfJ6JBgwax87XALeiDFmLy5MkDBw4komeeeebo0aOiw+EF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\ncOzYMUKDnR9AHzTwo4g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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lambda = seq(2, 5, 0.1)\n", "data_frame(lambda, logL = sapply(lambda, logL)) %>>% \n", " ggplot(aes(x = lambda, y = logL)) + \n", " geom_line() + \n", " geom_vline(xintercept = 3.56, linetype = 2) + \n", " scale_x_continuous(breaks = seq(2, 5, 0.5))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "対数尤度が最大となる$\\lambda$ を $\\hat\\lambda$ とする.\n", "対数尤度関数が最大値で傾きゼロとなるとなる$\\lambda$を探せばよい\n", "\n", "$$\n", "\\begin{align}\n", "\\frac{\\partial \\log L(\\lambda)}{\\partial \\lambda} &= \\sum\\limits_{i}\\left\\{ \\frac{y_i}{\\lambda} - 1 \\right\\} \\\\\n", " &= \\frac{1}{\\lambda}\\sum\\limits_{i}y_i - 50\n", "\\end{align}\n", "$$\n", "\n", "これが 0になるときの $\\lambda$ が $\\hat\\lambda$ なので,解くと,\n", "$$\n", "\\hat\\lambda = \\frac{1}{50}\\sum\\limits_{i}y_i\n", "$$\n", "これは標本平均のことなので $\\hat\\lambda = 3.56$\n", "となる\n", "\n", "* $\\hat\\lambda$: 最尤推定量\n", "* $\\hat\\lambda = 3.56$: 最尤推定値\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "一般化すると,パラメータ$\\theta$の確率分布から観測データ$y_i$が発生した時の確率を$p(y_i | \\theta)$とすると尤度と対数尤度は,\n", "\n", "$$ L(\\theta | \\boldsymbol{Y}) = \\prod\\limits_i p(y_i | \\theta) $$\n", "\n", "$$ \\log L(\\theta | \\boldsymbol{Y}) = \\sum\\limits_i \\log p(y_i | \\theta) $$\n", "\n", "となり,最尤推定で尤度(対数尤度)最大の$\\hat{\\theta}$を探す" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### コイン投げの尤度(共立出版[『Rで楽しむ統計』](https://github.com/okumuralab/RforFun) 3章 より)\n", "\n", "* 表の出る確率が$\\theta$の硬貨を10回投げて 4回表が出たとする.この確率は,以下の$\\theta$の関数になる($\\theta$ の尤度関数).\n", "\n", "$$ L(\\theta) = {}_{10}\\mathrm{C}_4\\theta^4(1 - \\theta)^6 $$\n", "\n", "* $\\theta$ の信頼区間は $[0.12, 0.74]$\n" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "\n", "\tExact binomial test\n", "\n", "data: 4 and 10\n", "number of successes = 4, number of trials = 10, p-value = 0.7539\n", "alternative hypothesis: true probability of success is not equal to 0.5\n", "95 percent confidence interval:\n", " 0.1215523 0.7376219\n", "sample estimates:\n", "probability of success \n", " 0.4 \n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "binom.test(4, 10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "この区間の中で,尤度が最大となる$\\theta$を求める(最尤推定).\n", "\n", "対数尤度は次のようになる.\n", "\n", "$$\\log L(\\theta) = \\log({}_{10}\\mathrm{C}_4) + 4\\log\\theta + 6\\log(1 - \\theta)$$\n", "\n", "これをプロットすると(定数項は除く)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false }, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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ACBZv78+UajsbKycv78+bxj4QMF2nvV1dVff/01EeHjQQB/6NSp04wZM4ho3bp1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\no0DX4biCDubxUlCRIE9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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "logL <- function(t){\n", " 4 * log(t) + 6 * log(1 - t)\n", "}\n", "ggplot(data_frame(x = c(0, 1)), aes(x)) + \n", " stat_function(fun = logL) + \n", " xlab(expression(theta)) + \n", " ylab(expression(\"L(\"~theta~\")\")) + \n", " geom_vline(xintercept = c(0.12, 0.74), linetype = 2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$L(\\theta)$ が最大になる$\\theta$を求める.\n", "\n", "$$ \\frac{d}{d\\theta} \\log L(\\theta) = \\frac{4}{\\theta} - \\frac{6}{1-\\theta} $$\n", "\n", "が0になる点なので,$\\theta = 0.4$\n", "\n", "(10枚中4枚表が出たので,表が出る確率は0.4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.4.1 疑似乱数と最尤推定値のばらつき\n", "\n", "推定値の標準誤差を見積もる\n", "\n", "* $\\lambda = 3.5$ のポアソン分布に従うデータを50個生成して尤度を計算\n", "* 3000回繰り返す." ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "data_frame(y = sapply(c(1:3000), function(x){\n", " rpois(50, lambda = 3.5) %>>% mean\n", "})) %>>% ggplot(aes(x = y)) + \n", " geom_histogram(colour = \"black\", fill = gray(0.6), binwidth = 0.1) + \n", " scale_x_continuous(limits = c(2.5, 4.5), breaks = seq(2.5, 4.5, 0.5)) + \n", " xlab(expression(\"Estimated \"~lambda~\"for each trial\"))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "調査個体数が多ければ標準誤差は小さくなる\n", "\n", "* 500個体" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false }, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "data_frame(y = sapply(c(1:3000), function(x){\n", " rpois(500, lambda = 3.5) %>>% mean\n", "})) %>>% ggplot(aes(x = y)) + \n", " geom_histogram(colour = \"black\", fill = gray(0.6), binwidth = 0.1) + \n", " scale_x_continuous(limits = c(2.5, 4.5), breaks = seq(2.5, 4.5, 0.5)) + \n", " xlab(expression(\"Estimated \"~lambda~\"for each trial\"))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2.5 統計モデルの要点: 乱数発生・推定・予測\n", "\n", "* 観測データの裏には「真の統計モデル」がある\n", "* 「真の統計モデル」はあるパラメータに従う確率分布\n", "* その確率分布から生成された乱数を観測個数サンプリングしたものが観測データ\n", "* パラメータを推定する or モデルをデータに当てはめる\n", "* 推定した統計モデルを使って未知データを予測する" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2.6 確率分布の選び方\n", "\n", "* 離散 or 連続\n", "* 範囲\n", "* 標本分散と標本平均の関係\n", "\n", "出てくる確率分布\n", "\n", "* ポアソン分布\n", "* 二項分布" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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vCF50TOAQACzYWqXdKP+B4xgIFnZQj1ZBjQerdvn9DQQLQu+QCbNukl+yjQlxpf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\nYAiHwxxrAABRFEVRZIxxr0Rd4qPRKN8yTCYTIUSSJEmSuFcSjUb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zM9Pn80W6/CvP/Prr9ptvBklqvuuYojCHo+G116SJE392WkEQnE4n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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ggplot(data_frame(x = c(0:40)), aes(x)) + \n", " stat_function(geom=\"point\", n=41, fun = dbinom, args = list(size = 10, prob = 0.4), colour = \"blue\") +\n", " stat_function(geom=\"point\", n=41, fun = dbinom, args = list(size = 20, prob = 0.7), colour = \"green\") + \n", " stat_function(geom=\"point\", n=41, fun = dbinom, args = list(size = 40, prob = 0.5), colour = \"red\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* 正規分布\n", "* ガンマ分布" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": false }, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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cfQ6YQsw+czAdTWsgVNRHnFgO5c374W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\nvqHohii6c06gqfVpGfu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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ggplot(data_frame(x = c(0, 20)), aes(x)) + \n", " stat_function(fun = dgamma, args = list(shape = 1, rate = 0.5), colour = \"red\") + \n", " stat_function(fun = dgamma, args = list(shape = 2, rate = 0.5), colour = \"orange\") + \n", " stat_function(fun = dgamma, args = list(shape = 1, rate = 1), colour = \"blue\") + \n", " stat_function(fun = dgamma, args = list(shape = 2, rate = 1), colour = \"green\") " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* 一様分布" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2.7 まとめ\n", "* 確率分布で考える\n", "* データへのモデルの当てはまりは尤度で評価できる\n", "* 最尤推定: 尤度最大となるパラメータを推定すること\n", "* 推定結果を用いた未知データへのあてはめ: 予測\n", "* 確率分布を混合することで複雑なばらつきを表現できる" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Session info -------------------------------------------------------------------\n", "Packages -----------------------------------------------------------------------\n" ] }, { "data": { "text/plain": [ " setting value \n", " version R version 3.3.0 (2016-05-03)\n", " system x86_64, mingw32 \n", " ui RTerm \n", " language (EN) \n", " collate Japanese_Japan.932 \n", " tz Asia/Tokyo \n", " date 2016-10-02 \n", "\n", " package * version date source \n", " assertthat 0.1 2013-12-06 CRAN (R 3.3.0) \n", " Cairo 1.5-9 2015-09-26 CRAN (R 3.3.0) \n", " colorspace 1.2-6 2015-03-11 CRAN (R 3.3.0) \n", " crayon 1.3.2 2016-06-28 CRAN (R 3.3.1) \n", " DBI 0.5 2016-08-11 CRAN (R 3.3.1) \n", " devtools 1.12.0 2016-06-24 CRAN (R 3.3.1) \n", " digest 0.6.10 2016-08-02 CRAN (R 3.3.1) \n", " dplyr * 0.5.0 2016-06-24 CRAN (R 3.3.1) \n", " evaluate 0.9 2016-04-29 CRAN (R 3.3.0) \n", " ggplot2 * 2.1.0.9001 2016-10-02 Github (hadley/ggplot2@feb3ffd) \n", " gridExtra * 2.2.1 2016-02-29 CRAN (R 3.3.1) \n", " gtable 0.2.0 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uuid 0.1-2 2015-07-28 CRAN (R 3.3.0) \n", " withr 1.0.2 2016-06-20 CRAN (R 3.3.1) " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "devtools::session_info()" ] } ], "metadata": { "kernelspec": { "display_name": "R 3.3", "language": "R", "name": "ir33" }, "language_info": { "codemirror_mode": "r", "file_extension": ".r", "mimetype": "text/x-r-source", "name": "R", "pygments_lexer": "r", "version": "3.3.0" }, "nav_menu": {}, "toc": { "navigate_menu": true, "number_sections": true, "sideBar": true, "threshold": 6, "toc_cell": false, "toc_section_display": "block", "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 0 }