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genkuroki/variational approximation by SymPy.ipynb

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Julia言語のSymPy.jlで変分ベイズの例題を理解する
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variational approximation by SymPy.ipynb
{
"cells": [
{
"metadata": {},
"cell_type": "markdown",
"source": "# Julia言語のSymPy.jlで変分ベイズの例題を理解する\n\n黒木玄\n\n2018-04-02, 2018-12-20\n\n<a href=\"http://statmodeling.hatenablog.com/entry/variational-bayesian-inference-with-sympy\">2018-04-01 PythonのSymPyで変分ベイズの例題を理解する</a> (StatModeling Memorandum) と同じことを, Julia言語からPython SymPyを利用してやってみよう. \n\nこのブログ記事は私が今までに見たSymPyの使い方に関する記事の中で最高のものであった. このノートでは詳しい解説は省略するが, ブログ記事の方には各実行結果に詳細なコメントが付けられており, SymPyを使いこなしたい人にとっては必見のブログ記事だと思った.\n\nほとんどの節は上のブログ記事のPython版のコードのJulia言語への翻訳である. 「変数変換をして再計算」の節と最後の「変分近似無しの計算」の節は私自身による. \n\nJuliaでSymPyを使いたい人は <a href=\"http://nbviewer.jupyter.org/github/jverzani/SymPy.jl/blob/master/examples/tutorial.ipynb\">tutorial</a> と <a href=\"http://takeshid.hatenadiary.jp/entry/2016/01/22/032053\">2016-01-22 Julia+SymPyの勝手なまとめ</a> (たけし備忘録) を参照するとよい."
},
{
"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=\"#SymPyの変数の準備\" data-toc-modified-id=\"SymPyの変数の準備-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>SymPyの変数の準備</a></span></li><li><span><a href=\"#確率密度函数を直接定義\" data-toc-modified-id=\"確率密度函数を直接定義-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>確率密度函数を直接定義</a></span><ul class=\"toc-item\"><li><span><a href=\"#積分計算の例\" data-toc-modified-id=\"積分計算の例-2.1\"><span class=\"toc-item-num\">2.1&nbsp;&nbsp;</span>積分計算の例</a></span></li><li><span><a href=\"#正規分布モデルの共役事前分布に関する事前予測分布\" data-toc-modified-id=\"正規分布モデルの共役事前分布に関する事前予測分布-2.2\"><span class=\"toc-item-num\">2.2&nbsp;&nbsp;</span>正規分布モデルの共役事前分布に関する事前予測分布</a></span></li></ul></li><li><span><a href=\"#同時分布の対数-($\\log-p$)-の準備\" data-toc-modified-id=\"同時分布の対数-($\\log-p$)-の準備-3\"><span class=\"toc-item-num\">3&nbsp;&nbsp;</span>同時分布の対数 ($\\log p$) の準備</a></span></li><li><span><a href=\"#できるところまで解析的に求める\" data-toc-modified-id=\"できるところまで解析的に求める-4\"><span class=\"toc-item-num\">4&nbsp;&nbsp;</span>できるところまで解析的に求める</a></span><ul class=\"toc-item\"><li><span><a href=\"#q1_μ\" data-toc-modified-id=\"q1_μ-4.1\"><span class=\"toc-item-num\">4.1&nbsp;&nbsp;</span>q1_μ</a></span></li><li><span><a href=\"#q1_τ-(何も工夫せずに計算できてしまった！しかし非常に汚い)\" data-toc-modified-id=\"q1_τ-(何も工夫せずに計算できてしまった！しかし非常に汚い)-4.2\"><span class=\"toc-item-num\">4.2&nbsp;&nbsp;</span>q1_τ (何も工夫せずに計算できてしまった！しかし非常に汚い)</a></span></li><li><span><a href=\"#変数変換をして再計算\" data-toc-modified-id=\"変数変換をして再計算-4.3\"><span class=\"toc-item-num\">4.3&nbsp;&nbsp;</span>変数変換をして再計算</a></span></li><li><span><a href=\"#q1_τ-の計算に再挑戦\" data-toc-modified-id=\"q1_τ-の計算に再挑戦-4.4\"><span class=\"toc-item-num\">4.4&nbsp;&nbsp;</span>q1_τ の計算に再挑戦</a></span></li></ul></li><li><span><a href=\"#数値的に求める\" data-toc-modified-id=\"数値的に求める-5\"><span class=\"toc-item-num\">5&nbsp;&nbsp;</span>数値的に求める</a></span></li><li><span><a href=\"#変分近似無しの計算\" data-toc-modified-id=\"変分近似無しの計算-6\"><span class=\"toc-item-num\">6&nbsp;&nbsp;</span>変分近似無しの計算</a></span><ul class=\"toc-item\"><li><span><a href=\"#分配函数の計算\" data-toc-modified-id=\"分配函数の計算-6.1\"><span class=\"toc-item-num\">6.1&nbsp;&nbsp;</span>分配函数の計算</a></span></li><li><span><a href=\"#事後分布の計算\" data-toc-modified-id=\"事後分布の計算-6.2\"><span class=\"toc-item-num\">6.2&nbsp;&nbsp;</span>事後分布の計算</a></span></li><li><span><a href=\"#変分近似との比較するためのプロット\" data-toc-modified-id=\"変分近似との比較するためのプロット-6.3\"><span class=\"toc-item-num\">6.3&nbsp;&nbsp;</span>変分近似との比較するためのプロット</a></span></li></ul></li></ul></div>"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "using Base.Meta: parse\nusing SpecialFunctions\nlinspace(a,b,L) = range(a, stop=b, length=L)\n\nusing PyPlot\nusing PyCall\nusing SymPy\n\n# https://docs.sympy.org/latest/modules/printing.html#sympy.printing.julia.julia_code\nconst julia_code = sympy[:julia_code]\n\n@show versioninfo()\nprintln()\n@show PyCall.pyprogramname\n@show PyCall.pyversion\n@show PyCall.conda\n@show PyCall.libpython\n@show sympy[:__version__];",
"execution_count": 1,
"outputs": [
{
"output_type": "stream",
"text": "Julia Version 1.0.3\nCommit 099e826241 (2018-12-18 01:34 UTC)\nPlatform Info:\n OS: Windows (x86_64-w64-mingw32)\n CPU: Intel(R) Core(TM) i7-4770HQ CPU @ 2.20GHz\n WORD_SIZE: 64\n LIBM: libopenlibm\n LLVM: libLLVM-6.0.0 (ORCJIT, haswell)\nEnvironment:\n JULIA_CMDSTAN_HOME = C:\\CmdStan\n JULIA_NUM_THREADS = 4\n JULIA_PKGDIR = C:\\JuliaPkg\nversioninfo() = nothing\n\nPyCall.pyprogramname = \"C:\\\\Anaconda3\\\\python.exe\"\nPyCall.pyversion = v\"3.6.5\"\nPyCall.conda = false\nPyCall.libpython = \"C:\\\\Anaconda3\\\\python36.dll\"\nsympy[:__version__] = \"1.3\"\n",
"name": "stdout"
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "## SymPyの変数の準備"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "y = symbols(\"y\", real=true)\nt = symbols(\"t\", positive=true)\nμ, μ₀ = symbols(\"μ μ₀\", real=true)\nY = symbols(\"Y1:4\", real=true)\nT = symbols(\"T1:4\", positive=true)\nτ, λ₀, a₀, b₀ = symbols(\"τ λ₀ a₀ b₀\", positive=true)\nσ, σ² = symbols(\"σ σ²\", positive=true)\nθ, α = symbols(\"θ α\", positive=true);",
"execution_count": 2,
"outputs": []
},
{
"metadata": {},
"cell_type": "markdown",
"source": "## 確率密度函数を直接定義"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "pdf_Normal(mu, s2, t) = exp(-(t-mu)^2/(2*s2))/√(2*PI*s2)\n@show pdf_Normal(μ, σ², y)",
"execution_count": 3,
"outputs": [
{
"output_type": "stream",
"text": "pdf_Normal(μ, σ², y) = sqrt(2)*exp(-(y - μ)^2/(2*σ²))/(2*sqrt(pi)*sqrt(σ²))\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 3,
"data": {
"text/plain": " 2 \n -(y - μ) \n ----------\n ___ 2*σ² \n\\/ 2 *e \n-----------------\n ____ ____ \n 2*\\/ pi *\\/ σ² ",
"text/latex": "\\begin{equation*}\\frac{\\sqrt{2} e^{- \\frac{\\left(y - μ\\right)^{2}}{2 σ²}}}{2 \\sqrt{\\pi} \\sqrt{σ²}}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "pdf_Gamma(alpha, theta, t) = exp(-t/theta)*t^(alpha-1)/(gamma(alpha)*theta^alpha)\n@show pdf_Gamma(α, θ, y)",
"execution_count": 4,
"outputs": [
{
"output_type": "stream",
"text": "pdf_Gamma(α, θ, y) = y^(α - 1)*θ^(-α)*exp(-y/θ)/gamma(α)\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 4,
"data": {
"text/plain": " -y \n ---\n α - 1 -α θ \ny *θ *e \n---------------\n Gamma(α) ",
"text/latex": "\\begin{equation*}\\frac{y^{α - 1} θ^{- α} e^{- \\frac{y}{θ}}}{\\Gamma\\left(α\\right)}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "p_y = pdf_Normal(μ, 1/τ, y)\n@show p_y",
"execution_count": 5,
"outputs": [
{
"output_type": "stream",
"text": "p_y = sqrt(2)*sqrt(τ)*exp(-τ*(y - μ)^2/2)/(2*sqrt(pi))\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 5,
"data": {
"text/plain": " 2 \n -τ*(y - μ) \n ------------\n ___ ___ 2 \n\\/ 2 *\\/ τ *e \n-------------------------\n ____ \n 2*\\/ pi ",
"text/latex": "\\begin{equation*}\\frac{\\sqrt{2} \\sqrt{τ} e^{- \\frac{τ \\left(y - μ\\right)^{2}}{2}}}{2 \\sqrt{\\pi}}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "p_μ = pdf_Normal(μ₀, 1/(λ₀*τ), μ)\n@show p_μ",
"execution_count": 6,
"outputs": [
{
"output_type": "stream",
"text": "p_μ = sqrt(2)*sqrt(λ₀)*sqrt(τ)*exp(-λ₀*τ*(μ - μ₀)^2/2)/(2*sqrt(pi))\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 6,
"data": {
"text/plain": " 2 \n -λ₀*τ*(μ - μ₀) \n ----------------\n ___ ____ ___ 2 \n\\/ 2 *\\/ λ₀ *\\/ τ *e \n------------------------------------\n ____ \n 2*\\/ pi ",
"text/latex": "\\begin{equation*}\\frac{\\sqrt{2} \\sqrt{λ₀} \\sqrt{τ} e^{- \\frac{λ₀ τ \\left(μ - μ₀\\right)^{2}}{2}}}{2 \\sqrt{\\pi}}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "p_τ = pdf_Gamma(a₀, 1/b₀, τ)\n@show p_τ",
"execution_count": 7,
"outputs": [
{
"output_type": "stream",
"text": "p_τ = b₀^a₀*τ^(a₀ - 1)*exp(-b₀*τ)/gamma(a₀)\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 7,
"data": {
"text/plain": " a₀ a₀ - 1 -b₀*τ\nb₀ *τ *e \n-------------------\n Gamma(a₀) ",
"text/latex": "\\begin{equation*}\\frac{b₀^{a₀} τ^{a₀ - 1} e^{- b₀ τ}}{\\Gamma\\left(a₀\\right)}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "### 積分計算の例"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "I1 = integrate(p_μ, (μ, -oo, oo))\n@show I1",
"execution_count": 8,
"outputs": [
{
"output_type": "stream",
"text": "I1 = 1\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 8,
"data": {
"text/plain": "1",
"text/latex": "\\begin{equation*}1\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "I2 = integrate(p_τ, (τ, 0, oo))\n@show I2",
"execution_count": 9,
"outputs": [
{
"output_type": "stream",
"text": "I2 = b₀^a₀*b₀^(-a₀ + 1)/b₀\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 9,
"data": {
"text/plain": " a₀ -a₀ + 1\nb₀ *b₀ \n--------------\n b₀ ",
"text/latex": "\\begin{equation*}\\frac{b₀^{a₀} b₀^{- a₀ + 1}}{b₀}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "I2 = simplify(I2)",
"execution_count": 10,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 10,
"data": {
"text/plain": "1",
"text/latex": "\\begin{equation*}1\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "### 正規分布モデルの共役事前分布に関する事前予測分布"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "まず, $\\mu$ について積分する."
