{ "cells": [ { "cell_type": "markdown", "id": "620cbf55", "metadata": {}, "source": [ "# Poisson分布モデルでの対数尤度比検定のP値とBayes因子の関係\n", "\n", "* 黒木玄\n", "* 2022-10-08\n", "$\n", "\\newcommand\\op{\\operatorname}\n", "\\newcommand\\kbar{{\\bar k}}\n", "\\newcommand\\lambdahat{{\\hat\\lambda}}\n", "\\newcommand\\pvalue{\\op{pvalue}}\n", "\\newcommand\\cdf{\\op{cdf}}\n", "\\newcommand\\ccdf{\\op{ccdf}}\n", "\\newcommand\\quantile{\\op{quantile}}\n", "$\n", "\n", "関連:\n", "\n", "* [二項分布モデルの場合のベイズ検定と通常の検定の関係](https://github.com/genkuroki/public/blob/main/0033/%E3%83%99%E3%82%A4%E3%82%BA%E6%A4%9C%E5%AE%9A%E3%81%A8%E9%80%9A%E5%B8%B8%E3%81%AE%E6%A4%9C%E5%AE%9A%E3%81%AE%E9%96%A2%E4%BF%82.ipynb)" ] }, { "cell_type": "markdown", "id": "4f5bafdd", "metadata": { "toc": true }, "source": [ "

目次

\n", "
" ] }, { "cell_type": "code", "execution_count": 1, "id": "42bd4a27", "metadata": {}, "outputs": [], "source": [ "using Distributions\n", "using Random\n", "using SpecialFunctions\n", "using StatsBase: ecdf\n", "using StatsPlots\n", "default(fmt=:png, size=(500, 300),\n", " titlefontsize=10, plot_titlefontsize=10, \n", " guidefontsize=9, tickfontsize=6)" ] }, { "cell_type": "markdown", "id": "26b5b117", "metadata": {}, "source": [ "## Poisson分布モデル" ] }, { "cell_type": "markdown", "id": "20249afe", "metadata": {}, "source": [ "### 対数尤度比検定のP値\n", "\n", "__データの数値:__ データの数値は $n$ 個の0以上の整数 $k=(k_1,\\ldots,k_n)$ で構成されているとする.\n", "\n", "__標本平均:__ $\\kbar = \\frac{1}{n}\\sum_{i=1}^n k_i$ とおく.\n", "\n", "__統計モデル1:__ パラメータ $\\lambda > 0$ を持つ統計モデル1を次のように定める:\n", "\n", "$$\n", "P(k|\\lambda) = \\prod_{i=1}^n \\frac{e^{-\\lambda}\\lambda^{k_i}}{k_i!} =\n", "\\frac{e^{-n\\lambda}\\lambda^{n\\kbar}}{k_1!\\cdots k_n!}.\n", "$$\n", "\n", "__統計モデル1での最尤推定:__ 与えられたデータの数値 $k=(k_1,\\ldots,k_n)$ について, $P(k|\\lambda)$ を最大化する $\\lambda$ は $\\lambda=\\kbar$ になる.\n", "\n", "__統計モデル0:__ $\\lambda_0 > 0$ を任意に固定し, 上のモデルを $\\lambda = \\lambda_0$ という条件で制限して得られるモデルを統計モデル0と呼ぶことにする.\n", "\n", "常に $P(k|\\bar) = \\max_\\lambda P(k|\\lambda) \\ge P(k|\\lambda_0)$ が成立していることに注意せよ.\n", "\n", "__対数尤度比:__ 与えられたデータの数値について, 対数尤度比 $\\op{LLR}$ を次のように定める:\n", "\n", "$$\n", "\\op{LLR} = 2\\log\\frac{P(k|\\kbar)}{P(k|\\lambda_0)}.\n", "$$\n", "\n", "$k$ が統計モデル0に従う確率変数であるとき, $n\\lambda_0$ を十分大きくすれば, 対数尤度比 $\\op{LLR}$ は近似的に自由度1のχ²分布に従う(以下で数値的に確認する).\n", "\n", "このことを用いて, 仮説 $\\lambda=\\lambda_0$ のP値を「自由度1のχ²分布で $\\op{LLR}$ 以上になる確率」と定める:\n", "\n", "$$\n", "\\pvalue(k|\\lambda_0) = 1 - \\cdf(\\op{Chisq}(1), \\op{LLR}).\n", "$$\n", "\n", "ここで $\\cdf(D, x)$ は確率分布 $D$ の累積分布函数(cumulative distribution function)である.\n", "\n", "このP値に基く検定を対数尤度比検定と呼ぶ. (最尤法に付随する漸近的に同値な検定としてスコア検定とWald検定もよく使われる.)