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genkuroki/正規分布の共役事前分布関連の公式のSymPyによる導出.ipynb

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正規分布の共役事前分布関連の公式のSymPyによる導出
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正規分布の共役事前分布関連の公式のSymPyによる導出.ipynb
{
"cells": [
{
"metadata": {},
"cell_type": "markdown",
"source": "# 正規分布の共役事前分布関連の公式のSymPyによる導出\n\n黒木玄\n\n2018-04-02, 2018-12-20\n\n* Copyright 2018 Gen Kuroki\n* License: MIT https://opensource.org/licenses/MIT\n\nhttp://nbviewer.jupyter.org/gist/genkuroki/8a342d0b7b249e279dd8ad6ae283c5db に書いた公式のSymPyによる導出."
},
{
"metadata": {
"toc": true
},
"cell_type": "markdown",
"source": "<h1>目次<span class=\"tocSkip\"></span></h1>\n<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#確率密度函数\" data-toc-modified-id=\"確率密度函数-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>確率密度函数</a></span></li><li><span><a href=\"#対数尤度函数とその二乗の期待値\" data-toc-modified-id=\"対数尤度函数とその二乗の期待値-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>対数尤度函数とその二乗の期待値</a></span></li><li><span><a href=\"#ベイズ更新\" data-toc-modified-id=\"ベイズ更新-3\"><span class=\"toc-item-num\">3&nbsp;&nbsp;</span>ベイズ更新</a></span></li><li><span><a href=\"#事後分布のプロット\" data-toc-modified-id=\"事後分布のプロット-4\"><span class=\"toc-item-num\">4&nbsp;&nbsp;</span>事後分布のプロット</a></span></li><li><span><a href=\"#SymPy-lambdify版と-Julia-eval-parse版の比較\" data-toc-modified-id=\"SymPy-lambdify版と-Julia-eval-parse版の比較-5\"><span class=\"toc-item-num\">5&nbsp;&nbsp;</span>SymPy lambdify版と Julia eval parse版の比較</a></span></li><li><span><a href=\"#続く\" data-toc-modified-id=\"続く-6\"><span class=\"toc-item-num\">6&nbsp;&nbsp;</span>続く</a></span></li></ul></div>"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "using Base.Meta: parse\nusing BenchmarkTools\nusing PyPlot\nusing SymPy\nusing SpecialFunctions\nusing Statistics\n\nconst latex = sympy[:latex]\nusing LaTeXStrings\nlatexstring_displaystyle(args...; kwargs...) = \n LaTeXString(raw\"$$\" * prod(latex.(args; kwargs...)) * raw\"$$\")\nlatexdisp(args...; kwargs...) = \n display(latexstring_displaystyle(args...; kwargs...))\nconst ls = latexstring_displaystyle\nconst ld = latexdisp",
"execution_count": 1,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 1,
"data": {
"text/plain": "latexdisp (generic function with 1 method)"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "@syms a b c d\n@syms x y μ μ₀ real=true\nY = [symbols(\"Y$i\", real=true) for i in 1:5]\n@syms σ λ λ₀ θ α β ξ η positive=true",
"execution_count": 2,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 2,
"data": {
"text/plain": "(σ, λ, λ₀, θ, α, β, ξ, η)"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "Y",
"execution_count": 3,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 3,
"data": {
"text/plain": "5-element Array{Sym,1}:\n Y1\n Y2\n Y3\n Y4\n Y5",
"text/latex": "\\[ \\left[ \\begin{array}{r}Y_{1}\\\\Y_{2}\\\\Y_{3}\\\\Y_{4}\\\\Y_{5}\\end{array} \\right] \\]"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "## 確率密度函数"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "p_N = 1/√(2PI)*exp(-λ*(y-μ)^2/2)*√λ",
"execution_count": 4,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 4,
"data": {
"text/plain": " 2 \n -λ*(y - μ) \n ------------\n ___ ___ 2 \n\\/ 2 *\\/ λ *e \n-------------------------\n ____ \n 2*\\/ pi ",
"text/latex": "\\begin{equation*}\\frac{\\sqrt{2} \\sqrt{λ} e^{- \\frac{λ \\left(y - μ\\right)^{2}}{2}}}{2 \\sqrt{\\pi}}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "p_μ = p_N(μ=>μ₀, y=>μ, λ=>λ*λ₀)",
"execution_count": 5,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 5,
"data": {
"text/plain": " 2 \n -λ*λ₀*(μ - μ₀) \n ----------------\n ___ ___ ____ 2 \n\\/ 2 *\\/ λ *\\/ λ₀ *e \n------------------------------------\n ____ \n 2*\\/ pi ",
"text/latex": "\\begin{equation*}\\frac{\\sqrt{2} \\sqrt{λ} \\sqrt{λ₀} e^{- \\frac{λ λ₀ \\left(μ - μ₀\\right)^{2}}{2}}}{2 \\sqrt{\\pi}}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "p_λ = exp(-λ/θ)*λ^(α-1)/(gamma(α)*θ^α)",
"execution_count": 6,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 6,
"data": {
"text/plain": " -λ \n ---\n -α α - 1 θ \nθ *λ *e \n---------------\n Gamma(α) ",
"text/latex": "\\begin{equation*}\\frac{θ^{- α} λ^{α - 1} e^{- \\frac{λ}{θ}}}{\\Gamma\\left(α\\right)}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "## 対数尤度函数とその二乗の期待値\n\nWAICやWBICを計算するためには対数尤度函数とその二乗の事後分布に関する期待値を計算しなければいけなくなる. 共役事前分布を採用した場合には事後分布も共役事前分布と同じ形になるので、共役事前分布に関する期待値の公式を作っておけば十分である. 以下ではその計算をSymPyを使って行う."
},
{
"metadata": {},
"cell_type": "markdown",
"source": "全体を $\\mu_0$ だけ平行移動すればいつでも $\\mu_0=0$ となるようにできる. 以下ではSymPyでの積分計算を易しくするために $\\mu_0=0$ と仮定する."