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "Z1_μ = simplify(integrate(p_y*p_μ, (μ, -oo, oo)))",
"execution_count": 11,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 11,
"data": {
"text/plain": " / 2\\\n | 2 2 (y - μ₀) |\n τ*|- y + 2*y*μ₀ - μ₀ + ---------|\n \\ λ₀ + 1 /\n -----------------------------------\n ___ ____ ___ 2 \n\\/ 2 *\\/ λ₀ *\\/ τ *e \n-------------------------------------------------------\n ____ ________ \n 2*\\/ pi *\\/ λ₀ + 1 ",
"text/latex": "\\begin{equation*}\\frac{\\sqrt{2} \\sqrt{λ₀} \\sqrt{τ} e^{\\frac{τ \\left(- y^{2} + 2 y μ₀ - μ₀^{2} + \\frac{\\left(y - μ₀\\right)^{2}}{λ₀ + 1}\\right)}{2}}}{2 \\sqrt{\\pi} \\sqrt{λ₀ + 1}}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "F1_μ = simplify(-log(Z1_μ))",
"execution_count": 12,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 12,
"data": {
"text/plain": " / 2 / 2 2\\\\ \nτ*\\- (y - μ₀) + (λ₀ + 1)*\\y - 2*y*μ₀ + μ₀ // log(λ₀) log(τ) log(λ₀ + 1\n---------------------------------------------- - ------- - ------ + ----------\n 2*(λ₀ + 1) 2 2 2 \n\n \n) log(2) log(pi)\n- + ------ + -------\n 2 2 ",
"text/latex": "\\begin{equation*}\\frac{τ \\left(- \\left(y - μ₀\\right)^{2} + \\left(λ₀ + 1\\right) \\left(y^{2} - 2 y μ₀ + μ₀^{2}\\right)\\right)}{2 \\left(λ₀ + 1\\right)} - \\frac{\\log{\\left (λ₀ \\right )}}{2} - \\frac{\\log{\\left (τ \\right )}}{2} + \\frac{\\log{\\left (λ₀ + 1 \\right )}}{2} + \\frac{\\log{\\left (2 \\right )}}{2} + \\frac{\\log{\\left (\\pi \\right )}}{2}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "以下では $\\mu_0=0$, $t=y$ と置いてから, $\\tau$ に関する積分を実行する. $t$ を $y-\\mu_0$ に置き換えれば $\\mu_0$ を復活させることができる. SymPyにとって積分計算を易しくなるように $t>0$ と仮定してある."
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "F1_0_μ = F1_μ(μ₀=>0, y=>t)",
"execution_count": 13,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 13,
"data": {
"text/plain": " / 2 2\\ \nτ*\\t *(λ₀ + 1) - t / log(λ₀) log(τ) log(λ₀ + 1) log(2) log(pi)\n-------------------- - ------- - ------ + ----------- + ------ + -------\n 2*(λ₀ + 1) 2 2 2 2 2 ",
"text/latex": "\\begin{equation*}\\frac{τ \\left(t^{2} \\left(λ₀ + 1\\right) - t^{2}\\right)}{2 \\left(λ₀ + 1\\right)} - \\frac{\\log{\\left (λ₀ \\right )}}{2} - \\frac{\\log{\\left (τ \\right )}}{2} + \\frac{\\log{\\left (λ₀ + 1 \\right )}}{2} + \\frac{\\log{\\left (2 \\right )}}{2} + \\frac{\\log{\\left (\\pi \\right )}}{2}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "F1_0_μ = expand(F1_0_μ)",
"execution_count": 14,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 14,
"data": {
"text/plain": " 2 \n t *λ₀*τ log(λ₀) log(τ) log(λ₀ + 1) log(2) log(pi)\n---------- - ------- - ------ + ----------- + ------ + -------\n2*(λ₀ + 1) 2 2 2 2 2 ",
"text/latex": "\\begin{equation*}\\frac{t^{2} λ₀ τ}{2 \\left(λ₀ + 1\\right)} - \\frac{\\log{\\left (λ₀ \\right )}}{2} - \\frac{\\log{\\left (τ \\right )}}{2} + \\frac{\\log{\\left (λ₀ + 1 \\right )}}{2} + \\frac{\\log{\\left (2 \\right )}}{2} + \\frac{\\log{\\left (\\pi \\right )}}{2}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "Z1_0_μ = simplify(exp(-F1_0_μ))",
"execution_count": 15,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 15,
"data": {
"text/plain": " 2 \n -t *λ₀*τ \n ----------\n ___ ____ ___ 2*(λ₀ + 1)\n\\/ 2 *\\/ λ₀ *\\/ τ *e \n------------------------------\n ____ ________ \n 2*\\/ pi *\\/ λ₀ + 1 ",
"text/latex": "\\begin{equation*}\\frac{\\sqrt{2} \\sqrt{λ₀} \\sqrt{τ} e^{- \\frac{t^{2} λ₀ τ}{2 \\left(λ₀ + 1\\right)}}}{2 \\sqrt{\\pi} \\sqrt{λ₀ + 1}}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "Z1_0 = integrate(Z1_0_μ*p_τ, (τ, 0, oo))",
"execution_count": 16,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 16,
"data": {
"text/plain": " -a₀ - 1/2 \n / 2 \\ \n ___ ____ | t *λ₀ | \n\\/ 2 *\\/ λ₀ *|1 + -------------| *Gamma(a₀ + 1/2)\n \\ 2*b₀*(λ₀ + 1)/ \n---------------------------------------------------------\n ____ ____ ________ \n 2*\\/ pi *\\/ b₀ *\\/ λ₀ + 1 *Gamma(a₀) ",
"text/latex": "\\begin{equation*}\\frac{\\sqrt{2} \\sqrt{λ₀} \\left(1 + \\frac{t^{2} λ₀}{2 b₀ \\left(λ₀ + 1\\right)}\\right)^{- a₀ - \\frac{1}{2}} \\Gamma\\left(a₀ + \\frac{1}{2}\\right)}{2 \\sqrt{\\pi} \\sqrt{b₀} \\sqrt{λ₀ + 1} \\Gamma\\left(a₀\\right)}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "これが正規分布モデルを共役事前分布で平均して得た事前予測分布の式である($t=y-\\mu_0$). t分布になっている."
},
{
"metadata": {},
"cell_type": "markdown",
"source": "## 同時分布の対数 ($\\log p$) の準備"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "log_p = sum(log(p_y(y=>x)) for x in Y) + log(p_μ) + log(p_τ)\nlog_p = simplify(log_p)\n@show log_p",
"execution_count": 17,
"outputs": [
{
"output_type": "stream",
"text": "log_p = -Y1^2*τ/2 + Y1*μ*τ - Y2^2*τ/2 + Y2*μ*τ - Y3^2*τ/2 + Y3*μ*τ + a₀*log(b₀) + a₀*log(τ) - b₀*τ - λ₀*μ^2*τ/2 + λ₀*μ*μ₀*τ - λ₀*μ₀^2*τ/2 - 3*μ^2*τ/2 + log(a₀) + log(λ₀)/2 + log(τ) - log(gamma(a₀ + 1)) - 2*log(pi) - 2*log(2)\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 17,
"data": {
"text/plain": " 2 2 2 \n Y1 *τ Y2 *τ Y3 *τ \n- ----- + Y1*μ*τ - ----- + Y2*μ*τ - ----- + Y3*μ*τ + a₀*log(b₀) + a₀*log(τ) - \n 2 2 2 \n\n 2 2 2 \n λ₀*μ *τ λ₀*μ₀ *τ 3*μ *τ log(λ₀) \nb₀*τ - ------- + λ₀*μ*μ₀*τ - -------- - ------ + log(a₀) + ------- + log(τ) - \n 2 2 2 2 \n\n \n \nlog(Gamma(a₀ + 1)) - 2*log(pi) - 2*log(2)\n ",
"text/latex": "\\begin{equation*}- \\frac{Y_{1}^{2} τ}{2} + Y_{1} μ τ - \\frac{Y_{2}^{2} τ}{2} + Y_{2} μ τ - \\frac{Y_{3}^{2} τ}{2} + Y_{3} μ τ + a₀ \\log{\\left (b₀ \\right )} + a₀ \\log{\\left (τ \\right )} - b₀ τ - \\frac{λ₀ μ^{2} τ}{2} + λ₀ μ μ₀ τ - \\frac{λ₀ μ₀^{2} τ}{2} - \\frac{3 μ^{2} τ}{2} + \\log{\\left (a₀ \\right )} + \\frac{\\log{\\left (λ₀ \\right )}}{2} + \\log{\\left (τ \\right )} - \\log{\\left (\\Gamma\\left(a₀ + 1\\right) \\right )} - 2 \\log{\\left (\\pi \\right )} - 2 \\log{\\left (2 \\right )}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "上の式の書き直し:\n\n$$\n\\begin{aligned}\n&- \\frac{Y_{1}^{2} τ}{2} + Y_{1} μ τ - \\frac{Y_{2}^{2} τ}{2} + Y_{2} μ τ - \\frac{Y_{3}^{2} τ}{2} + Y_{3} μ τ + a₀ \\log{\\left (b₀ \\right )} + a₀ \\log{\\left (τ \\right )} - b₀ τ \\\\\n&- \\frac{λ₀ τ}{2} μ^{2} + λ₀ μ μ₀ τ - \\frac{λ₀ τ}{2} μ₀^{2} - \\frac{3 τ}{2} μ^{2} + \\log{\\left (a₀ \\right )} + \\frac{1}{2} \\log{\\left (λ₀ \\right )} + \\log{\\left (τ \\right )} - \\log{\\left (\\Gamma{\\left(a₀ + 1 \\right)} \\right )} \\\\\n&- 2 \\log{\\left (\\pi \\right )} - 2 \\log{\\left (2 \\right )}\n\\end{aligned}\n$$"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "log_p_for_μ = integrate(diff(log_p, μ), μ)\n@show log_p_for_μ",
"execution_count": 18,
"outputs": [
{
"output_type": "stream",