\n", "\n", "対数尤度比検定のP値は統計モデルの尤度函数 $\\lambda\\mapsto P(k|\\lambda)$ だけで決まり, 尤度函数にパラメータ $\\lambda$ によらない正の定数をかけたものを尤度函数の代わりに使って定義し直してもP値は不変である." ] }, { "cell_type": "code", "execution_count": 2, "id": "bd9298d9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "plot_ecdf_LLR (generic function with 1 method)" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "\"\"\"\n", " loglikrat(k; λ₀ = 1.0)\n", "\n", "returns log likelihood ratio of Poisson model.\n", "\"\"\"\n", "function loglikrat(k; λ₀ = 1)\n", " n, k̄ = length(k), mean(k)\n", " logL1 = loglikelihood(Poisson(k̄), k)\n", " logL0 = loglikelihood(Poisson(λ₀), k)\n", " 2(logL1 - logL0)\n", "end\n", "\n", "function pvalue(k; λ₀ = 1)\n", " LLR = loglikrat(k; λ₀)\n", " ccdf(Chisq(1), LLR)\n", "end\n", "\n", "function sim_loglikrat(; λ₀ = 1, n = 100, L = 10^5)\n", " LLR = Vector{Float64}(undef, L)\n", " pval = Vector{Float64}(undef, L)\n", " tmp = [Vector{Int}(undef, n) for _ in 1:Threads.nthreads()]\n", " model0 = Poisson(λ₀)\n", " Threads.@threads for i in 1:L\n", " K = rand!(model0, tmp[Threads.threadid()])\n", " LLR[i] = loglikrat(K; λ₀)\n", " pval[i] = ccdf(Chisq(1), LLR[i])\n", " end\n", " _ecdf_LLR = ecdf(LLR)\n", " ecdf_LLR(x) = _ecdf_LLR(x)\n", " _ecdf_pval = ecdf(pval)\n", " ecdf_pval(x) = _ecdf_pval(x)\n", " ecdf_LLR, ecdf_pval\n", "end\n", "\n", "function plot_ecdf_LLR(; λ₀ = 1, n = 100, L = 10^5)\n", " ecdf_LLR, ecdf_pval = sim_loglikrat(; λ₀, n, L)\n", " \n", " P1 = plot(ecdf_LLR, -eps(), 8; label=\"ecdf of LLR\")\n", " plot!(x -> cdf(Chisq(1), x); label=\"cdf of Chisq(1)\", ls=:dash)\n", " plot!(legend=:bottomright)\n", " plot!(xguide=\"x\", yguide=\"probability of LLR ≤ x\")\n", " title!(\"λ₀=$λ₀, n=$n\")\n", " \n", " pval_LLR = ccdf.(Chisq(1), ecdf_LLR._ecdf_LLR.sorted_values)\n", " P2 = plot(ecdf_pval, 0, 1; label=\"ecdf of P-value\")\n", " plot!([0,1], [0,1]; label=\"\", ls=:dash)\n", " plot!(xtick=0:0.1:1, ytick=0:0.1:1)\n", " plot!(xguide=\"α\", yguide=\"probability of P-value ≤ α\")\n", " plot!(legend=:bottomright)\n", " title!(\"λ₀=$λ₀, n=$n\")\n", " \n", " plot(P1, P2; size=(800, 300), layout=@layout[a{0.625w} b])\n", " plot!(leftmargin=4Plots.mm, bottommargin=4Plots.mm)\n", "end" ] }, { "cell_type": "code", "execution_count": 3, "id": "9ff37b1e", "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot_ecdf_LLR(; λ₀ = 1, n = 10)" ] }, { "cell_type": "code", "execution_count": 4, "id": "0fe34041", "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot_ecdf_LLR(; λ₀ = 1, n = 100)" ] }, { "cell_type": "code", "execution_count": 5, "id": "c88f00b2", "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot_ecdf_LLR(; λ₀ = 10, n = 10)" ] }, { "cell_type": "markdown", "id": "4d05687c", "metadata": {}, "source": [ "グラフの上では, $n\\lambda_0 = 100$ のとき, 統計モデル0に従ってデータがランダムに生成されているとき, 対数尤度比 $\\op{LLR}$ が従う分布は自由度1のχ²分布 $\\op{Chisq}(1)$ でよく近似されることが分かった. (近似を累積分布函数の比較で確認した.)" ] }, { "cell_type": "markdown", "id": "ca52ba0e", "metadata": {}, "source": [ "### Bayes因子\n", "\n", "__事前分布:__ 統計モデル1(パラメータが固定されていないPoisson分布モデル)のパラメータ $\\lambda > 0$ に関する事前分布 $\\varphi(\\lambda)$ を考える.