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "# for simplicity, put μ₀ = 0.\np_μ = p_μ(μ₀=>0)",
"execution_count": 7,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 7,
"data": {
"text/plain": " 2 \n -λ*λ₀*μ \n ---------\n ___ ___ ____ 2 \n\\/ 2 *\\/ λ *\\/ λ₀ *e \n-----------------------------\n ____ \n 2*\\/ pi ",
"text/latex": "\\begin{equation*}\\frac{\\sqrt{2} \\sqrt{λ} \\sqrt{λ₀} e^{- \\frac{λ λ₀ μ^{2}}{2}}}{2 \\sqrt{\\pi}}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "logp_N = simplify(log(p_N))",
"execution_count": 8,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 8,
"data": {
"text/plain": " 2 \n λ*(y - μ) log(λ) log(pi) log(2)\n- ---------- + ------ - ------- - ------\n 2 2 2 2 ",
"text/latex": "\\begin{equation*}- \\frac{λ \\left(y - μ\\right)^{2}}{2} + \\frac{\\log{\\left (λ \\right )}}{2} - \\frac{\\log{\\left (\\pi \\right )}}{2} - \\frac{\\log{\\left (2 \\right )}}{2}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "logp_μ = simplify(log(p_μ))",
"execution_count": 9,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 9,
"data": {
"text/plain": " 2 \n λ*λ₀*μ log(λ) log(λ₀) log(pi) log(2)\n- ------- + ------ + ------- - ------- - ------\n 2 2 2 2 2 ",
"text/latex": "\\begin{equation*}- \\frac{λ λ₀ μ^{2}}{2} + \\frac{\\log{\\left (λ \\right )}}{2} + \\frac{\\log{\\left (λ₀ \\right )}}{2} - \\frac{\\log{\\left (\\pi \\right )}}{2} - \\frac{\\log{\\left (2 \\right )}}{2}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "logp_λ = expand(log(p_λ))",
"execution_count": 10,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 10,
"data": {
"text/plain": " λ\n-α*log(θ) + α*log(λ) - log(λ) - log(Gamma(α)) - -\n θ",
"text/latex": "\\begin{equation*}- α \\log{\\left (θ \\right )} + α \\log{\\left (λ \\right )} - \\log{\\left (λ \\right )} - \\log{\\left (\\Gamma\\left(α\\right) \\right )} - \\frac{λ}{θ}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "p_N = simplify(p_N)\np_μ = simplify(p_μ)\np_λ = simplify(p_λ)\nlogp_N = expand(logp_N)\nlogp_μ = expand(logp_μ)\nlogp_λ = expand(logp_λ)\n\n[p_N, p_μ, p_λ, logp_N, logp_μ, logp_λ]",
"execution_count": 11,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 11,
"data": {
"text/plain": "6-element Array{Sym,1}:\n sqrt(2)*sqrt(λ)*exp(-λ*(y - μ)^2/2)/(2*sqrt(pi))\n sqrt(2)*sqrt(λ)*sqrt(λ₀)*exp(-λ*λ₀*μ^2/2)/(2*sqrt(pi))\n θ^(-α)*λ^(α - 1)*exp(-λ/θ)/gamma(α)\n -y^2*λ/2 + y*λ*μ - λ*μ^2/2 + log(λ)/2 - log(pi)/2 - log(2)/2\n -λ*λ₀*μ^2/2 + log(λ)/2 + log(λ₀)/2 - log(pi)/2 - log(2)/2\n -α*log(θ) + α*log(λ) - log(λ) - log(gamma(α)) - λ/θ",
"text/latex": "\\[ \\left[ \\begin{array}{r}\\frac{\\sqrt{2} \\sqrt{λ} e^{- \\frac{λ \\left(y - μ\\right)^{2}}{2}}}{2 \\sqrt{\\pi}}\\\\\\frac{\\sqrt{2} \\sqrt{λ} \\sqrt{λ₀} e^{- \\frac{λ λ₀ μ^{2}}{2}}}{2 \\sqrt{\\pi}}\\\\\\frac{θ^{- α} λ^{α - 1} e^{- \\frac{λ}{θ}}}{\\Gamma\\left(α\\right)}\\\\- \\frac{y^{2} λ}{2} + y λ μ - \\frac{λ μ^{2}}{2} + \\frac{\\log{\\left (λ \\right )}}{2} - \\frac{\\log{\\left (\\pi \\right )}}{2} - \\frac{\\log{\\left (2 \\right )}}{2}\\\\- \\frac{λ λ₀ μ^{2}}{2} + \\frac{\\log{\\left (λ \\right )}}{2} + \\frac{\\log{\\left (λ₀ \\right )}}{2} - \\frac{\\log{\\left (\\pi \\right )}}{2} - \\frac{\\log{\\left (2 \\right )}}{2}\\\\- α \\log{\\left (θ \\right )} + α \\log{\\left (λ \\right )} - \\log{\\left (λ \\right )} - \\log{\\left (\\Gamma\\left(α\\right) \\right )} - \\frac{λ}{θ}\\end{array} \\right] \\]"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "@time I_μ = simplify(integrate(expand(logp_N*p_μ), (μ, -oo, oo)))",
"execution_count": 12,
"outputs": [
{
"output_type": "stream",
"text": " 0.667942 seconds (79.46 k allocations: 3.975 MiB)\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 12,
"data": {
"text/plain": " / 2 / λ \\\\ \nλ₀*|- y *λ + log|----|| - 1\n \\ \\2*pi// \n---------------------------\n 2*λ₀ ",
"text/latex": "\\begin{equation*}\\frac{λ₀ \\left(- y^{2} λ + \\log{\\left (\\frac{λ}{2 \\pi} \\right )}\\right) - 1}{2 λ₀}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "# 対数尤度函数の期待値\n\n@time Elogp_N = simplify(integrate(expand(I_μ*p_λ), (λ, 0, oo)))",
"execution_count": 13,
"outputs": [
{
"output_type": "stream",
"text": " 1.858062 seconds (80.13 k allocations: 4.003 MiB)\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 13,
"data": {
"text/plain": " 2 \n y *α*θ log(θ) polygamma(0, α) log(pi) log(2) 1 \n- ------ + ------ + --------------- - ------- - ------ - ----\n 2 2 2 2 2 2*λ₀",
"text/latex": "\\begin{equation*}- \\frac{y^{2} α θ}{2} + \\frac{\\log{\\left (θ \\right )}}{2} + \\frac{\\operatorname{polygamma}{\\left (0,α \\right )}}{2} - \\frac{\\log{\\left (\\pi \\right )}}{2} - \\frac{\\log{\\left (2 \\right )}}{2} - \\frac{1}{2 λ₀}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "A1 = -2Elogp_N",
"execution_count": 14,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 14,
"data": {
"text/plain": " 2 1 \ny *α*θ - log(θ) - polygamma(0, α) + log(2) + log(pi) + --\n λ₀",
"text/latex": "\\begin{equation*}y^{2} α θ - \\log{\\left (θ \\right )} - \\operatorname{polygamma}{\\left (0,α \\right )} + \\log{\\left (2 \\right )} + \\log{\\left (\\pi \\right )} + \\frac{1}{λ₀}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "A2 = log(2PI) + α*θ*y^2 + 1/λ₀ - (polygamma(Sym(0),α) + log(θ))",
"execution_count": 15,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 15,
"data": {
"text/plain": " 2 1 \ny *α*θ - log(θ) - polygamma(0, α) + log(2*pi) + --\n λ₀",
"text/latex": "\\begin{equation*}y^{2} α θ - \\log{\\left (θ \\right )} - \\operatorname{polygamma}{\\left (0,α \\right )} + \\log{\\left (2 \\pi \\right )} + \\frac{1}{λ₀}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "simplify(A1 - A2)",