"text": "log_p_for_μ = μ^2*(-λ₀*τ/2 - 3*τ/2) + μ*(Y1*τ + Y2*τ + Y3*τ + λ₀*μ₀*τ)\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 18,
"data": {
"text/plain": " 2 / λ₀*τ 3*τ\\ \nμ *|- ---- - ---| + μ*(Y1*τ + Y2*τ + Y3*τ + λ₀*μ₀*τ)\n \\ 2 2 / ",
"text/latex": "\\begin{equation*}μ^{2} \\left(- \\frac{λ₀ τ}{2} - \\frac{3 τ}{2}\\right) + μ \\left(Y_{1} τ + Y_{2} τ + Y_{3} τ + λ₀ μ₀ τ\\right)\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "expand(log_p_for_μ)",
"execution_count": 19,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 19,
"data": {
"text/plain": " 2 2 \n λ₀*μ *τ 3*μ *τ\nY1*μ*τ + Y2*μ*τ + Y3*μ*τ - ------- + λ₀*μ*μ₀*τ - ------\n 2 2 ",
"text/latex": "\\begin{equation*}Y_{1} μ τ + Y_{2} μ τ + Y_{3} μ τ - \\frac{λ₀ μ^{2} τ}{2} + λ₀ μ μ₀ τ - \\frac{3 μ^{2} τ}{2}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "collect(expand(log_p_for_μ), μ)",
"execution_count": 20,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 20,
"data": {
"text/plain": " 2 / λ₀*τ 3*τ\\ \nμ *|- ---- - ---| + μ*(Y1*τ + Y2*τ + Y3*τ + λ₀*μ₀*τ)\n \\ 2 2 / ",
"text/latex": "\\begin{equation*}μ^{2} \\left(- \\frac{λ₀ τ}{2} - \\frac{3 τ}{2}\\right) + μ \\left(Y_{1} τ + Y_{2} τ + Y_{3} τ + λ₀ μ₀ τ\\right)\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "log_p_for_τ = integrate(diff(log_p, τ), τ)\n@show log_p_for_τ",
"execution_count": 21,
"outputs": [
{
"output_type": "stream",
"text": "log_p_for_τ = τ*(-Y1^2 + 2*Y1*μ - Y2^2 + 2*Y2*μ - Y3^2 + 2*Y3*μ - 2*b₀ - λ₀*μ^2 + 2*λ₀*μ*μ₀ - λ₀*μ₀^2 - 3*μ^2)/2 + (a₀ + 1)*log(τ)\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 21,
"data": {
"text/plain": " / 2 2 2 2 \nτ*\\- Y1 + 2*Y1*μ - Y2 + 2*Y2*μ - Y3 + 2*Y3*μ - 2*b₀ - λ₀*μ + 2*λ₀*μ*μ₀ - λ\n------------------------------------------------------------------------------\n 2 \n\n 2 2\\ \n₀*μ₀ - 3*μ / \n------------- + (a₀ + 1)*log(τ)\n ",
"text/latex": "\\begin{equation*}\\frac{τ \\left(- Y_{1}^{2} + 2 Y_{1} μ - Y_{2}^{2} + 2 Y_{2} μ - Y_{3}^{2} + 2 Y_{3} μ - 2 b₀ - λ₀ μ^{2} + 2 λ₀ μ μ₀ - λ₀ μ₀^{2} - 3 μ^{2}\\right)}{2} + \\left(a₀ + 1\\right) \\log{\\left (τ \\right )}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "expand(log_p_for_τ)",
"execution_count": 22,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 22,
"data": {
"text/plain": " 2 2 2 2 \n Y1 *τ Y2 *τ Y3 *τ λ₀*μ *\n- ----- + Y1*μ*τ - ----- + Y2*μ*τ - ----- + Y3*μ*τ + a₀*log(τ) - b₀*τ - ------\n 2 2 2 2 \n\n 2 2 \nτ λ₀*μ₀ *τ 3*μ *τ \n- + λ₀*μ*μ₀*τ - -------- - ------ + log(τ)\n 2 2 ",
"text/latex": "\\begin{equation*}- \\frac{Y_{1}^{2} τ}{2} + Y_{1} μ τ - \\frac{Y_{2}^{2} τ}{2} + Y_{2} μ τ - \\frac{Y_{3}^{2} τ}{2} + Y_{3} μ τ + a₀ \\log{\\left (τ \\right )} - b₀ τ - \\frac{λ₀ μ^{2} τ}{2} + λ₀ μ μ₀ τ - \\frac{λ₀ μ₀^{2} τ}{2} - \\frac{3 μ^{2} τ}{2} + \\log{\\left (τ \\right )}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "log_p_for_τ = collect(expand(log_p_for_τ), τ)",
"execution_count": 23,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 23,
"data": {
"text/plain": " / 2 2 2 2 \n | Y1 Y2 Y3 λ₀*μ \na₀*log(τ) + τ*|- --- + Y1*μ - --- + Y2*μ - --- + Y3*μ - b₀ - ----- + λ₀*μ*μ₀ -\n \\ 2 2 2 2 \n\n 2 2\\ \n λ₀*μ₀ 3*μ | \n ------ - ----| + log(τ)\n 2 2 / ",
"text/latex": "\\begin{equation*}a₀ \\log{\\left (τ \\right )} + τ \\left(- \\frac{Y_{1}^{2}}{2} + Y_{1} μ - \\frac{Y_{2}^{2}}{2} + Y_{2} μ - \\frac{Y_{3}^{2}}{2} + Y_{3} μ - b₀ - \\frac{λ₀ μ^{2}}{2} + λ₀ μ μ₀ - \\frac{λ₀ μ₀^{2}}{2} - \\frac{3 μ^{2}}{2}\\right) + \\log{\\left (τ \\right )}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "## できるところまで解析的に求める"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "### q1_μ"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "log_q1_μ = integrate(log_p_for_μ * p_τ, (τ, 0, oo))\n@show log_q1_μ",
"execution_count": 24,
"outputs": [
{
"output_type": "stream",
"text": "log_q1_μ = Y1*μ*gamma(a₀ + 1)/(b₀*gamma(a₀)) + Y2*μ*gamma(a₀ + 1)/(b₀*gamma(a₀)) + Y3*μ*gamma(a₀ + 1)/(b₀*gamma(a₀)) - λ₀*μ^2*gamma(a₀ + 1)/(2*b₀*gamma(a₀)) + λ₀*μ*μ₀*gamma(a₀ + 1)/(b₀*gamma(a₀)) - 3*μ^2*gamma(a₀ + 1)/(2*b₀*gamma(a₀))\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 24,
"data": {
"text/plain": " 2 \nY1*μ*Gamma(a₀ + 1) Y2*μ*Gamma(a₀ + 1) Y3*μ*Gamma(a₀ + 1) λ₀*μ *Gamma(a₀ \n------------------ + ------------------ + ------------------ - ---------------\n b₀*Gamma(a₀) b₀*Gamma(a₀) b₀*Gamma(a₀) 2*b₀*Gamma(a\n\n 2 \n+ 1) λ₀*μ*μ₀*Gamma(a₀ + 1) 3*μ *Gamma(a₀ + 1)\n---- + --------------------- - ------------------\n₀) b₀*Gamma(a₀) 2*b₀*Gamma(a₀) ",
"text/latex": "\\begin{equation*}\\frac{Y_{1} μ \\Gamma\\left(a₀ + 1\\right)}{b₀ \\Gamma\\left(a₀\\right)} + \\frac{Y_{2} μ \\Gamma\\left(a₀ + 1\\right)}{b₀ \\Gamma\\left(a₀\\right)} + \\frac{Y_{3} μ \\Gamma\\left(a₀ + 1\\right)}{b₀ \\Gamma\\left(a₀\\right)} - \\frac{λ₀ μ^{2} \\Gamma\\left(a₀ + 1\\right)}{2 b₀ \\Gamma\\left(a₀\\right)} + \\frac{λ₀ μ μ₀ \\Gamma\\left(a₀ + 1\\right)}{b₀ \\Gamma\\left(a₀\\right)} - \\frac{3 μ^{2} \\Gamma\\left(a₀ + 1\\right)}{2 b₀ \\Gamma\\left(a₀\\right)}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "log_q1_μ = collect(expand(log_q1_μ), μ)\n@show log_q1_μ",
"execution_count": 25,
"outputs": [
{
"output_type": "stream",
"text": "log_q1_μ = μ^2*(-λ₀*gamma(a₀ + 1)/(2*b₀*gamma(a₀)) - 3*gamma(a₀ + 1)/(2*b₀*gamma(a₀))) + μ*(Y1*gamma(a₀ + 1)/(b₀*gamma(a₀)) + Y2*gamma(a₀ + 1)/(b₀*gamma(a₀)) + Y3*gamma(a₀ + 1)/(b₀*gamma(a₀)) + λ₀*μ₀*gamma(a₀ + 1)/(b₀*gamma(a₀)))\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 25,
"data": {
"text/plain": " 2 / λ₀*Gamma(a₀ + 1) 3*Gamma(a₀ + 1)\\ /Y1*Gamma(a₀ + 1) Y2*Gamma(a₀ \nμ *|- ---------------- - ---------------| + μ*|---------------- + ------------\n \\ 2*b₀*Gamma(a₀) 2*b₀*Gamma(a₀)/ \\ b₀*Gamma(a₀) b₀*Gamma(a\n\n+ 1) Y3*Gamma(a₀ + 1) λ₀*μ₀*Gamma(a₀ + 1)\\\n---- + ---------------- + -------------------|\n₀) b₀*Gamma(a₀) b₀*Gamma(a₀) /",
"text/latex": "\\begin{equation*}μ^{2} \\left(- \\frac{λ₀ \\Gamma\\left(a₀ + 1\\right)}{2 b₀ \\Gamma\\left(a₀\\right)} - \\frac{3 \\Gamma\\left(a₀ + 1\\right)}{2 b₀ \\Gamma\\left(a₀\\right)}\\right) + μ \\left(\\frac{Y_{1} \\Gamma\\left(a₀ + 1\\right)}{b₀ \\Gamma\\left(a₀\\right)} + \\frac{Y_{2} \\Gamma\\left(a₀ + 1\\right)}{b₀ \\Gamma\\left(a₀\\right)} + \\frac{Y_{3} \\Gamma\\left(a₀ + 1\\right)}{b₀ \\Gamma\\left(a₀\\right)} + \\frac{λ₀ μ₀ \\Gamma\\left(a₀ + 1\\right)}{b₀ \\Gamma\\left(a₀\\right)}\\right)\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "q1_μ = exp(log_q1_μ)\nz1_μ = simplify(integrate(q1_μ, (μ, -oo, oo)))\n@show z1_μ",
"execution_count": 26,
"outputs": [
{
"output_type": "stream",