\n", "\n", "統計モデル0ではパラメータ $\\lambda$ が $\\lambda_0$ に固定されているので, 事前分布は自明なものしかないことに注意せよ.\n", "\n", "__周辺尤度:__ 与えられたデータの数値 $k=(k_1,\\ldots,k_n)$ に関する統計モデル1+事前分布 $\\varphi(\\lambda)$ の周辺尤度 $Z_1$ が次のように定義される:\n", "\n", "$$\n", "Z_1 = \\int_0^\\infty P(k|\\lambda)\\varphi(\\lambda)\\,d\\lambda.\n", "$$\n", "\n", "統計モデル0の周辺尤度 $Z_0$ は尤度に等しい:\n", "\n", "$$\n", "Z_0 = P(k|\\lambda_0).\n", "$$\n", "\n", "一般に尤度は「データの数値へのモデルの相性の良さもしくは適藤度の指標の1つ」として利用できる. 周辺尤度も同様である.\n", "\n", "周辺尤度の比をBayes因子と呼び, 次のように書くことにする:\n", "\n", "$$\n", "\\op{BF} = \\frac{Z_1}{Z_0}.\n", "$$\n", "\n", "Bayes因子 $\\op{BF}$ が大きいほど, 統計モデル1+事前分布の方が統計モデル0よりもデータによく適合していると解釈可能である.\n", "\n", "Beyes因子は統計モデルの尤度函数 $\\lambda\\mapsto P(k|\\lambda)$ と事前分布 $\\varphi(\\lambda)$ だけで決まり, 尤度函数にパラメータ $\\lambda$ によらない正の定数をかけたものを尤度函数の代わりに使って定義し直してもBayes因子は不変である." ] }, { "cell_type": "markdown", "id": "f1c97462", "metadata": {}, "source": [ "### 対数尤度比とBayes因子の関係\n", "\n", "データの数値 $k=(k_1,\\ldots,k_n)$ の対数尤度比\n", "\n", "$$\n", "\\op{LLR} = 2\\log\\frac{P(k|\\kbar)}{P(k|\\lambda_0)}, \\quad\n", "P(k|\\lambda) = \\frac{e^{-n\\lambda}\\lambda^{n\\kbar}}{k_1!\\cdots k_n!}, \\quad\n", "\\kbar = \\frac{1}{n}\\sum_{i=1}^n k_i\n", "$$\n", "\n", "とBayes因子\n", "\n", "$$\n", "\\op{BF} = \\frac{Z_1}{Z_0} =\n", "\\int_0^\\infty \\frac{P(k|\\lambda)}{P(k|\\lambda_0)}\\varphi(\\lambda)\\,d\\lambda\n", "$$\n", "\n", "の $n$ が大きなときの近似的な関係式をLaplace近似によって示そう.\n", "\n", "以上の設定の下で, \n", "\n", "$$\n", "\\frac{P(k|\\lambda)}{P(k|\\lambda_0)} =\n", "e^{-n(\\lambda-\\lambda_0)}\\left(\\frac{\\lambda}{\\lambda_0}\\right)^{n\\kbar} =\n", "\\exp\\left(n\\left(\\kbar\\log\\frac{\\lambda}{\\lambda_0} - (\\lambda-\\lambda_0)\\right)\\right).\n", "$$\n", "\n", "なので, \n", "\n", "$$\n", "f(\\lambda) := 2\\log\\frac{P(k|\\lambda)}{P(k|\\lambda_0)} =\n", "2n\\left(\\kbar\\log\\frac{\\lambda}{\\lambda_0} - (\\lambda-\\lambda_0)\\right)\n", "$$\n", "\n", "とおくと, 対数尤度比は次のように書き直される:\n", "\n", "$$\n", "\\begin{aligned}\n", "\\op{LLR} = f(\\kbar) =\n", "2n\\left(\\kbar\\log\\frac{\\kbar}{\\lambda_0} - (\\kbar - \\lambda_0)\\right).\n", "\\end{aligned}\n", "$$\n", "\n", "対数尤度比 $\\op{LLR}$ は $f(\\lambda)$ の最大値になっている. そして,\n", "\n", "$$\n", "f'(\\lambda) = 2n\\left(\\frac{\\kbar}{\\lambda} - 1\\right), \\quad\n", "f'(\\kbar) = 0, \\quad\n", "f''(\\lambda) = -2n\\frac{\\kbar}{\\lambda^2}, \\quad\n", "f''(\\kbar) = -2n\\frac{1}{\\kbar}\n", "$$\n", "\n", "なので, $\\lambda$ が $\\kbar$ に近いとき, $f(\\lambda)$ の $\\lambda=\\kbar$ でのTaylor展開によって次を得る:\n", "\n", "$$\n", "f(\\lambda) \\approx \\op{LLR} - 2\\frac{(\\lambda-\\kbar)^2}{2\\kbar/n}.