"execution_count": 16,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 16,
"data": {
"text/plain": "0",
"text/latex": "\\begin{equation*}0\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "expand(logp_N^2)",
"execution_count": 17,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 17,
"data": {
"text/plain": " 4 2 2 2 2 2 2 2 \ny *λ 3 2 3*y *λ *μ y *λ*log(λ) y *λ*log(2) y *λ*log(pi) 2\n----- - y *λ *μ + ---------- - ----------- + ----------- + ------------ - y*λ \n 4 2 2 2 2 \n\n 2 4 2 2\n 3 λ *μ λ*μ *log(λ) λ*μ \n*μ + y*λ*μ*log(λ) - y*λ*μ*log(pi) - y*λ*μ*log(2) + ----- - ----------- + ----\n 4 2 \n\n 2 2 2 \n*log(2) λ*μ *log(pi) log (λ) log(pi)*log(λ) log(2)*log(λ) log (2) \n------- + ------------ + ------- - -------------- - ------------- + ------- + \n 2 2 4 2 2 4 \n\n 2 \nlog (pi) log(2)*log(pi)\n-------- + --------------\n 4 2 ",
"text/latex": "\\begin{equation*}\\frac{y^{4} λ^{2}}{4} - y^{3} λ^{2} μ + \\frac{3 y^{2} λ^{2} μ^{2}}{2} - \\frac{y^{2} λ \\log{\\left (λ \\right )}}{2} + \\frac{y^{2} λ \\log{\\left (2 \\right )}}{2} + \\frac{y^{2} λ \\log{\\left (\\pi \\right )}}{2} - y λ^{2} μ^{3} + y λ μ \\log{\\left (λ \\right )} - y λ μ \\log{\\left (\\pi \\right )} - y λ μ \\log{\\left (2 \\right )} + \\frac{λ^{2} μ^{4}}{4} - \\frac{λ μ^{2} \\log{\\left (λ \\right )}}{2} + \\frac{λ μ^{2} \\log{\\left (2 \\right )}}{2} + \\frac{λ μ^{2} \\log{\\left (\\pi \\right )}}{2} + \\frac{\\log{\\left (λ \\right )}^{2}}{4} - \\frac{\\log{\\left (\\pi \\right )} \\log{\\left (λ \\right )}}{2} - \\frac{\\log{\\left (2 \\right )} \\log{\\left (λ \\right )}}{2} + \\frac{\\log{\\left (2 \\right )}^{2}}{4} + \\frac{\\log{\\left (\\pi \\right )}^{2}}{4} + \\frac{\\log{\\left (2 \\right )} \\log{\\left (\\pi \\right )}}{2}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "@time J_μ = integrate(expand(logp_N^2*p_μ), (μ, -oo, oo))",
"execution_count": 18,
"outputs": [
{
"output_type": "stream",
"text": " 1.075623 seconds (36 allocations: 896 bytes)\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 18,
"data": {
"text/plain": " 4 2 2 2 2 2 2 \ny *λ y *λ*log(λ) y *λ*log(2) y *λ*log(pi) 3*y *λ log (λ) log(pi)*\n----- - ----------- + ----------- + ------------ + ------ + ------- - --------\n 4 2 2 2 2*λ₀ 4 2 \n \n\n 2 2 \nlog(λ) log(2)*log(λ) log (2) log (pi) log(2)*log(pi) log(λ) log(2)\n------ - ------------- + ------- + -------- + -------------- - ------ + ------\n 2 4 4 2 2*λ₀ 2*λ₀ \n \n\n \n log(pi) 3 \n + ------- + -----\n 2*λ₀ 2\n 4*λ₀ ",
"text/latex": "\\begin{equation*}\\frac{y^{4} λ^{2}}{4} - \\frac{y^{2} λ \\log{\\left (λ \\right )}}{2} + \\frac{y^{2} λ \\log{\\left (2 \\right )}}{2} + \\frac{y^{2} λ \\log{\\left (\\pi \\right )}}{2} + \\frac{3 y^{2} λ}{2 λ₀} + \\frac{\\log{\\left (λ \\right )}^{2}}{4} - \\frac{\\log{\\left (\\pi \\right )} \\log{\\left (λ \\right )}}{2} - \\frac{\\log{\\left (2 \\right )} \\log{\\left (λ \\right )}}{2} + \\frac{\\log{\\left (2 \\right )}^{2}}{4} + \\frac{\\log{\\left (\\pi \\right )}^{2}}{4} + \\frac{\\log{\\left (2 \\right )} \\log{\\left (\\pi \\right )}}{2} - \\frac{\\log{\\left (λ \\right )}}{2 λ₀} + \\frac{\\log{\\left (2 \\right )}}{2 λ₀} + \\frac{\\log{\\left (\\pi \\right )}}{2 λ₀} + \\frac{3}{4 λ₀^{2}}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "# 対数尤度函数の二乗の期待値\n\n@time Elogp_N2 = simplify(integrate(expand(J_μ*p_λ), (λ, 0, oo)))",
"execution_count": 19,
"outputs": [
{
"output_type": "stream",
"text": " 8.517231 seconds (24 allocations: 560 bytes)\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 19,
"data": {
"text/plain": " 4 2 2 4 2 2 2 2 \ny *α *θ y *α*θ y *α*θ*log(θ) y *α*θ*polygamma(0, α) y *α*θ*log(2) \n-------- + ------- - ------------- - ---------------------- + ------------- + \n 4 4 2 2 2 \n \n\n 2 2 2 2 \ny *α*θ*log(pi) 3*y *α*θ y *θ log (θ) log(θ)*polygamma(0, α) log(pi)*\n-------------- + -------- - ---- + ------- + ---------------------- - --------\n 2 2*λ₀ 2 4 2 2 \n \n\n 2 \nlog(θ) log(2)*log(θ) polygamma (0, α) log(pi)*polygamma(0, α) log(2)*p\n------ - ------------- + ---------------- - ----------------------- - --------\n 2 4 2 \n \n\n 2 2 \nolygamma(0, α) polygamma(1, α) log (2) log (pi) log(2)*log(pi) log(θ\n-------------- + --------------- + ------- + -------- + -------------- - -----\n 2 4 4 4 2 2*λ₀\n \n\n \n) polygamma(0, α) log(2) log(pi) 3 \n- - --------------- + ------ + ------- + -----\n 2*λ₀ 2*λ₀ 2*λ₀ 2\n 4*λ₀ ",
"text/latex": "\\begin{equation*}\\frac{y^{4} α^{2} θ^{2}}{4} + \\frac{y^{4} α θ^{2}}{4} - \\frac{y^{2} α θ \\log{\\left (θ \\right )}}{2} - \\frac{y^{2} α θ \\operatorname{polygamma}{\\left (0,α \\right )}}{2} + \\frac{y^{2} α θ \\log{\\left (2 \\right )}}{2} + \\frac{y^{2} α θ \\log{\\left (\\pi \\right )}}{2} + \\frac{3 y^{2} α θ}{2 λ₀} - \\frac{y^{2} θ}{2} + \\frac{\\log{\\left (θ \\right )}^{2}}{4} + \\frac{\\log{\\left (θ \\right )} \\operatorname{polygamma}{\\left (0,α \\right )}}{2} - \\frac{\\log{\\left (\\pi \\right )} \\log{\\left (θ \\right )}}{2} - \\frac{\\log{\\left (2 \\right )} \\log{\\left (θ \\right )}}{2} + \\frac{\\operatorname{polygamma}^{2}{\\left (0,α \\right )}}{4} - \\frac{\\log{\\left (\\pi \\right )} \\operatorname{polygamma}{\\left (0,α \\right )}}{2} - \\frac{\\log{\\left (2 \\right )} \\operatorname{polygamma}{\\left (0,α \\right )}}{2} + \\frac{\\operatorname{polygamma}{\\left (1,α \\right )}}{4} + \\frac{\\log{\\left (2 \\right )}^{2}}{4} + \\frac{\\log{\\left (\\pi \\right )}^{2}}{4} + \\frac{\\log{\\left (2 \\right )} \\log{\\left (\\pi \\right )}}{2} - \\frac{\\log{\\left (θ \\right )}}{2 λ₀} - \\frac{\\operatorname{polygamma}{\\left (0,α \\right )}}{2 λ₀} + \\frac{\\log{\\left (2 \\right )}}{2 λ₀} + \\frac{\\log{\\left (\\pi \\right )}}{2 λ₀} + \\frac{3}{4 λ₀^{2}}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "@syms ψ₀ ψ₁ \nB1 = 4Elogp_N2(polygamma(Sym(0),α)=>ψ₀, polygamma(Sym(1),α)=>ψ₁)",