"text": "z1_μ = sqrt(2)*sqrt(pi)*sqrt(b₀)*exp(Y1^2*a₀/(2*b₀*(λ₀ + 3)) + Y1*Y2*a₀/(b₀*(λ₀ + 3)) + Y1*Y3*a₀/(b₀*(λ₀ + 3)) + Y1*a₀*λ₀*μ₀/(b₀*(λ₀ + 3)) + Y2^2*a₀/(2*b₀*(λ₀ + 3)) + Y2*Y3*a₀/(b₀*(λ₀ + 3)) + Y2*a₀*λ₀*μ₀/(b₀*(λ₀ + 3)) + Y3^2*a₀/(2*b₀*(λ₀ + 3)) + Y3*a₀*λ₀*μ₀/(b₀*(λ₀ + 3)) + a₀*λ₀^2*μ₀^2/(2*b₀*(λ₀ + 3)))/(sqrt(a₀)*sqrt(λ₀ + 3))\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 26,
"data": {
"text/plain": " 2 \n Y1 *a₀ Y1*Y2*a₀ Y1*Y3*a₀ Y1*a₀*λ₀*μ₀ \n ------------- + ----------- + ----------- + ----------- +\n ___ ____ ____ 2*b₀*(λ₀ + 3) b₀*(λ₀ + 3) b₀*(λ₀ + 3) b₀*(λ₀ + 3) \n\\/ 2 *\\/ pi *\\/ b₀ *e \n------------------------------------------------------------------------------\n __\n \\/ a\n\n 2 2 \n Y2 *a₀ Y2*Y3*a₀ Y2*a₀*λ₀*μ₀ Y3 *a₀ Y3*a₀*λ₀*μ₀ a\n ------------- + ----------- + ----------- + ------------- + ----------- + ---\n 2*b₀*(λ₀ + 3) b₀*(λ₀ + 3) b₀*(λ₀ + 3) 2*b₀*(λ₀ + 3) b₀*(λ₀ + 3) 2*b\n \n------------------------------------------------------------------------------\n__ ________ \n₀ *\\/ λ₀ + 3 \n\n 2 2 \n₀*λ₀ *μ₀ \n----------\n₀*(λ₀ + 3)\n \n----------\n \n ",
"text/latex": "\\begin{equation*}\\frac{\\sqrt{2} \\sqrt{\\pi} \\sqrt{b₀} e^{\\frac{Y_{1}^{2} a₀}{2 b₀ \\left(λ₀ + 3\\right)} + \\frac{Y_{1} Y_{2} a₀}{b₀ \\left(λ₀ + 3\\right)} + \\frac{Y_{1} Y_{3} a₀}{b₀ \\left(λ₀ + 3\\right)} + \\frac{Y_{1} a₀ λ₀ μ₀}{b₀ \\left(λ₀ + 3\\right)} + \\frac{Y_{2}^{2} a₀}{2 b₀ \\left(λ₀ + 3\\right)} + \\frac{Y_{2} Y_{3} a₀}{b₀ \\left(λ₀ + 3\\right)} + \\frac{Y_{2} a₀ λ₀ μ₀}{b₀ \\left(λ₀ + 3\\right)} + \\frac{Y_{3}^{2} a₀}{2 b₀ \\left(λ₀ + 3\\right)} + \\frac{Y_{3} a₀ λ₀ μ₀}{b₀ \\left(λ₀ + 3\\right)} + \\frac{a₀ λ₀^{2} μ₀^{2}}{2 b₀ \\left(λ₀ + 3\\right)}}}{\\sqrt{a₀} \\sqrt{λ₀ + 3}}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "q1_μ = 1/z1_μ * exp(log_q1_μ)\n@show q1_μ",
"execution_count": 27,
"outputs": [
{
"output_type": "stream",
"text": "q1_μ = sqrt(2)*sqrt(a₀)*sqrt(λ₀ + 3)*exp(μ^2*(-λ₀*gamma(a₀ + 1)/(2*b₀*gamma(a₀)) - 3*gamma(a₀ + 1)/(2*b₀*gamma(a₀))) + μ*(Y1*gamma(a₀ + 1)/(b₀*gamma(a₀)) + Y2*gamma(a₀ + 1)/(b₀*gamma(a₀)) + Y3*gamma(a₀ + 1)/(b₀*gamma(a₀)) + λ₀*μ₀*gamma(a₀ + 1)/(b₀*gamma(a₀))))*exp(-Y1^2*a₀/(2*b₀*(λ₀ + 3)) - Y1*Y2*a₀/(b₀*(λ₀ + 3)) - Y1*Y3*a₀/(b₀*(λ₀ + 3)) - Y1*a₀*λ₀*μ₀/(b₀*(λ₀ + 3)) - Y2^2*a₀/(2*b₀*(λ₀ + 3)) - Y2*Y3*a₀/(b₀*(λ₀ + 3)) - Y2*a₀*λ₀*μ₀/(b₀*(λ₀ + 3)) - Y3^2*a₀/(2*b₀*(λ₀ + 3)) - Y3*a₀*λ₀*μ₀/(b₀*(λ₀ + 3)) - a₀*λ₀^2*μ₀^2/(2*b₀*(λ₀ + 3)))/(2*sqrt(pi)*sqrt(b₀))\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 27,
"data": {
"text/plain": " \n 2 / λ₀*Gamma(a₀ + 1) 3*Gamma(a₀ + 1)\\ /Y1*Gam\n μ *|- ---------------- - ---------------| + μ*|------\n ___ ____ ________ \\ 2*b₀*Gamma(a₀) 2*b₀*Gamma(a₀)/ \\ b₀*G\n\\/ 2 *\\/ a₀ *\\/ λ₀ + 3 *e \n------------------------------------------------------------------------------\n \n \n\n \nma(a₀ + 1) Y2*Gamma(a₀ + 1) Y3*Gamma(a₀ + 1) λ₀*μ₀*Gamma(a₀ + 1)\\ \n---------- + ---------------- + ---------------- + -------------------| - ---\namma(a₀) b₀*Gamma(a₀) b₀*Gamma(a₀) b₀*Gamma(a₀) / 2*b\n *e \n------------------------------------------------------------------------------\n ____ ____\n 2*\\/ pi *\\/ b₀ \n\n 2 2 \n Y1 *a₀ Y1*Y2*a₀ Y1*Y3*a₀ Y1*a₀*λ₀*μ₀ Y2 *a₀ Y2*Y3\n---------- - ----------- - ----------- - ----------- - ------------- - -------\n₀*(λ₀ + 3) b₀*(λ₀ + 3) b₀*(λ₀ + 3) b₀*(λ₀ + 3) 2*b₀*(λ₀ + 3) b₀*(λ₀ \n \n------------------------------------------------------------------------------\n \n \n\n 2 2 2 \n*a₀ Y2*a₀*λ₀*μ₀ Y3 *a₀ Y3*a₀*λ₀*μ₀ a₀*λ₀ *μ₀ \n---- - ----------- - ------------- - ----------- - -------------\n+ 3) b₀*(λ₀ + 3) 2*b₀*(λ₀ + 3) b₀*(λ₀ + 3) 2*b₀*(λ₀ + 3)\n \n----------------------------------------------------------------\n \n ",
"text/latex": "\\begin{equation*}\\frac{\\sqrt{2} \\sqrt{a₀} \\sqrt{λ₀ + 3} e^{μ^{2} \\left(- \\frac{λ₀ \\Gamma\\left(a₀ + 1\\right)}{2 b₀ \\Gamma\\left(a₀\\right)} - \\frac{3 \\Gamma\\left(a₀ + 1\\right)}{2 b₀ \\Gamma\\left(a₀\\right)}\\right) + μ \\left(\\frac{Y_{1} \\Gamma\\left(a₀ + 1\\right)}{b₀ \\Gamma\\left(a₀\\right)} + \\frac{Y_{2} \\Gamma\\left(a₀ + 1\\right)}{b₀ \\Gamma\\left(a₀\\right)} + \\frac{Y_{3} \\Gamma\\left(a₀ + 1\\right)}{b₀ \\Gamma\\left(a₀\\right)} + \\frac{λ₀ μ₀ \\Gamma\\left(a₀ + 1\\right)}{b₀ \\Gamma\\left(a₀\\right)}\\right)} e^{- \\frac{Y_{1}^{2} a₀}{2 b₀ \\left(λ₀ + 3\\right)} - \\frac{Y_{1} Y_{2} a₀}{b₀ \\left(λ₀ + 3\\right)} - \\frac{Y_{1} Y_{3} a₀}{b₀ \\left(λ₀ + 3\\right)} - \\frac{Y_{1} a₀ λ₀ μ₀}{b₀ \\left(λ₀ + 3\\right)} - \\frac{Y_{2}^{2} a₀}{2 b₀ \\left(λ₀ + 3\\right)} - \\frac{Y_{2} Y_{3} a₀}{b₀ \\left(λ₀ + 3\\right)} - \\frac{Y_{2} a₀ λ₀ μ₀}{b₀ \\left(λ₀ + 3\\right)} - \\frac{Y_{3}^{2} a₀}{2 b₀ \\left(λ₀ + 3\\right)} - \\frac{Y_{3} a₀ λ₀ μ₀}{b₀ \\left(λ₀ + 3\\right)} - \\frac{a₀ λ₀^{2} μ₀^{2}}{2 b₀ \\left(λ₀ + 3\\right)}}}{2 \\sqrt{\\pi} \\sqrt{b₀}}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "### q1_τ (何も工夫せずに計算できてしまった！しかし非常に汚い)"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "log_q1_τ = integrate(log_p_for_τ * p_μ, (μ, -oo, oo))\n@show log_q1_τ",
"execution_count": 28,
"outputs": [
{
"output_type": "stream",
"text": "log_q1_τ = -Y1^2*τ/2 + Y1*μ₀*τ - Y2^2*τ/2 + Y2*μ₀*τ - Y3^2*τ/2 + Y3*μ₀*τ + a₀*log(τ) - b₀*τ - 3*μ₀^2*τ/2 + log(τ) - 1/2 - 3/(2*λ₀)\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 28,
"data": {
"text/plain": " 2 2 2 \n Y1 *τ Y2 *τ Y3 *τ 3*μ\n- ----- + Y1*μ₀*τ - ----- + Y2*μ₀*τ - ----- + Y3*μ₀*τ + a₀*log(τ) - b₀*τ - ---\n 2 2 2 \n\n 2 \n₀ *τ 1 3 \n---- + log(τ) - - - ----\n2 2 2*λ₀",
"text/latex": "\\begin{equation*}- \\frac{Y_{1}^{2} τ}{2} + Y_{1} μ₀ τ - \\frac{Y_{2}^{2} τ}{2} + Y_{2} μ₀ τ - \\frac{Y_{3}^{2} τ}{2} + Y_{3} μ₀ τ + a₀ \\log{\\left (τ \\right )} - b₀ τ - \\frac{3 μ₀^{2} τ}{2} + \\log{\\left (τ \\right )} - \\frac{1}{2} - \\frac{3}{2 λ₀}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "log_q1_τ = integrate(diff(log_q1_τ, τ), τ)\n@show log_q1_τ",
"execution_count": 29,
"outputs": [
{
"output_type": "stream",
"text": "log_q1_τ = τ*(-Y1^2 + 2*Y1*μ₀ - Y2^2 + 2*Y2*μ₀ - Y3^2 + 2*Y3*μ₀ - 2*b₀ - 3*μ₀^2)/2 + (a₀ + 1)*log(τ)\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 29,
"data": {
"text/plain": " / 2 2 2 2\\ \nτ*\\- Y1 + 2*Y1*μ₀ - Y2 + 2*Y2*μ₀ - Y3 + 2*Y3*μ₀ - 2*b₀ - 3*μ₀ / \n------------------------------------------------------------------ + (a₀ + 1)*\n 2 \n\n \n \nlog(τ)\n ",
"text/latex": "\\begin{equation*}\\frac{τ \\left(- Y_{1}^{2} + 2 Y_{1} μ₀ - Y_{2}^{2} + 2 Y_{2} μ₀ - Y_{3}^{2} + 2 Y_{3} μ₀ - 2 b₀ - 3 μ₀^{2}\\right)}{2} + \\left(a₀ + 1\\right) \\log{\\left (τ \\right )}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "log_q1_τ = collect(log_q1_τ, τ)\n@show log_q1_τ",
"execution_count": 30,
"outputs": [
{
"output_type": "stream",
"text": "log_q1_τ = τ*(-Y1^2/2 + Y1*μ₀ - Y2^2/2 + Y2*μ₀ - Y3^2/2 + Y3*μ₀ - b₀ - 3*μ₀^2/2) + (a₀ + 1)*log(τ)\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 30,
