{ "cells": [ { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "
:16: warning: already initialized constant DATA_COUNTS\n", "
:16: warning: previous definition of DATA_COUNTS was here\n" ] }, { "data": { "text/html": [ "
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{}, "output_type": "display_data" } ], "source": [ "# ベイズ推定による正規分布の推定\n", "\n", "require 'rubystats/normal_distribution'\n", "require 'nyaplot'\n", "\n", "class Array\n", " def mean\n", " self.inject(:+) / self.size.to_f\n", " end\n", "end\n", "\n", "def normal_rand(mu = 0, sigma = 1.0)\n", " random = Random.new\n", " (Math.sqrt(-2 * Math.log(random.rand)) * Math.sin(2 * Math::PI * random.rand) * sigma) + mu\n", "end\n", "\n", "DATA_COUNTS = [2, 4, 10, 100]\n", "\n", "# 真の分布\n", "MU_TRUE = 2.0\n", "BETA_TRUE = 1.0\n", "\n", "# 事前分布\n", "MU_0 = -2.0\n", "BETA_0 = 1.0\n", "\n", "ds = 100.times.map do\n", " normal_rand(MU_TRUE, 1.0 / BETA_TRUE)\n", "end\n", "\n", "fig1 = Nyaplot::Frame.new\n", "fig2 = Nyaplot::Frame.new\n", "\n", "DATA_COUNTS.each_with_index do |n, c|\n", " train_set = ds[0..n-1]\n", " mu_ML = train_set.mean\n", " mu_N = (BETA_TRUE * mu_ML + BETA_0 * MU_0 / n) / (BETA_TRUE + BETA_0 / n)\n", " beta_N = BETA_0 + n * BETA_TRUE\n", "\n", "# 平均μの推定結果を表示\n", " plot = Nyaplot::Plot.new\n", " linex = (-10..10).step(0.01).to_a\n", "\n", " # 平均μの確率分布\n", " sigma = 1.0 / beta_N\n", " mu_est = Rubystats::NormalDistribution.new(mu_N, Math.sqrt(sigma))\n", " label = \"mu_N=%.2f var=%.2f\" % [mu_N, sigma]\n", " liney = linex.map {|x| mu_est.pdf(x) }\n", " line = plot.add(:line, linex, liney)\n", " line.title(label)\n", " line.color('red')\n", "\n", " # トレーニングセットを表示\n", " scatter = plot.add(:scatter, train_set, [0.2] * n)\n", " scatter.title('train_set')\n", " scatter.color('blue')\n", "\n", " plot.configure do\n", " x_label(\"N=#{n}\")\n", " y_label('')\n", " xrange([-5, 5])\n", " yrange([0, liney.max * 1.1])\n", " legend(true)\n", " height(300)\n", " width(490)\n", " end\n", "\n", " fig1.add(plot)\n", "\n", "# 次に得られるデータの推定分布を表示\n", " plot = Nyaplot::Plot.new\n", " \n", " # 真の分布を表示\n", " orig = Rubystats::NormalDistribution.new(MU_TRUE, Math.sqrt(1.0 / BETA_TRUE))\n", " liney = linex.map {|x| orig.pdf(x)}\n", " y_max = liney.max * 1.1\n", " line = plot.add(:line, linex, liney)\n", " line.title('original')\n", " line.color('green')\n", " \n", " # 推定分布を表示\n", " sigma = 1.0 / BETA_TRUE + 1.0 / beta_N\n", " mu_est = Rubystats::NormalDistribution.new(mu_N, Math.sqrt(sigma))\n", " label = \"mu_N=%.2f var=%.2f\" % [mu_N, sigma]\n", " liney = linex.map {|x| mu_est.pdf(x) }\n", " line = plot.add(:line, linex, liney)\n", " line.title(label)\n", " line.color('red')\n", " \n", " # トレーニングセットを表示\n", " scatter = plot.add(:scatter, train_set, train_set.map {|x| orig.pdf(x) })\n", " scatter.title('train_set')\n", " scatter.color('blue')\n", "\n", " plot.configure do\n", " x_label(\"N=#{n}\")\n", " y_label('')\n", " xrange([-5, 5])\n", " yrange([0, y_max])\n", " legend(true)\n", " height(300)\n", " width(490)\n", " end\n", "\n", " fig2.add(plot)\n", "end\n", "\n", "fig1.show\n", "fig2.show\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { 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