"execution_count": 20,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 20,
"data": {
"text/plain": " \n 4 2 2 4 2 2 2 2 2 \ny *α *θ + y *α*θ - 2*y *α*θ*ψ₀ - 2*y *α*θ*log(θ) + 2*y *α*θ*log(2) + 2*y *α*\n \n \n\n 2 \n 6*y *α*θ 2 2 \nθ*log(pi) + -------- - 2*y *θ + ψ₀ + 2*ψ₀*log(θ) - 2*ψ₀*log(pi) - 2*ψ₀*log(2)\n λ₀ \n \n\n \n 2 2 2 \n + ψ₁ + log (θ) - 2*log(pi)*log(θ) - 2*log(2)*log(θ) + log (2) + log (pi) + 2*\n \n \n\n \n 2*ψ₀ 2*log(θ) 2*log(2) 2*log(pi) 3 \nlog(2)*log(pi) - ---- - -------- + -------- + --------- + ---\n λ₀ λ₀ λ₀ λ₀ 2\n λ₀ ",
"text/latex": "\\begin{equation*}y^{4} α^{2} θ^{2} + y^{4} α θ^{2} - 2 y^{2} α θ ψ₀ - 2 y^{2} α θ \\log{\\left (θ \\right )} + 2 y^{2} α θ \\log{\\left (2 \\right )} + 2 y^{2} α θ \\log{\\left (\\pi \\right )} + \\frac{6 y^{2} α θ}{λ₀} - 2 y^{2} θ + ψ₀^{2} + 2 ψ₀ \\log{\\left (θ \\right )} - 2 ψ₀ \\log{\\left (\\pi \\right )} - 2 ψ₀ \\log{\\left (2 \\right )} + ψ₁ + \\log{\\left (θ \\right )}^{2} - 2 \\log{\\left (\\pi \\right )} \\log{\\left (θ \\right )} - 2 \\log{\\left (2 \\right )} \\log{\\left (θ \\right )} + \\log{\\left (2 \\right )}^{2} + \\log{\\left (\\pi \\right )}^{2} + 2 \\log{\\left (2 \\right )} \\log{\\left (\\pi \\right )} - \\frac{2 ψ₀}{λ₀} - \\frac{2 \\log{\\left (θ \\right )}}{λ₀} + \\frac{2 \\log{\\left (2 \\right )}}{λ₀} + \\frac{2 \\log{\\left (\\pi \\right )}}{λ₀} + \\frac{3}{λ₀^{2}}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "B2 = (\n (log(2PI))^2\n + (α+1)*α*θ^2*y^4 + 6α*θ/λ₀*y^2 + 3/λ₀^2\n + ψ₁ + (ψ₀ + log(θ))^2\n + 2log(2PI)*(α*θ*y^2 + 1/λ₀)\n - 2log(2PI)*(ψ₀ + log(θ))\n - 2( y^2*(θ + α*θ*(ψ₀ + log(θ))) + (ψ₀+log(θ))/λ₀)\n)",
"execution_count": 21,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 21,
"data": {
"text/plain": " 2 \n 4 2 6*y *α*θ 2 \ny *α*θ *(α + 1) + -------- - 2*y *(α*θ*(ψ₀ + log(θ)) + θ) + ψ₁ + (ψ₀ + log(θ))\n λ₀ \n \n\n \n2 / 2 1 \\ 2 2*(ψ₀\n - 2*(ψ₀ + log(θ))*log(2*pi) + 2*|y *α*θ + --|*log(2*pi) + log (2*pi) - -----\n \\ λ₀/ \n \n\n \n + log(θ)) 3 \n---------- + ---\n λ₀ 2\n λ₀ ",
"text/latex": "\\begin{equation*}y^{4} α θ^{2} \\left(α + 1\\right) + \\frac{6 y^{2} α θ}{λ₀} - 2 y^{2} \\left(α θ \\left(ψ₀ + \\log{\\left (θ \\right )}\\right) + θ\\right) + ψ₁ + \\left(ψ₀ + \\log{\\left (θ \\right )}\\right)^{2} - 2 \\left(ψ₀ + \\log{\\left (θ \\right )}\\right) \\log{\\left (2 \\pi \\right )} + 2 \\left(y^{2} α θ + \\frac{1}{λ₀}\\right) \\log{\\left (2 \\pi \\right )} + \\log{\\left (2 \\pi \\right )}^{2} - \\frac{2 \\left(ψ₀ + \\log{\\left (θ \\right )}\\right)}{λ₀} + \\frac{3}{λ₀^{2}}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "simplify(B1 - B2)",
"execution_count": 22,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 22,
"data": {
"text/plain": "0",
"text/latex": "\\begin{equation*}0\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "## ベイズ更新\n\nサンプルサイズ $n=5$ の場合の共役事前分布のベイズ公式の公式を求めよう. サンプルによって共役事前分布の4つのパラメーター $\\mu_0, \\lambda_0, \\theta, \\alpha$ が更新される.\n\nこの節では $\\mu_0$ を復活させる. "
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "p_μ = p_μ(μ=>μ-μ₀)",
"execution_count": 23,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 23,
"data": {
"text/plain": " 2 \n -λ*λ₀*(μ - μ₀) \n ----------------\n ___ ___ ____ 2 \n\\/ 2 *\\/ λ *\\/ λ₀ *e \n------------------------------------\n ____ \n 2*\\/ pi ",
"text/latex": "\\begin{equation*}\\frac{\\sqrt{2} \\sqrt{λ} \\sqrt{λ₀} e^{- \\frac{λ λ₀ \\left(μ - μ₀\\right)^{2}}{2}}}{2 \\sqrt{\\pi}}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "n = length(Y)\nYbar = mean(Y)",
"execution_count": 24,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 24,
"data": {
"text/plain": "Y1 Y2 Y3 Y4 Y5\n-- + -- + -- + -- + --\n5 5 5 5 5 ",
"text/latex": "\\begin{equation*}\\frac{Y_{1}}{5} + \\frac{Y_{2}}{5} + \\frac{Y_{3}}{5} + \\frac{Y_{4}}{5} + \\frac{Y_{5}}{5}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "Yvar = sum((Y.-Ybar).^2)/length(Y)",
"execution_count": 25,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 25,
"data": {
"text/plain": " 2 2 \n/ Y1 Y2 Y3 Y4 4*Y5\\ / Y1 Y2 Y3 4*Y4 Y5\\ / Y1 Y2 4\n|- -- - -- - -- - -- + ----| |- -- - -- - -- + ---- - --| |- -- - -- + -\n\\ 5 5 5 5 5 / \\ 5 5 5 5 5 / \\ 5 5 \n----------------------------- + ----------------------------- + --------------\n 5 5 \n\n 2 2 2\n*Y3 Y4 Y5\\ / Y1 4*Y2 Y3 Y4 Y5\\ /4*Y1 Y2 Y3 Y4 Y5\\ \n--- - -- - --| |- -- + ---- - -- - -- - --| |---- - -- - -- - -- - --| \n5 5 5 / \\ 5 5 5 5 5 / \\ 5 5 5 5 5 / \n--------------- + ----------------------------- + ---------------------------\n5 5 5 ",
"text/latex": "\\begin{equation*}\\frac{\\left(- \\frac{Y_{1}}{5} - \\frac{Y_{2}}{5} - \\frac{Y_{3}}{5} - \\frac{Y_{4}}{5} + \\frac{4 Y_{5}}{5}\\right)^{2}}{5} + \\frac{\\left(- \\frac{Y_{1}}{5} - \\frac{Y_{2}}{5} - \\frac{Y_{3}}{5} + \\frac{4 Y_{4}}{5} - \\frac{Y_{5}}{5}\\right)^{2}}{5} + \\frac{\\left(- \\frac{Y_{1}}{5} - \\frac{Y_{2}}{5} + \\frac{4 Y_{3}}{5} - \\frac{Y_{4}}{5} - \\frac{Y_{5}}{5}\\right)^{2}}{5} + \\frac{\\left(- \\frac{Y_{1}}{5} + \\frac{4 Y_{2}}{5} - \\frac{Y_{3}}{5} - \\frac{Y_{4}}{5} - \\frac{Y_{5}}{5}\\right)^{2}}{5} + \\frac{\\left(\\frac{4 Y_{1}}{5} - \\frac{Y_{2}}{5} - \\frac{Y_{3}}{5} - \\frac{Y_{4}}{5} - \\frac{Y_{5}}{5}\\right)^{2}}{5}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "# 共役事前分布\n\nprior = simplify(p_μ*p_λ)",