"data": {
"text/plain": " / 2 2 2 2\\ \n | Y1 Y2 Y3 3*μ₀ | \nτ*|- --- + Y1*μ₀ - --- + Y2*μ₀ - --- + Y3*μ₀ - b₀ - -----| + (a₀ + 1)*log(τ)\n \\ 2 2 2 2 / ",
"text/latex": "\\begin{equation*}τ \\left(- \\frac{Y_{1}^{2}}{2} + Y_{1} μ₀ - \\frac{Y_{2}^{2}}{2} + Y_{2} μ₀ - \\frac{Y_{3}^{2}}{2} + Y_{3} μ₀ - b₀ - \\frac{3 μ₀^{2}}{2}\\right) + \\left(a₀ + 1\\right) \\log{\\left (τ \\right )}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "q1_τ = logcombine(exp(log_q1_τ))\n@show q1_τ",
"execution_count": 31,
"outputs": [
{
"output_type": "stream",
"text": "q1_τ = τ^(a₀ + 1)*exp(τ*(-Y1^2/2 + Y1*μ₀ - Y2^2/2 + Y2*μ₀ - Y3^2/2 + Y3*μ₀ - b₀ - 3*μ₀^2/2))\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 31,
"data": {
"text/plain": " / 2 2 2 2\\\n | Y1 Y2 Y3 3*μ₀ |\n τ*|- --- + Y1*μ₀ - --- + Y2*μ₀ - --- + Y3*μ₀ - b₀ - -----|\n a₀ + 1 \\ 2 2 2 2 /\nτ *e ",
"text/latex": "\\begin{equation*}τ^{a₀ + 1} e^{τ \\left(- \\frac{Y_{1}^{2}}{2} + Y_{1} μ₀ - \\frac{Y_{2}^{2}}{2} + Y_{2} μ₀ - \\frac{Y_{3}^{2}}{2} + Y_{3} μ₀ - b₀ - \\frac{3 μ₀^{2}}{2}\\right)}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "z1_τ = integrate(q1_τ, (τ, 0, oo))\n@show z1_τ",
"execution_count": 32,
"outputs": [
{
"output_type": "stream",
"text": "z1_τ = Piecewise((2*(exp_polar(I*pi)*polar_lift(-Y1^2/2 + Y1*μ₀ - Y2^2/2 + Y2*μ₀ - Y3^2/2 + Y3*μ₀ - b₀ - 3*μ₀^2/2))^(-a₀ - 1)*gamma(a₀ + 2)/(Y1^2 - 2*Y1*μ₀ + Y2^2 - 2*Y2*μ₀ + Y3^2 - 2*Y3*μ₀ + 2*b₀ + 3*μ₀^2), pi/2 > Abs(arg(-Y1^2/2 + Y1*μ₀ - Y2^2/2 + Y2*μ₀ - Y3^2/2 + Y3*μ₀ - b₀ - 3*μ₀^2/2) + pi)), (Integral(τ^(a₀ + 1)*exp(τ*(-Y1^2/2 + Y1*μ₀ - Y2^2/2 + Y2*μ₀ - Y3^2/2 + Y3*μ₀ - b₀ - 3*μ₀^2/2)), (τ, 0, oo)), True))\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 32,
"data": {
"text/plain": "/ -\n| / / 2 2 2 2\\\\ \n| | I*pi | Y1 Y2 Y3 3*μ₀ || \n|2*|e *polar_lift|- --- + Y1*μ₀ - --- + Y2*μ₀ - --- + Y3*μ₀ - b₀ - -----|| \n| \\ \\ 2 2 2 2 // \n|-----------------------------------------------------------------------------\n| 2 2 2 \n| Y1 - 2*Y1*μ₀ + Y2 - 2*Y2*μ₀ + Y3 - 2*Y3*μ₀ + 2*b₀ + 3*μ\n| \n| oo \n< / \n| | \n| | / 2 2 2 \n| | | Y1 Y2 Y3 3\n| | τ*|- --- + Y1*μ₀ - --- + Y2*μ₀ - --- + Y3*μ₀ - b₀ - -\n| | a₀ + 1 \\ 2 2 2 \n| | τ *e \n| | \n| / \n| 0 \n\\ \n\na₀ - 1 \n \n \n *Gamma(a₀ + 2) | / 2 2 2 \n pi | | Y1 Y2 Y3 \n-------------------- for -- > |arg|- --- + Y1*μ₀ - --- + Y2*μ₀ - --- + Y3*μ₀ \n 2 2 | \\ 2 2 2 \n₀ \n \n \n \n \n 2\\ \n*μ₀ | \n----| \n 2 / \n dτ otherwise \n \n \n \n \n\n \n \n \n 2\\ |\n 3*μ₀ | |\n- b₀ - -----| + pi|\n 2 / |\n \n \n \n \n \n \n \n \n \n \n \n \n \n ",
"text/latex": "\\begin{equation*}\\begin{cases} \\frac{2 \\left(e^{i \\pi} \\operatorname{polar\\_lift}{\\left (- \\frac{Y_{1}^{2}}{2} + Y_{1} μ₀ - \\frac{Y_{2}^{2}}{2} + Y_{2} μ₀ - \\frac{Y_{3}^{2}}{2} + Y_{3} μ₀ - b₀ - \\frac{3 μ₀^{2}}{2} \\right )}\\right)^{- a₀ - 1} \\Gamma\\left(a₀ + 2\\right)}{Y_{1}^{2} - 2 Y_{1} μ₀ + Y_{2}^{2} - 2 Y_{2} μ₀ + Y_{3}^{2} - 2 Y_{3} μ₀ + 2 b₀ + 3 μ₀^{2}} & \\text{for}\\: \\frac{\\pi}{2} > \\left|{\\arg{\\left (- \\frac{Y_{1}^{2}}{2} + Y_{1} μ₀ - \\frac{Y_{2}^{2}}{2} + Y_{2} μ₀ - \\frac{Y_{3}^{2}}{2} + Y_{3} μ₀ - b₀ - \\frac{3 μ₀^{2}}{2} \\right )} + \\pi}\\right| \\\\\\int\\limits_{0}^{\\infty} τ^{a₀ + 1} e^{τ \\left(- \\frac{Y_{1}^{2}}{2} + Y_{1} μ₀ - \\frac{Y_{2}^{2}}{2} + Y_{2} μ₀ - \\frac{Y_{3}^{2}}{2} + Y_{3} μ₀ - b₀ - \\frac{3 μ₀^{2}}{2}\\right)}\\, dτ & \\text{otherwise} \\end{cases}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "**↑何も工夫せずに積分がそのまま計算できてしまった！** **しかし非常に汚い！**"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "q1_τ = 1/z1_τ * q1_τ\n@show q1_τ",
"execution_count": 33,
"outputs": [
{
"output_type": "stream",
"text": "q1_τ = τ^(a₀ + 1)*Piecewise(((exp_polar(I*pi)*polar_lift(-Y1^2/2 + Y1*μ₀ - Y2^2/2 + Y2*μ₀ - Y3^2/2 + Y3*μ₀ - b₀ - 3*μ₀^2/2))^(a₀ + 1)*(Y1^2 - 2*Y1*μ₀ + Y2^2 - 2*Y2*μ₀ + Y3^2 - 2*Y3*μ₀ + 2*b₀ + 3*μ₀^2)/(2*gamma(a₀ + 2)), pi/2 > Abs(arg(-Y1^2/2 + Y1*μ₀ - Y2^2/2 + Y2*μ₀ - Y3^2/2 + Y3*μ₀ - b₀ - 3*μ₀^2/2) + pi)), (1/Integral(τ^(a₀ + 1)*exp(τ*(-Y1^2/2 + Y1*μ₀ - Y2^2/2 + Y2*μ₀ - Y3^2/2 + Y3*μ₀ - b₀ - 3*μ₀^2/2)), (τ, 0, oo)), True))*exp(τ*(-Y1^2/2 + Y1*μ₀ - Y2^2/2 + Y2*μ₀ - Y3^2/2 + Y3*μ₀ - b₀ - 3*μ₀^2/2))\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 33,
"data": {
"text/plain": " // \n ||/ / 2 2 2 \n ||| I*pi | Y1 Y2 Y3 3\n |||e *polar_lift|- --- + Y1*μ₀ - --- + Y2*μ₀ - --- + Y3*μ₀ - b₀ - -\n ||\\ \\ 2 2 2 \n ||--------------------------------------------------------------------\n || 2*Ga\n || \n || \n a₀ + 1 || ----------------------------------\nτ *|< oo \n || / \n || | \n || | / 2 \n || | | Y1 Y2\n || | τ*|- --- + Y1*μ₀ - --\n || | a₀ + 1 \\ 2 2\n || | τ *e \n || | \n || / \n \\\\ 0 \n\n a₀ + 1 \n 2\\\\ \n*μ₀ || / 2 2 2 2\\ \n----|| *\\Y1 - 2*Y1*μ₀ + Y2 - 2*Y2*μ₀ + Y3 - 2*Y3*μ₀ + 2*b₀ + 3*μ₀ / \n 2 // \n--------------------------------------------------------------------------- f\nmma(a₀ + 2) \n \n 1 \n---------------------------------------- \n \n \n \n2 2 2\\ \n Y3 3*μ₀ | \n- + Y2*μ₀ - --- + Y3*μ₀ - b₀ - -----| \n 2 2 / \n dτ \n \n \n \n\n \\ \n | \n | \n | / 2 2 2 2\\ || \n pi | | Y1 Y2 Y3 3*μ₀ | || \nor -- > |arg|- --- + Y1*μ₀ - --- + Y2*μ₀ - --- + Y3*μ₀ - b₀ - -----| + pi|| \n 2 | \\ 2 2 2 2 / || \n | \n | τ\n otherwise | \n |*e \n | \n | \n | \n | \n | \n | \n | \n | \n | \n / \n\n \n \n \n \n \n \n / 2 2 2 2\\\n | Y1 Y2 Y3 3*μ₀ |\n*|- --- + Y1*μ₀ - --- + Y2*μ₀ - --- + Y3*μ₀ - b₀ - -----|\n \\ 2 2 2 2 /\n \n \n \n \n \n \n \n \n \n \n ",
"text/latex": "\\begin{equation*}τ^{a₀ + 1} \\left(\\begin{cases} \\frac{\\left(e^{i \\pi} \\operatorname{polar\\_lift}{\\left (- \\frac{Y_{1}^{2}}{2} + Y_{1} μ₀ - \\frac{Y_{2}^{2}}{2} + Y_{2} μ₀ - \\frac{Y_{3}^{2}}{2} + Y_{3} μ₀ - b₀ - \\frac{3 μ₀^{2}}{2} \\right )}\\right)^{a₀ + 1} \\left(Y_{1}^{2} - 2 Y_{1} μ₀ + Y_{2}^{2} - 2 Y_{2} μ₀ + Y_{3}^{2} - 2 Y_{3} μ₀ + 2 b₀ + 3 μ₀^{2}\\right)}{2 \\Gamma\\left(a₀ + 2\\right)} & \\text{for}\\: \\frac{\\pi}{2} > \\left|{\\arg{\\left (- \\frac{Y_{1}^{2}}{2} + Y_{1} μ₀ - \\frac{Y_{2}^{2}}{2} + Y_{2} μ₀ - \\frac{Y_{3}^{2}}{2} + Y_{3} μ₀ - b₀ - \\frac{3 μ₀^{2}}{2} \\right )} + \\pi}\\right| \\\\\\frac{1}{\\int\\limits_{0}^{\\infty} τ^{a₀ + 1} e^{τ \\left(- \\frac{Y_{1}^{2}}{2} + Y_{1} μ₀ - \\frac{Y_{2}^{2}}{2} + Y_{2} μ₀ - \\frac{Y_{3}^{2}}{2} + Y_{3} μ₀ - b₀ - \\frac{3 μ₀^{2}}{2}\\right)}\\, dτ} & \\text{otherwise} \\end{cases}\\right) e^{τ \\left(- \\frac{Y_{1}^{2}}{2} + Y_{1} μ₀ - \\frac{Y_{2}^{2}}{2} + Y_{2} μ₀ - \\frac{Y_{3}^{2}}{2} + Y_{3} μ₀ - b₀ - \\frac{3 μ₀^{2}}{2}\\right)}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "### 変数変換をして再計算\n\n計算できたが, 出力汚な過ぎるので, $\\mu_0=0$, $Y_i=T_i>0$ と置いてやり直してみる."