\n", "$$\n", "\n", "このとき,\n", "\n", "$$\n", "\\frac{P(k|\\lambda)}{P(k|\\lambda_0)} = e^{f(\\lambda)/2}\n", "\\approx e^{\\op{LLR}/2}e^{-(\\lambda-\\kbar)^2/(2\\kbar/n)}.\n", "$$\n", "\n", "したがって, $n$ が大きなとき, 次のLaplace近似が得られる:\n", "\n", "$$\n", "\\op{BF}\n", "\\approx e^{\\op{LLR}/2} \\int e^{-(\\lambda-\\kbar)^2/(\\kbar/n)}\\varphi(\\lambda)\\,d\\lambda\n", "\\approx e^{\\op{LLR}/2} \\varphi(\\kbar) \\sqrt{\\frac{2\\pi\\kbar}{n}}.\n", "$$\n", "\n", "この近似は非常に良い近似になり易いことを数値的に確認できる.\n", "\n", "さらに, $\\kbar$ が $\\lambda_0$ に近いならば次の近似も成立する(近似は粗くなる):\n", "\n", "$$\n", "\\op{BF}\n", "\\approx e^{\\op{LLR}/2} \\varphi(\\lambda_0) \\sqrt{\\frac{2\\pi\\lambda_0}{n}}.\n", "$$\n", "\n", "このとき,\n", "\n", "$$\n", "2\\log\\op{BF}\n", "\\approx \\op{LLR} - \\log n + \\log(2\\pi\\lambda_0) + 2\\log\\varphi(\\lambda_0).\n", "$$\n", "\n", "これが欲しい結果である.\n", "\n", "__注意:__ この近似の右辺における $\\op{LLR} - \\log n$ の部分は統計モデル0のBIC(Bayes情報量基準)から統計モデル1のBICを引いた結果に等しい. BICによるモデル選択は上の近似の $n$ に関する定数項 $\\log(2\\pi\\lambda_0) + 2\\log\\varphi(\\lambda_0)$ を無視するさらに粗い近似を利用していると考えられる." ] }, { "cell_type": "markdown", "id": "69810a88", "metadata": {}, "source": [ "### 対数尤度比検定のP値とBayes因子の関係\n", "\n", "$C > 0$, $0\\le\\alpha\\le 1$ と仮定する.\n", "\n", "前節の近似\n", "\n", "$$\n", "2\\log\\op{BF}\n", "\\approx \\op{LLR} - \\log n + \\log(2\\pi\\lambda_0) + 2\\log\\varphi(\\lambda_0).\n", "$$\n", "\n", "を仮定し, 近似的に同値であることも $\\iff$ と書くと, \n", "\n", "$$\n", "\\begin{aligned}\n", "\\op{BF} > C &\\iff 2\\log\\op{BF} > 2\\log C\n", "\\\\ &\\iff\n", "\\op{LLR} > 2\\log C + \\log n - \\log(2\\pi\\lambda_0) - 2\\log\\varphi(\\lambda_0)\n", "\\\\ &\\iff\n", "\\cdf(\\op{Chisq}(1), \\op{LLR}) >\n", "\\cdf(\\op{Chisq}(1), 2\\log C + \\log n - \\log(2\\pi\\lambda_0) - 2\\log\\varphi(\\lambda_0))\n", "\\\\ &\\iff\n", "\\pvalue(k|\\lambda_0) <\n", "1 - \\cdf(\\op{Chisq}(1), 2\\log C + \\log n - \\log(2\\pi\\lambda_0) - 2\\log\\varphi(\\lambda_0))\n", "\\end{aligned}\n", "$$\n", "\n", "なので,\n", "\n", "$$\n", "\\alpha = 1 - \\cdf(\\op{Chisq}(1), 2\\log C + \\log n - \\log(2\\pi\\lambda_0) - 2\\log\\varphi(\\lambda_0))\n", "$$\n", "\n", "すなわち\n", "\n", "$$\n", "2\\log C =\n", "\\quantile(\\op{Chisq}(1), 1 - \\alpha) - \\log n + \\log(2\\pi\\lambda_0) + 2\\log\\varphi(\\lambda_0)\n", "$$\n", "\n", "とおくと($\\quantile(D, p)$ は分布 $D$ の分位点函数 = $\\cdf$ の逆函数), 近似的に\n", "\n", "$$\n", "\\op{BF} > C \\iff \\pvalue(k|\\lambda_0) < \\alpha.\n", "$$\n", "\n", "以下ではこの近似的な同値性を数値的に確認しよう." ] }, { "cell_type": "markdown", "id": "653ad0a5", "metadata": {}, "source": [ "### 数値的な確認\n", "\n", "計算を簡単にするために事前分布として共役事前分布のガンマ分布 $\\op{Gamma}(\\alpha_0, 1/\\tau_0)$ を採用しよう:\n", "\n", "$$\n", "\\varphi(\\lambda) = \\frac{\\tau_0^{\\alpha_0}}{\\Gamma(\\alpha_0)}\\lambda^{\\alpha_0-1}e^{-\\tau_0\\lambda}.\n", "$$\n", "\n", "例えば $\\alpha_0 = 1$, $\\tau_0 = 1$ のとき, この事前分布は期待値 $1$ の指数分布になる.