"execution_count": 26,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 26,
"data": {
"text/plain": " / 2 2 \\\n | λ₀*μ λ₀*μ₀ 1|\n λ*|- ----- + λ₀*μ*μ₀ - ------ - -|\n ___ -α α - 1/2 ____ \\ 2 2 θ/\n\\/ 2 *θ *λ *\\/ λ₀ *e \n-------------------------------------------------------------\n ____ \n 2*\\/ pi *Gamma(α) ",
"text/latex": "\\begin{equation*}\\frac{\\sqrt{2} θ^{- α} λ^{α - \\frac{1}{2}} \\sqrt{λ₀} e^{λ \\left(- \\frac{λ₀ μ^{2}}{2} + λ₀ μ μ₀ - \\frac{λ₀ μ₀^{2}}{2} - \\frac{1}{θ}\\right)}}{2 \\sqrt{\\pi} \\Gamma\\left(α\\right)}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "p5_N = simplify(prod(p_N(y=>v)^β for v in Y))",
"execution_count": 27,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 27,
"data": {
"text/plain": " β\n/ / 2 2 2 2 2\\ \\ \n| -λ*\\(Y1 - μ) + (Y2 - μ) + (Y3 - μ) + (Y4 - μ) + (Y5 - μ) / | \n| ---------------------------------------------------------------| \n| ___ 5/2 2 | \n|\\/ 2 *λ *e | \n|---------------------------------------------------------------------------| \n| 5/2 | \n\\ 8*pi / ",
"text/latex": "\\begin{equation*}\\left(\\frac{\\sqrt{2} λ^{\\frac{5}{2}} e^{- \\frac{λ \\left(\\left(Y_{1} - μ\\right)^{2} + \\left(Y_{2} - μ\\right)^{2} + \\left(Y_{3} - μ\\right)^{2} + \\left(Y_{4} - μ\\right)^{2} + \\left(Y_{5} - μ\\right)^{2}\\right)}{2}}}{8 \\pi^{\\frac{5}{2}}}\\right)^{β}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "# 次の p5 を分配函数で割ったものが事後分布になる.\n\np5 = simplify(p5_N*p_μ*p_λ)\n\n# 以下の式を μ, λ に関する定数倍を除いて上の共役事前分布と等しくするためには, \n# 共役事前分布の4つのパラメーターをどのように変えなければいけないかを以下で計算する.",
"execution_count": 28,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 28,
"data": {
"text/plain": " / 2 2 \n 5*β 1 5*β 1 | Y1 *β Y2 *β \n α + --- - - - --- - - λ*|- ----- + Y1*β*μ - ----- + Y2*β*μ \n -α 2 2 ____ 2 2 \\ 2 2 \nθ *λ *\\/ λ₀ *(2*pi) *e \n------------------------------------------------------------------------------\n \n\n 2 2 2 2 2 \n Y3 *β Y4 *β Y5 *β 5*β*μ λ₀*μ \n- ----- + Y3*β*μ - ----- + Y4*β*μ - ----- + Y5*β*μ - ------ - ----- + λ₀*μ*μ₀ \n 2 2 2 2 2 \n \n------------------------------------------------------------------------------\n Gamma(α) \n\n 2 \\\n λ₀*μ₀ 1|\n- ------ - -|\n 2 θ/\n \n-------------\n ",
"text/latex": "\\begin{equation*}\\frac{θ^{- α} λ^{α + \\frac{5 β}{2} - \\frac{1}{2}} \\sqrt{λ₀} \\left(2 \\pi\\right)^{- \\frac{5 β}{2} - \\frac{1}{2}} e^{λ \\left(- \\frac{Y_{1}^{2} β}{2} + Y_{1} β μ - \\frac{Y_{2}^{2} β}{2} + Y_{2} β μ - \\frac{Y_{3}^{2} β}{2} + Y_{3} β μ - \\frac{Y_{4}^{2} β}{2} + Y_{4} β μ - \\frac{Y_{5}^{2} β}{2} + Y_{5} β μ - \\frac{5 β μ^{2}}{2} - \\frac{λ₀ μ^{2}}{2} + λ₀ μ μ₀ - \\frac{λ₀ μ₀^{2}}{2} - \\frac{1}{θ}\\right)}}{\\Gamma\\left(α\\right)}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "# n=5 の場合の対数尤度函数\nlogp5 = expand(log(p5))",
"execution_count": 29,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 29,
"data": {
"text/plain": " 2 2 2 2 \n Y1 *β*λ Y2 *β*λ Y3 *β*λ Y4 *β*λ \n- ------- + Y1*β*λ*μ - ------- + Y2*β*λ*μ - ------- + Y3*β*λ*μ - ------- + Y4*\n 2 2 2 2 \n\n 2 2 \n Y5 *β*λ 5*β*λ*μ 5*β*log(λ) 5*β\nβ*λ*μ - ------- + Y5*β*λ*μ - α*log(θ) + α*log(λ) - -------- + ---------- - ---\n 2 2 2 \n\n 2 2 \n*log(pi) 5*β*log(2) λ*λ₀*μ λ*λ₀*μ₀ log(λ) log(λ₀) \n-------- - ---------- - ------- + λ*λ₀*μ*μ₀ - -------- - ------ + ------- - lo\n 2 2 2 2 2 2 \n\n \n log(pi) log(2) λ\ng(Gamma(α)) - ------- - ------ - -\n 2 2 θ",
"text/latex": "\\begin{equation*}- \\frac{Y_{1}^{2} β λ}{2} + Y_{1} β λ μ - \\frac{Y_{2}^{2} β λ}{2} + Y_{2} β λ μ - \\frac{Y_{3}^{2} β λ}{2} + Y_{3} β λ μ - \\frac{Y_{4}^{2} β λ}{2} + Y_{4} β λ μ - \\frac{Y_{5}^{2} β λ}{2} + Y_{5} β λ μ - α \\log{\\left (θ \\right )} + α \\log{\\left (λ \\right )} - \\frac{5 β λ μ^{2}}{2} + \\frac{5 β \\log{\\left (λ \\right )}}{2} - \\frac{5 β \\log{\\left (\\pi \\right )}}{2} - \\frac{5 β \\log{\\left (2 \\right )}}{2} - \\frac{λ λ₀ μ^{2}}{2} + λ λ₀ μ μ₀ - \\frac{λ λ₀ μ₀^{2}}{2} - \\frac{\\log{\\left (λ \\right )}}{2} + \\frac{\\log{\\left (λ₀ \\right )}}{2} - \\log{\\left (\\Gamma\\left(α\\right) \\right )} - \\frac{\\log{\\left (\\pi \\right )}}{2} - \\frac{\\log{\\left (2 \\right )}}{2} - \\frac{λ}{θ}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "# exp() の中の式における -λ の係数\nc_λ = -coeff(collect(logp5, λ), λ)",
"execution_count": 30,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 30,
"data": {
"text/plain": " 2 2 2 2 2 \nY1 *β Y2 *β Y3 *β Y4 *β Y5 *β \n----- - Y1*β*μ + ----- - Y2*β*μ + ----- - Y3*β*μ + ----- - Y4*β*μ + ----- - Y5\n 2 2 2 2 2 \n\n 2 2 2 \n 5*β*μ λ₀*μ λ₀*μ₀ 1\n*β*μ + ------ + ----- - λ₀*μ*μ₀ + ------ + -\n 2 2 2 θ",
"text/latex": "\\begin{equation*}\\frac{Y_{1}^{2} β}{2} - Y_{1} β μ + \\frac{Y_{2}^{2} β}{2} - Y_{2} β μ + \\frac{Y_{3}^{2} β}{2} - Y_{3} β μ + \\frac{Y_{4}^{2} β}{2} - Y_{4} β μ + \\frac{Y_{5}^{2} β}{2} - Y_{5} β μ + \\frac{5 β μ^{2}}{2} + \\frac{λ₀ μ^{2}}{2} - λ₀ μ μ₀ + \\frac{λ₀ μ₀^{2}}{2} + \\frac{1}{θ}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "@syms a b c\ns = solve(c_λ - a/2*(μ-b)^2 - c, [a,b,c])[1]\nld(\"a = \", s[a])\nld(\"b = \", s[b])\nld(\"c = \", s[c])",
"execution_count": 31,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "L\"$$a = 5 β + λ₀$$\"",
"text/latex": "$$a = 5 β + λ₀$$"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": "L\"$$b = \\frac{Y_{1} β + Y_{2} β + Y_{3} β + Y_{4} β + Y_{5} β + λ₀ μ₀}{5 β + λ₀}$$\"",