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "q2_τ = logcombine(exp(log_q1_τ))\n@show q2_τ",
"execution_count": 34,
"outputs": [
{
"output_type": "stream",
"text": "q2_τ = τ^(a₀ + 1)*exp(τ*(-Y1^2/2 + Y1*μ₀ - Y2^2/2 + Y2*μ₀ - Y3^2/2 + Y3*μ₀ - b₀ - 3*μ₀^2/2))\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 34,
"data": {
"text/plain": " / 2 2 2 2\\\n | Y1 Y2 Y3 3*μ₀ |\n τ*|- --- + Y1*μ₀ - --- + Y2*μ₀ - --- + Y3*μ₀ - b₀ - -----|\n a₀ + 1 \\ 2 2 2 2 /\nτ *e ",
"text/latex": "\\begin{equation*}τ^{a₀ + 1} e^{τ \\left(- \\frac{Y_{1}^{2}}{2} + Y_{1} μ₀ - \\frac{Y_{2}^{2}}{2} + Y_{2} μ₀ - \\frac{Y_{3}^{2}}{2} + Y_{3} μ₀ - b₀ - \\frac{3 μ₀^{2}}{2}\\right)}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "q2_0_τ = subs(q2_τ, (μ₀, 0), zip(Y,T)...)",
"execution_count": 35,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 35,
"data": {
"text/plain": " / 2 2 2 \\\n | T1 T2 T3 |\n τ*|- --- - --- - --- - b₀|\n a₀ + 1 \\ 2 2 2 /\nτ *e ",
"text/latex": "\\begin{equation*}τ^{a₀ + 1} e^{τ \\left(- \\frac{T_{1}^{2}}{2} - \\frac{T_{2}^{2}}{2} - \\frac{T_{3}^{2}}{2} - b₀\\right)}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "z2_0_τ = integrate(q2_0_τ, (τ, 0, oo))\n@show z2_0_τ",
"execution_count": 36,
"outputs": [
{
"output_type": "stream",
"text": "z2_0_τ = (T3^2/(2*(T1^2/2 + T2^2/2 + b₀)) + 1)^(-a₀ - 2)*(T1^2/2 + T2^2/2 + b₀)^(-a₀ - 1)*gamma(a₀ + 2)/(T1^2/2 + T2^2/2 + b₀)\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 36,
"data": {
"text/plain": " -a₀ - 2 -a₀ - 1 \n/ 2 \\ / 2 2 \\ \n| T3 | |T1 T2 | \n|------------------ + 1| *|--- + --- + b₀| *Gamma(a₀ + 2)\n| / 2 2 \\ | \\ 2 2 / \n| |T1 T2 | | \n|2*|--- + --- + b₀| | \n\\ \\ 2 2 / / \n---------------------------------------------------------------------\n 2 2 \n T1 T2 \n --- + --- + b₀ \n 2 2 ",
"text/latex": "\\begin{equation*}\\frac{\\left(\\frac{T_{3}^{2}}{2 \\left(\\frac{T_{1}^{2}}{2} + \\frac{T_{2}^{2}}{2} + b₀\\right)} + 1\\right)^{- a₀ - 2} \\left(\\frac{T_{1}^{2}}{2} + \\frac{T_{2}^{2}}{2} + b₀\\right)^{- a₀ - 1} \\Gamma\\left(a₀ + 2\\right)}{\\frac{T_{1}^{2}}{2} + \\frac{T_{2}^{2}}{2} + b₀}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "z2_0_τ = simplify(z2_0_τ)\n@show z2_0_τ",
"execution_count": 37,
"outputs": [
{
"output_type": "stream",
"text": "z2_0_τ = 2^(a₀ + 2)*(T1^2 + T2^2 + T3^2 + 2*b₀)^(-a₀ - 2)*gamma(a₀ + 2)\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 37,
"data": {
"text/plain": " -a₀ - 2 \n a₀ + 2 / 2 2 2 \\ \n2 *\\T1 + T2 + T3 + 2*b₀/ *Gamma(a₀ + 2)",
"text/latex": "\\begin{equation*}2^{a₀ + 2} \\left(T_{1}^{2} + T_{2}^{2} + T_{3}^{2} + 2 b₀\\right)^{- a₀ - 2} \\Gamma\\left(a₀ + 2\\right)\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "q2_0_τ = 1/z2_0_τ * q2_0_τ\n@show q2_0_τ",
"execution_count": 38,
"outputs": [
{
"output_type": "stream",
"text": "q2_0_τ = 2^(-a₀ - 2)*τ^(a₀ + 1)*(T1^2 + T2^2 + T3^2 + 2*b₀)^(a₀ + 2)*exp(τ*(-T1^2/2 - T2^2/2 - T3^2/2 - b₀))/gamma(a₀ + 2)\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 38,
"data": {
"text/plain": " / 2 2 2 \\\n | T1 T2 T3 |\n a₀ + 2 τ*|- --- - --- - --- - b₀|\n -a₀ - 2 a₀ + 1 / 2 2 2 \\ \\ 2 2 2 /\n2 *τ *\\T1 + T2 + T3 + 2*b₀/ *e \n---------------------------------------------------------------------------\n Gamma(a₀ + 2) ",
"text/latex": "\\begin{equation*}\\frac{2^{- a₀ - 2} τ^{a₀ + 1} \\left(T_{1}^{2} + T_{2}^{2} + T_{3}^{2} + 2 b₀\\right)^{a₀ + 2} e^{τ \\left(- \\frac{T_{1}^{2}}{2} - \\frac{T_{2}^{2}}{2} - \\frac{T_{3}^{2}}{2} - b₀\\right)}}{\\Gamma\\left(a₀ + 2\\right)}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "### q1_τ の計算に再挑戦"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "q1_τ = logcombine(exp(log_q1_τ))\ndisplay(q1_τ)",
"execution_count": 39,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": " / 2 2 2 2\\\n | Y1 Y2 Y3 3*μ₀ |\n τ*|- --- + Y1*μ₀ - --- + Y2*μ₀ - --- + Y3*μ₀ - b₀ - -----|\n a₀ + 1 \\ 2 2 2 2 /\nτ *e ",
"text/latex": "\\begin{equation*}τ^{a₀ + 1} e^{τ \\left(- \\frac{Y_{1}^{2}}{2} + Y_{1} μ₀ - \\frac{Y_{2}^{2}}{2} + Y_{2} μ₀ - \\frac{Y_{3}^{2}}{2} + Y_{3} μ₀ - b₀ - \\frac{3 μ₀^{2}}{2}\\right)}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "coef = coeff(collect(log_q1_τ, τ), τ)\ndisplay(coef)\n\nsol = solve(diff(coef, Y[1]), Y[1])[1]\ndisplay(sol) #-> μ₀\n\nreplacements = [(var, sol) for var in Y]\ndisplay(subs(coef, replacements...)) #-> -b₀",
"execution_count": 40,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": " 2 2 2 2\n Y1 Y2 Y3 3*μ₀ \n- --- + Y1*μ₀ - --- + Y2*μ₀ - --- + Y3*μ₀ - b₀ - -----\n 2 2 2 2 ",
"text/latex": "\\begin{equation*}- \\frac{Y_{1}^{2}}{2} + Y_{1} μ₀ - \\frac{Y_{2}^{2}}{2} + Y_{2} μ₀ - \\frac{Y_{3}^{2}}{2} + Y_{3} μ₀ - b₀ - \\frac{3 μ₀^{2}}{2}\\end{equation*}"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": "μ₀",
"text/latex": "\\begin{equation*}μ₀\\end{equation*}"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": "-b₀",
"text/latex": "\\begin{equation*}- b₀\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "ξ = symbols(\"ξ\", positive=true)\nz1_τ = simplify(integrate(τ^(a₀+1)*exp(-ξ*τ), (τ, 0, oo)))\nz1_τ = subs(z1_τ, (ξ, -coef))\n@show z1_τ",
"execution_count": 41,
"outputs": [
{
"output_type": "stream",
"text": "z1_τ = (Y1^2/2 - Y1*μ₀ + Y2^2/2 - Y2*μ₀ + Y3^2/2 - Y3*μ₀ + b₀ + 3*μ₀^2/2)^(-a₀ - 2)*gamma(a₀ + 2)\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 41,
"data": {
"text/plain": " -a₀ - 2 \n/ 2 2 2 2\\ \n|Y1 Y2 Y3 3*μ₀ | \n|--- - Y1*μ₀ + --- - Y2*μ₀ + --- - Y3*μ₀ + b₀ + -----| *Gamma(a₀ + 2)\n\\ 2 2 2 2 / ",
"text/latex": "\\begin{equation*}\\left(\\frac{Y_{1}^{2}}{2} - Y_{1} μ₀ + \\frac{Y_{2}^{2}}{2} - Y_{2} μ₀ + \\frac{Y_{3}^{2}}{2} - Y_{3} μ₀ + b₀ + \\frac{3 μ₀^{2}}{2}\\right)^{- a₀ - 2} \\Gamma\\left(a₀ + 2\\right)\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "q1_τ = 1/z1_τ * q1_τ\nq1_τ",
"execution_count": 42,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 42,
"data": {
"text/plain": " / 2\n a₀ + 2 | Y1 \n / 2 2 2 2\\ τ*|- ---\n a₀ + 1 |Y1 Y2 Y3 3*μ₀ | \\ 2 \nτ *|--- - Y1*μ₀ + --- - Y2*μ₀ + --- - Y3*μ₀ + b₀ + -----| *e \n \\ 2 2 2 2 / \n------------------------------------------------------------------------------\n Gamma(a₀ + 2) \n\n 2 2 2\\\n Y2 Y3 3*μ₀ |\n + Y1*μ₀ - --- + Y2*μ₀ - --- + Y3*μ₀ - b₀ - -----|\n 2 2 2 /\n \n \n--------------------------------------------------\n ",
"text/latex": "\\begin{equation*}\\frac{τ^{a₀ + 1} \\left(\\frac{Y_{1}^{2}}{2} - Y_{1} μ₀ + \\frac{Y_{2}^{2}}{2} - Y_{2} μ₀ + \\frac{Y_{3}^{2}}{2} - Y_{3} μ₀ + b₀ + \\frac{3 μ₀^{2}}{2}\\right)^{a₀ + 2} e^{τ \\left(- \\frac{Y_{1}^{2}}{2} + Y_{1} μ₀ - \\frac{Y_{2}^{2}}{2} + Y_{2} μ₀ - \\frac{Y_{3}^{2}}{2} + Y_{3} μ₀ - b₀ - \\frac{3 μ₀^{2}}{2}\\right)}}{\\Gamma\\left(a₀ + 2\\right)}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "## 数値的に求める"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "data = [1.1, 1.0, 1.3]\nreplacements = [(a₀, 1.0), (b₀, 1.0), (μ₀, 0.0), (λ₀, 1.0), zip(Y,data)...]",
"execution_count": 43,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 43,
"data": {
"text/plain": "7-element Array{Tuple{Sym,Float64},1}:\n (a₀, 1.0)\n (b₀, 1.0)\n (μ₀, 0.0)\n (λ₀, 1.0)\n (Y1, 1.1)\n (Y2, 1.0)\n (Y3, 1.3)"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "log_p_for_μ_subs = subs(log_p_for_μ, replacements...)\nlog_p_for_τ_subs = subs(log_p_for_τ, replacements...)\n[log_p_for_μ_subs, log_p_for_τ_subs]",
"execution_count": 44,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 44,
"data": {
"text/plain": "2-element Array{Sym,1}:\n -2.0*μ^2*τ + 3.4*μ*τ\n τ*(-2.0*μ^2 + 3.4*μ - 2.95) + 2.0*log(τ)",
"text/latex": "\\[ \\left[ \\begin{array}{r}- 2.0 μ^{2} τ + 3.4 μ τ\\\\τ \\left(- 2.0 μ^{2} + 3.4 μ - 2.95\\right) + 2.0 \\log{\\left (τ \\right )}\\end{array} \\right] \\]"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "q_τ = N(subs(p_τ, replacements...))\nq_τ",
"execution_count": 45,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 45,
"data": {
"text/plain": " -1.0*τ\n1.0*e ",
"text/latex": "\\begin{equation*}1.0 e^{- 1.0 τ}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "q_μ = Sym(1)\nfor i in 1:7\n log_q_μ = N(integrate(log_p_for_μ_subs * q_τ, (τ, 0, oo)))\n z_q_μ = N(integrate(exp(log_q_μ), (μ, -oo, oo)))\n q_μ = 1/z_q_μ * exp(log_q_μ)\n\n log_q_τ = N(integrate(log_p_for_τ_subs * q_μ, (μ, -oo, oo))(π=>float(π))) # (π=>float(π) が必要なのはちょっと嫌)\n z_q_τ = N(integrate(exp(log_q_τ), (τ, 0, oo)))\n q_τ = 1/z_q_τ * exp(log_q_τ)\n\n display([q_μ, q_τ])\nend",
"execution_count": 46,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "2-element Array{Sym,1}:\n 0.188098154753774*exp(-2.0*μ^2 + 3.4*μ)\n 4.03007506250001*τ^2.0*exp(-2.005*τ)",
"text/latex": "\\[ \\left[ \\begin{array}{r}0.188098154753774 e^{- 2.0 μ^{2} + 3.4 μ}\\\\4.03007506250001 τ^{2.0} e^{- 2.005 τ}\\end{array} \\right] \\]"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": "2-element Array{Sym,1}:\n 0.112320150163227*exp(-2.99251870324189*μ^2 + 5.08728179551122*μ)\n 3.11052191637731*τ^2.0*exp(-1.83916666666667*τ)",