\n", "\n", "このとき, 簡単な積分計算によって, Bayes因子は次のように書けることがわかる:\n", "\n", "$$\n", "\\op{BF} =\n", "\\frac{1}{\\lambda_0^{n\\kbar}e^{-n\\lambda_0}}\n", "\\frac{\\tau_0^{\\alpha_0}}{\\Gamma(\\alpha_0)}\n", "\\frac{\\Gamma(\\alpha_0+n\\kbar)}{(\\tau_0 + n)^{\\alpha_0+n\\kbar}}.\n", "$$\n", "\n", "すなわち\n", "\n", "$$\n", "\\begin{aligned}\n", "2\\log\\op{BF}\n", "&=\n", "2(\\log\\Gamma(\\alpha_0+n\\kbar) - (\\alpha_0+n\\kbar)\\log(\\tau_0 + n))\n", "-2(\\log\\Gamma(\\alpha_0) - \\alpha_0\\log\\tau_0)\n", "\\\\ &\\,+\n", "2n(\\lambda_0 - \\kbar\\log\\lambda_0).\n", "\\end{aligned}\n", "$$\n", "\n", "この公式を使って, 対数尤度比とBayes因子を比較しよう." ] }, { "cell_type": "code", "execution_count": 6, "id": "fe54ecfd", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "alpha2C (generic function with 1 method)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function C2alpha(C, n; λ₀=1, α₀=1, τ₀=α₀/λ₀)\n", " ccdf(Chisq(1), 2log(C) + log(n) - log(2π*λ₀) - 2logpdf(Gamma(α₀, 1/τ₀), λ₀))\n", "end\n", "\n", "function alpha2C(α, n; λ₀=1, α₀=1, τ₀=α₀/λ₀)\n", " twologC = quantile(Chisq(1), 1-α) - log(n) + log(2π*λ₀) + 2logpdf(Gamma(α₀, 1/τ₀), λ₀)\n", " exp(twologC/2)\n", "end" ] }, { "cell_type": "code", "execution_count": 7, "id": "c8150cdd", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "alpha2C(C2alpha(10, 100), 100) ≈ 10 = true\n", "C2alpha(alpha2C(0.1, 100), 100) ≈ 0.1 = true\n" ] } ], "source": [ "@show alpha2C(C2alpha(10, 100), 100) ≈ 10\n", "@show C2alpha(alpha2C(0.1, 100), 100) ≈ 0.1;" ] }, { "cell_type": "code", "execution_count": 8, "id": "800aed28", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "α = 2 * ccdf(Normal(), 2) = 0.04550026389635841\n" ] }, { "data": { "text/plain": [ "8-element Vector{NamedTuple{(:n, :C), Tuple{Int64, Float64}}}:\n", " (n = 10, C = 2.154688114663622)\n", " (n = 100, C = 0.6813722089631095)\n", " (n = 1000, C = 0.21546881146636224)\n", " (n = 10000, C = 0.06813722089631094)\n", " (n = 100000, C = 0.021546881146636224)\n", " (n = 1000000, C = 0.006813722089631096)\n", " (n = 10000000, C = 0.002154688114663621)\n", " (n = 100000000, C = 0.0006813722089631088)" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# 2σ case\n", "@show α = 2ccdf(Normal(), 2)\n", "[(n=n, C=alpha2C(α, n)) for n in 10 .^ (1:8)]" ] }, { "cell_type": "code", "execution_count": 9, "id": "fc658cdc", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "α = 2 * ccdf(Normal(), 3) = 0.002699796063260186\n" ] }, { "data": { "text/plain": [ "8-element Vector{NamedTuple{(:n, :C), Tuple{Int64, Float64}}}:\n", " (n = 10, C = 26.249474944088995)\n", " (n = 100, C = 8.300812820684223)\n", " (n = 1000, C = 2.6249474944089)\n", " (n = 10000, C = 0.8300812820684221)\n", " (n = 100000, C = 0.26249474944088996)\n", " (n = 1000000, C = 0.08300812820684227)\n", " (n = 10000000, C = 0.02624947494408899)\n", " (n = 100000000, C = 0.008300812820684214)" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# 3σ case\n", "@show α = 2ccdf(Normal(), 3)\n", "[(n=n, C=alpha2C(α, n)) for n in 10 .