"text/latex": "$$b = \\frac{Y_{1} β + Y_{2} β + Y_{3} β + Y_{4} β + Y_{5} β + λ₀ μ₀}{5 β + λ₀}$$"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": "L\"$$c = \\frac{2 Y_{1}^{2} β^{2} θ + \\frac{Y_{1}^{2} β θ λ₀}{2} - Y_{1} Y_{2} β^{2} θ - Y_{1} Y_{3} β^{2} θ - Y_{1} Y_{4} β^{2} θ - Y_{1} Y_{5} β^{2} θ - Y_{1} β θ λ₀ μ₀ + 2 Y_{2}^{2} β^{2} θ + \\frac{Y_{2}^{2} β θ λ₀}{2} - Y_{2} Y_{3} β^{2} θ - Y_{2} Y_{4} β^{2} θ - Y_{2} Y_{5} β^{2} θ - Y_{2} β θ λ₀ μ₀ + 2 Y_{3}^{2} β^{2} θ + \\frac{Y_{3}^{2} β θ λ₀}{2} - Y_{3} Y_{4} β^{2} θ - Y_{3} Y_{5} β^{2} θ - Y_{3} β θ λ₀ μ₀ + 2 Y_{4}^{2} β^{2} θ + \\frac{Y_{4}^{2} β θ λ₀}{2} - Y_{4} Y_{5} β^{2} θ - Y_{4} β θ λ₀ μ₀ + 2 Y_{5}^{2} β^{2} θ + \\frac{Y_{5}^{2} β θ λ₀}{2} - Y_{5} β θ λ₀ μ₀ + \\frac{5 β θ λ₀ μ₀^{2}}{2} + 5 β + λ₀}{θ \\left(5 β + λ₀\\right)}$$\"",
"text/latex": "$$c = \\frac{2 Y_{1}^{2} β^{2} θ + \\frac{Y_{1}^{2} β θ λ₀}{2} - Y_{1} Y_{2} β^{2} θ - Y_{1} Y_{3} β^{2} θ - Y_{1} Y_{4} β^{2} θ - Y_{1} Y_{5} β^{2} θ - Y_{1} β θ λ₀ μ₀ + 2 Y_{2}^{2} β^{2} θ + \\frac{Y_{2}^{2} β θ λ₀}{2} - Y_{2} Y_{3} β^{2} θ - Y_{2} Y_{4} β^{2} θ - Y_{2} Y_{5} β^{2} θ - Y_{2} β θ λ₀ μ₀ + 2 Y_{3}^{2} β^{2} θ + \\frac{Y_{3}^{2} β θ λ₀}{2} - Y_{3} Y_{4} β^{2} θ - Y_{3} Y_{5} β^{2} θ - Y_{3} β θ λ₀ μ₀ + 2 Y_{4}^{2} β^{2} θ + \\frac{Y_{4}^{2} β θ λ₀}{2} - Y_{4} Y_{5} β^{2} θ - Y_{4} β θ λ₀ μ₀ + 2 Y_{5}^{2} β^{2} θ + \\frac{Y_{5}^{2} β θ λ₀}{2} - Y_{5} β θ λ₀ μ₀ + \\frac{5 β θ λ₀ μ₀^{2}}{2} + 5 β + λ₀}{θ \\left(5 β + λ₀\\right)}$$"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "# μ に関する平方完成\nsimplify(c_λ - s[a]/2*(μ-s[b])^2 - s[c])",
"execution_count": 32,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 32,
"data": {
"text/plain": "0",
"text/latex": "\\begin{equation*}0\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "# α₅ は対数尤度函数における log(λ) の係数に 1/2 を足したもの\n\nα₅ = coeff(collect(logp5, log(λ)), log(λ)) + Sym(1)/2",
"execution_count": 33,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 33,
"data": {
"text/plain": " 5*β\nα + ---\n 2 ",
"text/latex": "\\begin{equation*}α + \\frac{5 β}{2}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "λ₀₅ = s[a]",
"execution_count": 34,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 34,
"data": {
"text/plain": "5*β + λ₀",
"text/latex": "\\begin{equation*}5 β + λ₀\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "μ₀₅ = s[b]",
"execution_count": 35,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 35,
"data": {
"text/plain": "Y1*β + Y2*β + Y3*β + Y4*β + Y5*β + λ₀*μ₀\n----------------------------------------\n 5*β + λ₀ ",
"text/latex": "\\begin{equation*}\\frac{Y_{1} β + Y_{2} β + Y_{3} β + Y_{4} β + Y_{5} β + λ₀ μ₀}{5 β + λ₀}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "θ₅ = 1/simplify(s[c])",
"execution_count": 36,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 36,
"data": {
"text/plain": " \n------------------------------------------------------------------------------\n 2 \n 2 2 Y1 *β*θ*λ₀ 2 2 2 2 \n2*Y1 *β *θ + ---------- - Y1*Y2*β *θ - Y1*Y3*β *θ - Y1*Y4*β *θ - Y1*Y5*β *θ - \n 2 \n\n \n------------------------------------------------------------------------------\n 2 \n 2 2 Y2 *β*θ*λ₀ 2 2 2 \nY1*β*θ*λ₀*μ₀ + 2*Y2 *β *θ + ---------- - Y2*Y3*β *θ - Y2*Y4*β *θ - Y2*Y5*β *θ \n 2 \n\n θ*(5*β + λ₀) \n------------------------------------------------------------------------------\n 2 \n 2 2 Y3 *β*θ*λ₀ 2 2 \n- Y2*β*θ*λ₀*μ₀ + 2*Y3 *β *θ + ---------- - Y3*Y4*β *θ - Y3*Y5*β *θ - Y3*β*θ*λ₀\n 2 \n\n \n------------------------------------------------------------------------------\n 2 2 \n 2 2 Y4 *β*θ*λ₀ 2 2 2 Y5 *β\n*μ₀ + 2*Y4 *β *θ + ---------- - Y4*Y5*β *θ - Y4*β*θ*λ₀*μ₀ + 2*Y5 *β *θ + -----\n 2 2\n\n \n----------------------------------------------\n 2 \n*θ*λ₀ 5*β*θ*λ₀*μ₀ \n----- - Y5*β*θ*λ₀*μ₀ + ------------ + 5*β + λ₀\n 2 ",
"text/latex": "\\begin{equation*}\\frac{θ \\left(5 β + λ₀\\right)}{2 Y_{1}^{2} β^{2} θ + \\frac{Y_{1}^{2} β θ λ₀}{2} - Y_{1} Y_{2} β^{2} θ - Y_{1} Y_{3} β^{2} θ - Y_{1} Y_{4} β^{2} θ - Y_{1} Y_{5} β^{2} θ - Y_{1} β θ λ₀ μ₀ + 2 Y_{2}^{2} β^{2} θ + \\frac{Y_{2}^{2} β θ λ₀}{2} - Y_{2} Y_{3} β^{2} θ - Y_{2} Y_{4} β^{2} θ - Y_{2} Y_{5} β^{2} θ - Y_{2} β θ λ₀ μ₀ + 2 Y_{3}^{2} β^{2} θ + \\frac{Y_{3}^{2} β θ λ₀}{2} - Y_{3} Y_{4} β^{2} θ - Y_{3} Y_{5} β^{2} θ - Y_{3} β θ λ₀ μ₀ + 2 Y_{4}^{2} β^{2} θ + \\frac{Y_{4}^{2} β θ λ₀}{2} - Y_{4} Y_{5} β^{2} θ - Y_{4} β θ λ₀ μ₀ + 2 Y_{5}^{2} β^{2} θ + \\frac{Y_{5}^{2} β θ λ₀}{2} - Y_{5} β θ λ₀ μ₀ + \\frac{5 β θ λ₀ μ₀^{2}}{2} + 5 β + λ₀}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "α₅ - (α + n*β/2)",
"execution_count": 37,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 37,
"data": {
"text/plain": "0",
"text/latex": "\\begin{equation*}0\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "λ₀₅ - (λ₀+n*β)",
"execution_count": 38,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 38,
"data": {
"text/plain": "0",
"text/latex": "\\begin{equation*}0\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "simplify(μ₀₅ - (λ₀*μ₀+n*β*Ybar)/(λ₀+n*β))",
"execution_count": 39,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 39,
"data": {
"text/plain": "0",
"text/latex": "\\begin{equation*}0\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "tmp = (1/θ)*(1 + (n*β*θ/2)*(λ₀/(λ₀+n*β)*(Ybar - μ₀)^2 + Yvar))\nsimplify(1/θ₅ - tmp)",
"execution_count": 40,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 40,
"data": {
"text/plain": "0",