"text/latex": "\\[ \\left[ \\begin{array}{r}0.112320150163227 e^{- 2.99251870324189 μ^{2} + 5.08728179551122 μ}\\\\3.11052191637731 τ^{2.0} e^{- 1.83916666666667 τ}\\end{array} \\right] \\]"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": "2-element Array{Sym,1}:\n 0.0965024138432034*exp(-3.26234707748074*μ^2 + 5.54599003171727*μ)\n 2.97238456804457*τ^2.0*exp(-1.81152777777778*τ)",
"text/latex": "\\[ \\left[ \\begin{array}{r}0.0965024138432034 e^{- 3.26234707748074 μ^{2} + 5.54599003171727 μ}\\\\2.97238456804457 τ^{2.0} e^{- 1.81152777777778 τ}\\end{array} \\right] \\]"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": "2-element Array{Sym,1}:\n 0.0938011432750369*exp(-3.31212144445296*μ^2 + 5.63060645557004*μ)\n 2.94976700750461*τ^2.0*exp(-1.8069212962963*τ)",
"text/latex": "\\[ \\left[ \\begin{array}{r}0.0938011432750369 e^{- 3.31212144445296 μ^{2} + 5.63060645557004 μ}\\\\2.94976700750461 τ^{2.0} e^{- 1.8069212962963 τ}\\end{array} \\right] \\]"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": "2-element Array{Sym,1}:\n 0.0933494031271016*exp(-3.32056521349236*μ^2 + 5.64496086293701*μ)\n 2.94600860516469*τ^2.0*exp(-1.80615354938272*τ)",
"text/latex": "\\[ \\left[ \\begin{array}{r}0.0933494031271016 e^{- 3.32056521349236 μ^{2} + 5.64496086293701 μ}\\\\2.94600860516469 τ^{2.0} e^{- 1.80615354938272 τ}\\end{array} \\right] \\]"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": "2-element Array{Sym,1}:\n 0.0932740721319143*exp(-3.32197669575248*μ^2 + 5.64736038277921*μ)\n 2.94538251532282*τ^2.0*exp(-1.80602559156379*τ)",
"text/latex": "\\[ \\left[ \\begin{array}{r}0.0932740721319143 e^{- 3.32197669575248 μ^{2} + 5.64736038277921 μ}\\\\2.94538251532282 τ^{2.0} e^{- 1.80602559156379 τ}\\end{array} \\right] \\]"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": "2-element Array{Sym,1}:\n 0.0932615158350226*exp(-3.32221205946743*μ^2 + 5.64776050109463*μ)\n 2.94527817564072*τ^2.0*exp(-1.80600426526063*τ)",
"text/latex": "\\[ \\left[ \\begin{array}{r}0.0932615158350226 e^{- 3.32221205946743 μ^{2} + 5.64776050109463 μ}\\\\2.94527817564072 τ^{2.0} e^{- 1.80600426526063 τ}\\end{array} \\right] \\]"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "q_μ*q_τ",
"execution_count": 47,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 47,
"data": {
"text/plain": " 2 \n 2.0 -1.80600426526063*τ - 3.32221205946743*μ + 5.6477605\n0.274681107216063*τ *e *e \n\n \n0109463*μ\n ",
"text/latex": "\\begin{equation*}0.274681107216063 τ^{2.0} e^{- 1.80600426526063 τ} e^{- 3.32221205946743 μ^{2} + 5.64776050109463 μ}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "julia_code(q_μ*q_τ)",
"execution_count": 48,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 48,
"data": {
"text/plain": "\"0.274681107216063*τ.^2.0.*exp(-1.80600426526063*τ).*exp(-3.32221205946743*μ.^2 + 5.64776050109463*μ)\""
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "\"$(q_μ*q_τ)\"",
"execution_count": 49,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 49,
"data": {
"text/plain": "\"0.274681107216063*τ^2.0*exp(-1.80600426526063*τ)*exp(-3.32221205946743*μ^2 + 5.64776050109463*μ)\""
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "delta = 0.05\nμs = -0.4:delta:2.0\nτs = 0.0:delta:5.5\n\neval(parse(\"f(μ,τ) = $(q_μ*q_τ)\"))\n@time c_f = f.(μs', τs);",
"execution_count": 50,
"outputs": [
{
"output_type": "stream",
"text": " 0.195528 seconds (718.20 k allocations: 35.829 MiB, 5.98% gc time)\n",
"name": "stdout"
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "figure(figsize=(5,4))\nCS = contour(μs, τs, c_f)\nclabel(CS, inline=1, fontsize=10)\nxlabel(\"μ\")\nylabel(\"τ\")\ngrid(ls=\":\")",
"execution_count": 51,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "Figure(PyObject <Figure size 500x400 with 1 Axes>)",
"image/png": 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"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "figure(figsize=(6.4, 4))\npcolormesh(μs, τs, c_f, cmap=\"CMRmap\")\ncolorbar()\nxlabel(\"μ\")\nylabel(\"τ\")\ngrid(ls=\":\")",
"execution_count": 52,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "Figure(PyObject <Figure size 640x400 with 2 Axes>)",
"image/png": 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"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "## 変分近似無しの計算"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "### 分配函数の計算"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "p3 = simplify(exp(log_p))",
"execution_count": 53,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 53,
"data": {
"text/plain": " / 2 2 2 2 \n | Y1 Y2 Y3 λ₀*μ \n τ*|- --- + Y1*μ - --- + Y2*μ - --- + Y3*μ - b₀ - ----- + \n a₀ ____ a₀ + 1 \\ 2 2 2 2 \nb₀ *\\/ λ₀ *τ *e \n------------------------------------------------------------------------------\n 2 \n 4*pi *Gamma(a₀) \n\n 2 2\\\n λ₀*μ₀ 3*μ |\nλ₀*μ*μ₀ - ------ - ----|\n 2 2 /\n \n------------------------\n \n ",
"text/latex": "\\begin{equation*}\\frac{b₀^{a₀} \\sqrt{λ₀} τ^{a₀ + 1} e^{τ \\left(- \\frac{Y_{1}^{2}}{2} + Y_{1} μ - \\frac{Y_{2}^{2}}{2} + Y_{2} μ - \\frac{Y_{3}^{2}}{2} + Y_{3} μ - b₀ - \\frac{λ₀ μ^{2}}{2} + λ₀ μ μ₀ - \\frac{λ₀ μ₀^{2}}{2} - \\frac{3 μ^{2}}{2}\\right)}}{4 \\pi^{2} \\Gamma\\left(a₀\\right)}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "Z3_μ = integrate(p3, (μ, -oo, oo))\nZ3_μ = simplify(Z3_μ)",
"execution_count": 54,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 54,
"data": {
"text/plain": " / 2 2 \n | Y1 Y1 Y1*Y2 Y1*Y3 Y1*λ₀*μ\n τ*|- --- + ---------- + ------ + ------ + -------\n ___ a₀ ____ a₀ + 1/2 \\ 2 2*(λ₀ + 3) λ₀ + 3 λ₀ + 3 λ₀ + 3\n\\/ 2 *b₀ *\\/ λ₀ *τ *e \n------------------------------------------------------------------------------\n \n 4*pi\n\n 2 2 2 2 \n₀ Y2 Y2 Y2*Y3 Y2*λ₀*μ₀ Y3 Y3 Y3*λ₀*μ₀ \n- - --- + ---------- + ------ + -------- - --- + ---------- + -------- - b₀ + \n 2 2*(λ₀ + 3) λ₀ + 3 λ₀ + 3 2 2*(λ₀ + 3) λ₀ + 3 \n \n------------------------------------------------------------------------------\n3/2 ________ \n *\\/ λ₀ + 3 *Gamma(a₀) \n\n 2 2 2\\\n λ₀ *μ₀ λ₀*μ₀ |\n---------- - ------|\n2*(λ₀ + 3) 2 /\n \n--------------------\n \n ",
"text/latex": "\\begin{equation*}\\frac{\\sqrt{2} b₀^{a₀} \\sqrt{λ₀} τ^{a₀ + \\frac{1}{2}} e^{τ \\left(- \\frac{Y_{1}^{2}}{2} + \\frac{Y_{1}^{2}}{2 \\left(λ₀ + 3\\right)} + \\frac{Y_{1} Y_{2}}{λ₀ + 3} + \\frac{Y_{1} Y_{3}}{λ₀ + 3} + \\frac{Y_{1} λ₀ μ₀}{λ₀ + 3} - \\frac{Y_{2}^{2}}{2} + \\frac{Y_{2}^{2}}{2 \\left(λ₀ + 3\\right)} + \\frac{Y_{2} Y_{3}}{λ₀ + 3} + \\frac{Y_{2} λ₀ μ₀}{λ₀ + 3} - \\frac{Y_{3}^{2}}{2} + \\frac{Y_{3}^{2}}{2 \\left(λ₀ + 3\\right)} + \\frac{Y_{3} λ₀ μ₀}{λ₀ + 3} - b₀ + \\frac{λ₀^{2} μ₀^{2}}{2 \\left(λ₀ + 3\\right)} - \\frac{λ₀ μ₀^{2}}{2}\\right)}}{4 \\pi^{\\frac{3}{2}} \\sqrt{λ₀ + 3} \\Gamma\\left(a₀\\right)}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "F3_μ = expand(-log(Z3_μ))",
"execution_count": 55,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 55,
"data": {
"text/plain": " 2 2 2 2 \nY1 *τ Y1 *τ Y1*Y2*τ Y1*Y3*τ Y1*λ₀*μ₀*τ Y2 *τ Y2 *τ Y2*\n----- - ---------- - ------- - ------- - ---------- + ----- - ---------- - ---\n 2 2*(λ₀ + 3) λ₀ + 3 λ₀ + 3 λ₀ + 3 2 2*(λ₀ + 3) λ₀\n\n 2 2 \nY3*τ Y2*λ₀*μ₀*τ Y3 *τ Y3 *τ Y3*λ₀*μ₀*τ \n---- - ---------- + ----- - ---------- - ---------- - a₀*log(b₀) - a₀*log(τ) +\n + 3 λ₀ + 3 2 2*(λ₀ + 3) λ₀ + 3 \n\n 2 2 2 \n λ₀ *μ₀ *τ λ₀*μ₀ *τ log(λ₀) log(τ) log(λ₀ + 3) \n b₀*τ - ---------- + -------- - ------- - ------ + ----------- + log(Gamma(a₀)\n 2*(λ₀ + 3) 2 2 2 2 \n\n \n 3*log(2) 3*log(pi)\n) + -------- + ---------\n 2 2 ",
"text/latex": "\\begin{equation*}\\frac{Y_{1}^{2} τ}{2} - \\frac{Y_{1}^{2} τ}{2 \\left(λ₀ + 3\\right)} - \\frac{Y_{1} Y_{2} τ}{λ₀ + 3} - \\frac{Y_{1} Y_{3} τ}{λ₀ + 3} - \\frac{Y_{1} λ₀ μ₀ τ}{λ₀ + 3} + \\frac{Y_{2}^{2} τ}{2} - \\frac{Y_{2}^{2} τ}{2 \\left(λ₀ + 3\\right)} - \\frac{Y_{2} Y_{3} τ}{λ₀ + 3} - \\frac{Y_{2} λ₀ μ₀ τ}{λ₀ + 3} + \\frac{Y_{3}^{2} τ}{2} - \\frac{Y_{3}^{2} τ}{2 \\left(λ₀ + 3\\right)} - \\frac{Y_{3} λ₀ μ₀ τ}{λ₀ + 3} - a₀ \\log{\\left (b₀ \\right )} - a₀ \\log{\\left (τ \\right )} + b₀ τ - \\frac{λ₀^{2} μ₀^{2} τ}{2 \\left(λ₀ + 3\\right)} + \\frac{λ₀ μ₀^{2} τ}{2} - \\frac{\\log{\\left (λ₀ \\right )}}{2} - \\frac{\\log{\\left (τ \\right )}}{2} + \\frac{\\log{\\left (λ₀ + 3 \\right )}}{2} + \\log{\\left (\\Gamma\\left(a₀\\right) \\right )} + \\frac{3 \\log{\\left (2 \\right )}}{2} + \\frac{3 \\log{\\left (\\pi \\right )}}{2}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "coef = coeff(collect(F3_μ, τ), τ)",
"execution_count": 56,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 56,
"data": {
"text/plain": " 2 2 2 2 \nY1 Y1 Y1*Y2 Y1*Y3 Y1*λ₀*μ₀ Y2 Y2 Y2*Y3 Y2\n--- - ---------- - ------ - ------ - -------- + --- - ---------- - ------ - --\n 2 2*(λ₀ + 3) λ₀ + 3 λ₀ + 3 λ₀ + 3 2 2*(λ₀ + 3) λ₀ + 3 λ\n\n 2 2 2 2 2\n*λ₀*μ₀ Y3 Y3 Y3*λ₀*μ₀ λ₀ *μ₀ λ₀*μ₀ \n------ + --- - ---------- - -------- + b₀ - ---------- + ------\n₀ + 3 2 2*(λ₀ + 3) λ₀ + 3 2*(λ₀ + 3) 2 ",