^ (1:8)]" ] }, { "cell_type": "code", "execution_count": 10, "id": "63f727ef", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "α = 2 * ccdf(Normal(), 4) = 6.334248366623977e-5\n" ] }, { "data": { "text/plain": [ "8-element Vector{NamedTuple{(:n, :C), Tuple{Int64, Float64}}}:\n", " (n = 10, C = 869.2632264518805)\n", " (n = 100, C = 274.8851681814667)\n", " (n = 1000, C = 86.92632264518811)\n", " (n = 10000, C = 27.488516818146692)\n", " (n = 100000, C = 8.692632264518805)\n", " (n = 1000000, C = 2.7488516818146698)\n", " (n = 10000000, C = 0.8692632264518804)\n", " (n = 100000000, C = 0.2748851681814667)" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# 4σ case\n", "@show α = 2ccdf(Normal(), 4)\n", "[(n=n, C=alpha2C(α, n)) for n in 10 .^ (1:8)]" ] }, { "cell_type": "code", "execution_count": 11, "id": "64448b9b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "α = 2 * ccdf(Normal(), 5) = 5.733031437583873e-7\n" ] }, { "data": { "text/plain": [ "8-element Vector{NamedTuple{(:n, :C), Tuple{Int64, Float64}}}:\n", " (n = 10, C = 78248.58199317353)\n", " (n = 100, C = 24744.374277686667)\n", " (n = 1000, C = 7824.858199317358)\n", " (n = 10000, C = 2474.4374277686643)\n", " (n = 100000, C = 782.4858199317364)\n", " (n = 1000000, C = 247.44374277686657)\n", " (n = 10000000, C = 78.24858199317356)\n", " (n = 100000000, C = 24.74437427768663)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# 5σ case\n", "@show α = 2ccdf(Normal(), 5)\n", "[(n=n, C=alpha2C(α, n)) for n in 10 .^ (1:8)]" ] }, { "cell_type": "markdown", "id": "c89e1c1c", "metadata": {}, "source": [ "この場合には, $5\\sigma$ の有意水準に対応する $\\op{BF} > C$ という条件における $C$ は $n=10^8$ のような巨大な $n$ の下であっても十分に大きくなる." ] }, { "cell_type": "code", "execution_count": 12, "id": "b91c0398", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "plot_C2alpha (generic function with 1 method)" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function plot_C2alpha(C; n=10:1000, λ₀=1, α₀=1, τ₀=α₀/λ₀, kwargs...)\n", " plot(n, n -> C2alpha(C, n; λ₀, α₀, τ₀); label=\"\")\n", " plot!(ylim=(0, C2alpha(C, n[begin]; λ₀, α₀, τ₀)))\n", " plot!(xguide=\"n\", yguide=\"α\")\n", " title!(\"α corresponding to C=$C, λ₀=$λ₀, α₀=$α₀, τ₀=$τ₀\")\n", " plot!(; kwargs...)