"text/latex": "\\begin{equation*}0\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "**まとめ:** 以上は $n=5$ の場合の公式. 一般の場合の正規分布モデルの事前共役分布に関するベイズ更新の公式は以下の通り:\n\n$$\n\\begin{aligned}\n&\n\\tilde\\mu_0 = \\frac{\\lambda_0\\mu_0 + \\beta n \\bar Y}{\\lambda_0 + \\beta n}, %\\quad\n& &\n\\tilde\\lambda_0 = \\lambda_0 + \\beta n, \\quad\n\\\\ &\n\\tilde\\alpha = \\alpha + \\frac{1}{2}\\beta n, %\\quad\n& &\n{\\tilde\\theta}^{-1} = \\theta^{-1}\\left[\n1 + \\frac{\\beta n\\theta}{2}\\left(\n\\frac{\\lambda_0}{\\lambda_0 + \\beta n}\\left(\\bar Y - \\mu_0\\right)^2 + V(Y)\n\\right)\n\\right].\n\\end{aligned}\n$$\n\nここでサイズ $n$ のサンプルを $Y_1,\\ldots,Y_n$ と書くと, \n\n$$\n\\bar Y = \\frac{1}{2}\\sum_{i=1}^n Y_i, \\qquad\nV(Y) = \\frac{1}{2}\\sum_{i=1}^n (Y_i - \\bar Y)^2.\n$$"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "ゆえに $\\beta\\to\\infty$ で\n\n$$\n\\tilde\\mu_0 = \\frac{\\lambda_0\\mu_0 + \\beta n \\bar Y}{\\lambda_0 + \\beta n} \\to \\bar Y,\n\\qquad\n\\tilde\\alpha \\tilde\\theta = \n\\frac{(\\alpha + \\frac{1}{2}\\beta n)\\theta}\n{\n\\left[\n1 + \\frac{\\beta n\\theta}{2}\\left(\n\\frac{\\lambda_0}{\\lambda_0 + \\beta n}\\left(\\bar Y - \\mu_0\\right)^2 + V(Y)\n\\right)\n\\right]\n}\\to\\frac{1}{V(Y)}.\n$$\n\nこのことから $\\beta\\to\\infty$ の極限でベイズ更新は最尤法に一致していることもわかる."
},
{
"metadata": {},
"cell_type": "markdown",
"source": "**注意:** ガンマ分布 $p_\\lambda(\\lambda|\\alpha,\\theta)$ の平均と分散はそれぞれ $\\alpha\\theta$, $\\alpha\\theta^2$ である. 平均 $\\alpha\\theta$ を固定したままで分散 $\\alpha\\theta^2=(\\alpha\\theta)^2/\\alpha$ を小さくするためには $\\alpha$ を大きくすればよい. そのベイズ更新結果の平均と分散は $\\beta\\to\\infty$ でそれぞれ $1/V(Y)$ と $0$ に近付く.\n\n正規分布 $p_\\mu(\\mu|\\mu_0,\\lambda\\lambda_0)$ ($\\lambda\\lambda_0$ は分散の逆数) の分散を小さくするためには $\\lambda\\lambda_0$ を大きくすればよい. そのベイズ公式結果の平均と分散はそれぞれ $\\bar Y$ と $0$ に近付く.\n\n薄く広がった共役事前分布が欲しければ, $\\alpha\\theta$ と $\\mu_0$ を固定したままで $\\alpha$ と $\\lambda_0$ を小さくすればよい. 例えば, $\\alpha\\theta=1$, $\\mu_0=0$ と固定したとき, $\\alpha$, $\\lambda_0$ を小さくして $\\theta=1/\\alpha$ と設定すれば薄く広がった事前分布が得られる."
},
{
"metadata": {},
"cell_type": "markdown",
"source": "## 事後分布のプロット"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "prior_param = (μ₀=>0.0, θ=>1/α, λ₀=>0.001, α=>0.000001)\nposterior_param = (μ₀=>μ₀₅, λ₀=>λ₀₅, α=>α₅, θ=>θ₅)\ndata_sample = (Y[1]=>0.7, Y[2]=>1.1, Y[3]=>1.2, Y[4]=>1.2, Y[5]=>1.5)",
"execution_count": 41,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 41,
"data": {
"text/plain": "(Y1 => 0.7, Y2 => 1.1, Y3 => 1.2, Y4 => 1.2, Y5 => 1.5)"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "prior = (p_μ*p_λ)(prior_param...)",
"execution_count": 42,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 42,
"data": {
"text/plain": " 2\n ___ -0.499999 -1.0e-6*λ -0.0005*λ*μ \n1.58111789863934e-8*\\/ 2 *λ *e *e \n-------------------------------------------------------------\n ____ \n \\/ pi ",
"text/latex": "\\begin{equation*}\\frac{1.58111789863934 \\cdot 10^{-8} \\sqrt{2} e^{- 1.0 \\cdot 10^{-6} λ} e^{- 0.0005 λ μ^{2}}}{\\sqrt{\\pi} λ^{0.499999}}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "posterior = (p_μ*p_λ)(posterior_param...)(β=>1.0, prior_param..., data_sample...)\nposterior = posterior(β=>1.0, prior_param..., data_sample...)\nposterior = simplify(posterior)",
"execution_count": 43,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 43,
"data": {
"text/plain": " / 2 \n ___ 2.000001 -λ*\\2.5005*(μ - 0.56994300569943) + 0.16\n0.00953627593040395*\\/ 2 *λ *e \n------------------------------------------------------------------------------\n ____ \n \\/ pi \n\n \\\n6650670065987/\n \n--------------\n \n ",
"text/latex": "\\begin{equation*}\\frac{0.00953627593040395 \\sqrt{2} λ^{2.000001} e^{- λ \\left(2.5005 \\left(μ - 0.56994300569943\\right)^{2} + 0.166650670065987\\right)}}{\\sqrt{\\pi}}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "# lambdify版\nf_prior = lambdify(prior, [μ, λ])\nf_posterior = lambdify(posterior, [μ, λ])\n\nμs = -1:0.03:2\nλs = 10 .^(-1:0.04:3)\nz_prior = f_prior.(μs', λs)\nz_posterior = f_posterior.(μs', λs)\n\nsleep(0.1)\nfigure(figsize=(10,4))\n\nsubplot(121)\npcolormesh(μs, λs, z_prior, cmap=\"CMRmap\")\ncolorbar()\ngrid(ls=\":\")\nxlabel(\"μ\")\nylabel(\"λ\")\nyscale(\"log\")\ntitle(\"prior\")\n\nsubplot(122)\npcolormesh(μs, λs, z_posterior, cmap=\"CMRmap\")\ncolorbar()\ngrid(ls=\":\")\nxlabel(\"μ\")\nylabel(\"λ\")\nyscale(\"log\")\ntitle(\"posterior\")\n\ntight_layout()",
"execution_count": 44,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "Figure(PyObject <Figure size 1000x400 with 4 Axes>)",
"image/png": 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"
},
"metadata": {}
}
]
},
{
"metadata": {
"scrolled": false,
"trusted": true
},
"cell_type": "code",
"source": "# eval parse 版\neval(parse(\"g_prior(μ,λ) = $prior\"))\neval(parse(\"g_posterior(μ,λ) = $posterior\"))\n\nμs = -1:0.03:2\nλs = 10 .^(-1:0.04:3)\nz_prior = g_prior.(μs', λs)\nz_posterior = g_posterior.(μs', λs)\n\nsleep(0.1)\nfigure(figsize=(10,4))\n\nsubplot(121)\npcolormesh(μs, λs, z_prior, cmap=\"CMRmap\")\ncolorbar()\ngrid(ls=\":\")\nxlabel(\"μ\")\nylabel(\"λ\")\nyscale(\"log\")\ntitle(\"prior\")\n\nsubplot(122)\npcolormesh(μs, λs, z_posterior, cmap=\"CMRmap\")\ncolorbar()\ngrid(ls=\":\")\nxlabel(\"μ\")\nylabel(\"λ\")\nyscale(\"log\")\ntitle(\"posterior\")\n\ntight_layout()",
"execution_count": 45,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "Figure(PyObject <Figure size 1000x400 with 4 Axes>)",
"image/png": 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"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "## SymPy lambdify版と Julia eval parse版の比較"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "# SymPy expression\nposterior",
"execution_count": 46,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 46,
"data": {
"text/plain": " / 2 \n ___ 2.000001 -λ*\\2.5005*(μ - 0.56994300569943) + 0.16\n0.00953627593040395*\\/ 2 *λ *e \n------------------------------------------------------------------------------\n ____ \n \\/ pi \n\n \\\n6650670065987/\n \n--------------\n \n ",