"text/latex": "\\begin{equation*}\\frac{Y_{1}^{2}}{2} - \\frac{Y_{1}^{2}}{2 \\left(λ₀ + 3\\right)} - \\frac{Y_{1} Y_{2}}{λ₀ + 3} - \\frac{Y_{1} Y_{3}}{λ₀ + 3} - \\frac{Y_{1} λ₀ μ₀}{λ₀ + 3} + \\frac{Y_{2}^{2}}{2} - \\frac{Y_{2}^{2}}{2 \\left(λ₀ + 3\\right)} - \\frac{Y_{2} Y_{3}}{λ₀ + 3} - \\frac{Y_{2} λ₀ μ₀}{λ₀ + 3} + \\frac{Y_{3}^{2}}{2} - \\frac{Y_{3}^{2}}{2 \\left(λ₀ + 3\\right)} - \\frac{Y_{3} λ₀ μ₀}{λ₀ + 3} + b₀ - \\frac{λ₀^{2} μ₀^{2}}{2 \\left(λ₀ + 3\\right)} + \\frac{λ₀ μ₀^{2}}{2}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "C = simplify(exp(-simplify(F3_μ - τ*coef))/τ^(a₀+1/Sym(2)))",
"execution_count": 57,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 57,
"data": {
"text/plain": " ___ a₀ ____ \n \\/ 2 *b₀ *\\/ λ₀ \n----------------------------\n 3/2 ________ \n4*pi *\\/ λ₀ + 3 *Gamma(a₀)",
"text/latex": "\\begin{equation*}\\frac{\\sqrt{2} b₀^{a₀} \\sqrt{λ₀}}{4 \\pi^{\\frac{3}{2}} \\sqrt{λ₀ + 3} \\Gamma\\left(a₀\\right)}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "sol1 = solve(diff(coef, Y[1]), Y[1])[1]",
"execution_count": 58,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 58,
"data": {
"text/plain": "Y2 + Y3 + λ₀*μ₀\n---------------\n λ₀ + 2 ",
"text/latex": "\\begin{equation*}\\frac{Y_{2} + Y_{3} + λ₀ μ₀}{λ₀ + 2}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "coef1 = simplify(subs(coef, (Y[1], sol1)))",
"execution_count": 59,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 59,
"data": {
"text/plain": " 2 2 2 2 \nY2 *λ₀ Y2 Y3 *λ₀ Y3 \n------ + --- - Y2*Y3 - Y2*λ₀*μ₀ + ------ + --- - Y3*λ₀*μ₀ + b₀*λ₀ + 2*b₀ + λ₀*\n 2 2 2 2 \n------------------------------------------------------------------------------\n λ₀ + 2 \n\n \n 2\nμ₀ \n \n---\n ",
"text/latex": "\\begin{equation*}\\frac{\\frac{Y_{2}^{2} λ₀}{2} + \\frac{Y_{2}^{2}}{2} - Y_{2} Y_{3} - Y_{2} λ₀ μ₀ + \\frac{Y_{3}^{2} λ₀}{2} + \\frac{Y_{3}^{2}}{2} - Y_{3} λ₀ μ₀ + b₀ λ₀ + 2 b₀ + λ₀ μ₀^{2}}{λ₀ + 2}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "sol2 = solve(diff(coef1, Y[2]), Y[2])[1]",
"execution_count": 60,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 60,
"data": {
"text/plain": "Y3 + λ₀*μ₀\n----------\n λ₀ + 1 ",
"text/latex": "\\begin{equation*}\\frac{Y_{3} + λ₀ μ₀}{λ₀ + 1}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "coef2 = simplify(subs(coef1, (Y[2], sol2)))",
"execution_count": 61,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 61,
"data": {
"text/plain": " 2 2\nY3 *λ₀ λ₀*μ₀ \n------ - Y3*λ₀*μ₀ + b₀*λ₀ + b₀ + ------\n 2 2 \n---------------------------------------\n λ₀ + 1 ",
"text/latex": "\\begin{equation*}\\frac{\\frac{Y_{3}^{2} λ₀}{2} - Y_{3} λ₀ μ₀ + b₀ λ₀ + b₀ + \\frac{λ₀ μ₀^{2}}{2}}{λ₀ + 1}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "sol = solve(diff(coef2, Y[3]), Y[3])[1]",
"execution_count": 62,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 62,
"data": {
"text/plain": "μ₀",
"text/latex": "\\begin{equation*}μ₀\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "simplify(subs(coef, ((y, sol) for y in Y)...)) # -> b₀ > 0 and hence coef > 0.",
"execution_count": 63,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 63,
"data": {
"text/plain": "b₀",
"text/latex": "\\begin{equation*}b₀\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "ξ = symbols(\"ξ\", positive=true)\nZ3 = simplify(integrate(τ^(a₀+1)*exp(-ξ*τ), (τ, 0, oo)))\nZ3 = Z3(ξ=>coef)\nZ3 = simplify(C*simplify(Z3))",
"execution_count": 64,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 64,
"data": {
"text/plain": " \n a₀ + 1/2 a₀ ____ a₀ + 3/2 / 2 2 \n2 *a₀*b₀ *\\/ λ₀ *(a₀ + 1)*(λ₀ + 3) *\\Y1 *λ₀ + 2*Y1 - 2*Y1*Y2 -\n------------------------------------------------------------------------------\n \n \n\n \n 2 2 2 2\n 2*Y1*Y3 - 2*Y1*λ₀*μ₀ + Y2 *λ₀ + 2*Y2 - 2*Y2*Y3 - 2*Y2*λ₀*μ₀ + Y3 *λ₀ + 2*Y3 \n------------------------------------------------------------------------------\n 3/2 \n pi \n\n -a₀ - 2\n 2\\ \n - 2*Y3*λ₀*μ₀ + 2*b₀*λ₀ + 6*b₀ + 3*λ₀*μ₀ / \n-------------------------------------------------\n \n ",
"text/latex": "\\begin{equation*}\\frac{2^{a₀ + \\frac{1}{2}} a₀ b₀^{a₀} \\sqrt{λ₀} \\left(a₀ + 1\\right) \\left(λ₀ + 3\\right)^{a₀ + \\frac{3}{2}} \\left(Y_{1}^{2} λ₀ + 2 Y_{1}^{2} - 2 Y_{1} Y_{2} - 2 Y_{1} Y_{3} - 2 Y_{1} λ₀ μ₀ + Y_{2}^{2} λ₀ + 2 Y_{2}^{2} - 2 Y_{2} Y_{3} - 2 Y_{2} λ₀ μ₀ + Y_{3}^{2} λ₀ + 2 Y_{3}^{2} - 2 Y_{3} λ₀ μ₀ + 2 b₀ λ₀ + 6 b₀ + 3 λ₀ μ₀^{2}\\right)^{- a₀ - 2}}{\\pi^{\\frac{3}{2}}}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "### 事後分布の計算"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "q3 = p3/Z3\nq3 = q3(ξ=>coef) # posterior",
"execution_count": 65,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 65,
"data": {
"text/plain": " \n \n \n -a₀ - 1/2 a₀ + 1 -a₀ - 3/2 / 2 2 \n2 *τ *(λ₀ + 3) *\\Y1 *λ₀ + 2*Y1 - 2*Y1*Y2 - 2*Y1*Y3 - 2*Y\n------------------------------------------------------------------------------\n \n \n\n \n \n \n 2 2 2 2 \n1*λ₀*μ₀ + Y2 *λ₀ + 2*Y2 - 2*Y2*Y3 - 2*Y2*λ₀*μ₀ + Y3 *λ₀ + 2*Y3 - 2*Y3*λ₀*μ₀ \n------------------------------------------------------------------------------\n ____ \n 4*\\/ pi *a₀*(a₀ + 1)*Gamma(a₀) \n\n / 2 2 2 \n | Y1 Y2 Y3 \n a₀ + 2 τ*|- --- + Y1*μ - --- + Y2*μ - --- + Y3*μ \n 2\\ \\ 2 2 2 \n+ 2*b₀*λ₀ + 6*b₀ + 3*λ₀*μ₀ / *e \n------------------------------------------------------------------------------\n \n \n\n 2 2 2\\\n λ₀*μ λ₀*μ₀ 3*μ |\n- b₀ - ----- + λ₀*μ*μ₀ - ------ - ----|\n 2 2 2 /\n \n---------------------------------------\n \n ",
"text/latex": "\\begin{equation*}\\frac{2^{- a₀ - \\frac{1}{2}} τ^{a₀ + 1} \\left(λ₀ + 3\\right)^{- a₀ - \\frac{3}{2}} \\left(Y_{1}^{2} λ₀ + 2 Y_{1}^{2} - 2 Y_{1} Y_{2} - 2 Y_{1} Y_{3} - 2 Y_{1} λ₀ μ₀ + Y_{2}^{2} λ₀ + 2 Y_{2}^{2} - 2 Y_{2} Y_{3} - 2 Y_{2} λ₀ μ₀ + Y_{3}^{2} λ₀ + 2 Y_{3}^{2} - 2 Y_{3} λ₀ μ₀ + 2 b₀ λ₀ + 6 b₀ + 3 λ₀ μ₀^{2}\\right)^{a₀ + 2} e^{τ \\left(- \\frac{Y_{1}^{2}}{2} + Y_{1} μ - \\frac{Y_{2}^{2}}{2} + Y_{2} μ - \\frac{Y_{3}^{2}}{2} + Y_{3} μ - b₀ - \\frac{λ₀ μ^{2}}{2} + λ₀ μ μ₀ - \\frac{λ₀ μ₀^{2}}{2} - \\frac{3 μ^{2}}{2}\\right)}}{4 \\sqrt{\\pi} a₀ \\left(a₀ + 1\\right) \\Gamma\\left(a₀\\right)}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "Nq3 = N(subs(q3, replacements...)) # numerical posterior",
"execution_count": 66,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 66,
"data": {
"text/plain": " / 2 \\\n 2.0 τ*\\- 2.0*μ + 3.4*μ - 2.95/\n2.41042987827087*τ *e \n--------------------------------------------------\n ____ \n \\/ pi ",
"text/latex": "\\begin{equation*}\\frac{2.41042987827087 τ^{2.0} e^{τ \\left(- 2.0 μ^{2} + 3.4 μ - 2.95\\right)}}{\\sqrt{\\pi}}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "simplify(q_μ*q_τ)",
"execution_count": 67,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 67,
"data": {
"text/plain": " 2 \n 2.0 - 3.32221205946743*μ + 5.64776050109463*μ - 1.8060042\n0.274681107216063*τ *e \n\n \n6526063*τ\n ",
"text/latex": "\\begin{equation*}0.274681107216063 τ^{2.0} e^{- 3.32221205946743 μ^{2} + 5.64776050109463 μ - 1.80600426526063 τ}\\end{equation*}"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "### 変分近似との比較するためのプロット"
},
{
"metadata": {
"scrolled": false,
"trusted": true
},
"cell_type": "code",
"source": "eval(parse(\"g(μ,τ) = $Nq3\")) # numerical posterior\n@time c_g = g.(μs', τs);",
"execution_count": 68,
"outputs": [
{
"output_type": "stream",
"text": " 0.075039 seconds (225.81 k allocations: 10.485 MiB)\n",
"name": "stdout"
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "figure(figsize=(10,4))\n\nsubplot(121)\nCS = contour(μs, τs, c_f)\nclabel(CS, inline=1, fontsize=10)\nxlabel(\"μ\")\nylabel(\"τ\")\ngrid(ls=\":\")\ntitle(\"variational approximation\")\n\nsubplot(122)\nCS = contour(μs, τs, c_g)\nclabel(CS, inline=1, fontsize=10)\nxlabel(\"μ\")\nylabel(\"τ\")\ngrid(ls=\":\")\ntitle(\"exact posterior\")",
"execution_count": 69,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "Figure(PyObject <Figure size 1000x400 with 2 Axes>)",
"image/png": 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"
},
"metadata": {}
},
{
"output_type": "execute_result",
"execution_count": 69,
"data": {
"text/plain": "PyObject Text(0.5,1,'exact posterior')"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "figure(figsize=(10, 3))\n\nsubplot(121)\npcolormesh(μs, τs, c_f, cmap=\"CMRmap\")\ncolorbar()\nxlabel(\"μ\")\nylabel(\"τ\")\ngrid(ls=\":\")\ntitle(\"variational approximation\")\n\nsubplot(122)\npcolormesh(μs, τs, c_g, cmap=\"CMRmap\")\ncolorbar()\nxlabel(\"μ\")\nylabel(\"τ\")\ngrid(ls=\":\")\ntitle(\"exact posterior\")",
"execution_count": 70,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "Figure(PyObject <Figure size 1000x300 with 4 Axes>)",
"image/png": 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"
},
"metadata": {}
},
{
"output_type": "execute_result",
"execution_count": 70,
"data": {
"text/plain": "PyObject Text(0.5,1,'exact posterior')"
},
"metadata": {}
}
]
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