\n", "end" ] }, { "cell_type": "markdown", "id": "5e636460", "metadata": {}, "source": [ "$\\op{BF} > C$ に対応する有意水準 $\\alpha$ は $n$ の単調減少函数になる." ] }, { "cell_type": "code", "execution_count": 13, "id": "d273bca5", "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot_C2alpha(1; n=10^2:10^2:10^4, ytick=0:0.001:1)" ] }, { "cell_type": "code", "execution_count": 14, "id": "1c6332aa", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.04550026389635841" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "2ccdf(Normal(), 2) # significance level of 2σ" ] }, { "cell_type": "code", "execution_count": 15, "id": "8fff9283", "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot_C2alpha(10; n=100:10^2:10^4, ytick=0:0.0001:1)" ] }, { "cell_type": "code", "execution_count": 16, "id": "1162a020", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.002699796063260186" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "2ccdf(Normal(), 3) # significance level of 3σ" ] }, { "cell_type": "code", "execution_count": 17, "id": "d11444f1", "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot_C2alpha(100; n=100:10^2:10^4, ytick=0:0.00001:1)" ] }, { "cell_type": "code", "execution_count": 18, "id": "8dfb79f5", "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot_C2alpha(1000; n=100:10^2:10^4, ytick=0:1e-6:1)" ] }, { "cell_type": "code", "execution_count": 19, "id": "092db79e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "6.334248366623977e-5" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "2ccdf(Normal(), 4) # significance level of 4σ" ] }, { "cell_type": "code", "execution_count": 20, "id": "220461df", "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot_C2alpha(10000; n=10^2:10^2:10^4, ytick=0:1e-7:1)" ] }, { "cell_type": "code", "execution_count": 21, "id": "0ad94df1", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "5.733031437583873e-7" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "2ccdf(Normal(), 5) # significance level of 5σ" ] }, { "cell_type": "markdown", "id": "999472b8", "metadata": {}, "source": [ "$n \\le 10^4$ では, $5\\sigma$ に対応する小さな有意水準を実現するためには非常に大きな $C$ に関する $\\op{BF} > C$ という条件を考える必要がある. " ] }, { "cell_type": "code", "execution_count": 22, "id": "28d325fb", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "twologBF_approx0 (generic function with 1 method)" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "logZ_Gamma(α, τ) = loggamma(α) - α*log(τ)\n", "\n", "function twologBF(k; λ₀=1, α₀=1, τ₀=α₀/λ₀)\n", " n, k̄ = length(k), mean(k)\n", " 2logZ_Gamma(α₀+n*k̄, τ₀+n) - 2logZ_Gamma(α₀, τ₀) + 2n*(λ₀ - k̄*log(λ₀))\n", "end\n", "\n", "function twologBF_approx(k; λ₀=1, α₀=1, τ₀=α₀/λ₀)\n", " n = length(k)\n", " loglikrat(k; λ₀) - log(n) + log(2π*λ₀) + 2logpdf(Gamma(α₀, 1/τ₀), λ₀)\n", "end\n", "\n", "function twologBF_approx0(k; λ₀=1, α₀=1, τ₀=α₀/λ₀)\n", " n, k̄ = length(k), mean(k)\n", " loglikrat(k; λ₀) - log(n) + log(2π*k̄) + 2log(pdf(Gamma(α₀, 1/τ₀), k̄))\n", "end" ] }, { "cell_type": "code", "execution_count": 