"text/latex": "\\begin{equation*}\\frac{0.00953627593040395 \\sqrt{2} λ^{2.000001} e^{- λ \\left(2.5005 \\left(μ - 0.56994300569943\\right)^{2} + 0.166650670065987\\right)}}{\\sqrt{\\pi}}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "# String version of SymPy expression\n\"$posterior\"",
"execution_count": 47,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 47,
"data": {
"text/plain": "\"0.00953627593040395*sqrt(2)*λ^2.000001*exp(-λ*(2.5005*(μ - 0.56994300569943)^2 + 0.166650670065987))/sqrt(pi)\""
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "# 101×101 ≈ 10^4 (μ, λ)'s\nμs = collect(-1:0.03:2)\nλs = 10 .^(-1:0.04:3)\n@show length.((μs,λs));",
"execution_count": 48,
"outputs": [
{
"output_type": "stream",
"text": "length.((μs, λs)) = (101, 101)\n",
"name": "stdout"
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "# SymPy lambdify 版\nf_posterior = lambdify(posterior, [μ, λ])\n@benchmark z_posterior = f_posterior.(μs', λs)",
"execution_count": 49,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 49,
"data": {
"text/plain": "BenchmarkTools.Trial: \n memory estimate: 1.01 MiB\n allocs estimate: 51017\n --------------\n minimum time: 2.796 ms (0.00% GC)\n median time: 2.912 ms (0.00% GC)\n mean time: 3.189 ms (4.28% GC)\n maximum time: 64.073 ms (92.81% GC)\n --------------\n samples: 1564\n evals/sample: 1"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "# Julia eval parse 版\neval(parse(\"g_posterior(μ,λ) = $posterior\"))\n@benchmark z_posterior = g_posterior.(μs', λs)",
"execution_count": 50,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 50,
"data": {
"text/plain": "BenchmarkTools.Trial: \n memory estimate: 79.89 KiB\n allocs estimate: 5\n --------------\n minimum time: 1.162 ms (0.00% GC)\n median time: 1.183 ms (0.00% GC)\n mean time: 1.241 ms (2.11% GC)\n maximum time: 62.258 ms (98.05% GC)\n --------------\n samples: 4028\n evals/sample: 1"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "N(posterior)",
"execution_count": 51,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 51,
"data": {
"text/plain": " / 2 \n ___ 2.000001 -λ*\\2.5005*(μ - 0.56994300569943) + 0.16\n0.00953627593040395*\\/ 2 *λ *e \n------------------------------------------------------------------------------\n ____ \n \\/ pi \n\n \\\n6650670065987/\n \n--------------\n \n ",
"text/latex": "\\begin{equation*}\\frac{0.00953627593040395 \\sqrt{2} λ^{2.000001} e^{- λ \\left(2.5005 \\left(μ - 0.56994300569943\\right)^{2} + 0.166650670065987\\right)}}{\\sqrt{\\pi}}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "# Julia eval parse N 版\neval(parse(\"h_posterior(μ,λ) = $(N(posterior))\"))\n@benchmark z_posterior = h_posterior.(μs', λs)",
"execution_count": 52,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 52,
"data": {
"text/plain": "BenchmarkTools.Trial: \n memory estimate: 79.89 KiB\n allocs estimate: 5\n --------------\n minimum time: 1.148 ms (0.00% GC)\n median time: 1.220 ms (0.00% GC)\n mean time: 1.377 ms (2.50% GC)\n maximum time: 82.969 ms (98.31% GC)\n --------------\n samples: 3621\n evals/sample: 1"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "ちなみにJuliaにおいて meshgrid は次のセルのようにして実現できる.\n\nしかし, meshgridは, 同一のデータを大量に複製することによって, メモリを無駄に使用する. 可能ならば避けた方がコンピューターの効率的な利用という観点からは合理的である."
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "# SymPy lambdify 版 meshgrid ケース\n\nμ_grid = repeat(μs, 1, length(λs))'\nλ_grid = repeat(λs, 1, length(μs))\n\nf_posterior = lambdify(posterior, [μ, λ])\n@benchmark z_posterior = f_posterior.(μ_grid, λ_grid)",
"execution_count": 53,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 53,
"data": {
"text/plain": "BenchmarkTools.Trial: \n memory estimate: 1.01 MiB\n allocs estimate: 51016\n --------------\n minimum time: 2.809 ms (0.00% GC)\n median time: 2.862 ms (0.00% GC)\n mean time: 3.066 ms (4.38% GC)\n maximum time: 65.052 ms (95.40% GC)\n --------------\n samples: 1630\n evals/sample: 1"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "figure(figsize=(5,4))\npcolormesh(μs, λs, z_posterior, cmap=\"CMRmap\")\ncolorbar()\ngrid(ls=\":\")\nxlabel(\"μ\")\nylabel(\"λ\")\nyscale(\"log\")\ntitle(\"posterior\")",
"execution_count": 54,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "Figure(PyObject <Figure size 500x400 with 2 Axes>)",
"image/png": 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"
},
"metadata": {}
},
{
"output_type": "execute_result",
"execution_count": 54,
"data": {
"text/plain": "PyObject Text(0.5,1,'posterior')"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "## 続く\n\nかもしれない。"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "",
"execution_count": null,
"outputs": []
}
],
"metadata": {
"_draft": {
"nbviewer_url": "https://gist.github.com/89fc7435bf2c031a2f11c280e89b23ff"
},
"gist": {
"id": "89fc7435bf2c031a2f11c280e89b23ff",
"data": {
"description": "正規分布の共役事前分布関連の公式のSymPyによる導出",
"public": true
}
},
"kernelspec": {
"name": "julia-1.0",
"display_name": "Julia 1.0.3",
"language": "julia"
},
"language_info": {
"file_extension": ".jl",
"name": "julia",
"mimetype": "application/julia",
"version": "1.0.3"
},
"toc": {
"nav_menu": {},
"number_sections": true,
"sideBar": true,
"skip_h1_title": true,
"title_cell": "目次",
"title_sidebar": "目次",
"toc_cell": true,
"toc_position": {},
"toc_section_display": true,
"toc_window_display": false
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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