23, "id": "fd10aebb", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "twologBF(k; α₀, τ₀) = -14.300051817889198\n", "twologBF_approx0(k; α₀, τ₀) = -14.300198751392475\n", "twologBF_approx(k; α₀, τ₀) = -14.299218251058893\n" ] } ], "source": [ "k = rand(Poisson(1), 1000)\n", "α₀, τ₀ = 1, 1e-2\n", "@show twologBF(k; α₀, τ₀)\n", "@show twologBF_approx0(k; α₀, τ₀)\n", "@show twologBF_approx(k; α₀, τ₀);" ] }, { "cell_type": "code", "execution_count": 24, "id": "915c9ea9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "plot_BF (generic function with 1 method)" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function sim_BF(; n=100, λ₀=1, α₀=1, τ₀=α₀/λ₀, L=10^5)\n", " TLBF = Vector{Float64}(undef, L)\n", " TLBF_approx0 = Vector{Float64}(undef, L)\n", " TLBF_approx = Vector{Float64}(undef, L)\n", " tmp = [Vector{Int}(undef, n) for _ in 1:Threads.nthreads()]\n", " model0 = Poisson(λ₀)\n", " Threads.@threads for i in 1:L\n", " K = rand!(model0, tmp[Threads.threadid()])\n", " TLBF[i] = twologBF(K; λ₀, α₀, τ₀)\n", " TLBF_approx0[i] = twologBF_approx0(K; λ₀, α₀, τ₀)\n", " TLBF_approx[i] = twologBF_approx(K; λ₀, α₀, τ₀)\n", " end\n", " _TLBF = ecdf(TLBF)\n", " _TLBF_approx0 = ecdf(TLBF_approx0)\n", " _TLBF_approx = ecdf(TLBF_approx)\n", " ecdf_TLBF(x) = _TLBF(x)\n", " ecdf_TLBF_approx0(x) = _TLBF_approx0(x)\n", " ecdf_TLBF_approx(x) = _TLBF_approx(x)\n", " (; ecdf_TLBF, ecdf_TLBF_approx0, ecdf_TLBF_approx, TLBF, TLBF_approx0, TLBF_approx)\n", "end\n", "\n", "function plot_BF(; n=100, λ₀=1, α₀=1, τ₀=α₀/λ₀, L=10^4)\n", " (; ecdf_TLBF, ecdf_TLBF_approx0, ecdf_TLBF_approx, TLBF, TLBF_approx0, TLBF_approx) =\n", " sim_BF(; n, λ₀, α₀, τ₀, L)\n", " lim = collect(extrema(TLBF))\n", " \n", " P1 = scatter(TLBF, TLBF_approx0; ms=1, ma=0.7, msw=0, label=\"\")\n", " plot!(lim, lim; label=\"\", ls=:dash, lw=0.5)\n", " plot!(xguide=\"2log(BF)\", yguide=\"approx0\")\n", " \n", " P2 = scatter(TLBF, TLBF_approx; ms=1.5, ma=0.7, msw=0, label=\"\")\n", " plot!(lim, lim; label=\"\", ls=:dash, lw=0.7)\n", " plot!(xguide=\"2log(BF)\", yguide=\"approx\")\n", " \n", " plot(P1, P2; size=(600, 300))\n", " plot!(plot_title=\"n=$n, λ₀=$λ₀, α₀=$α₀, τ₀=$τ₀\")\n", "end" ] }, { "cell_type": "code", "execution_count": 25, "id": "1939ee24", "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot_BF(n=10)" ] }, { "cell_type": "code", "execution_count": 26, "id": "c8893b9b", "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot_BF(n=100)" ] }, { "cell_type": "code", "execution_count": 27, "id": "3534bfc4", "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot_BF(n=1000)" ] }, { "cell_type": "code", "execution_count": 28, "id": "6669b8f6", "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot_BF(n=10000)" ] }, { "cell_type": "code", "execution_count": 29, "id": "58e37c87", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "pvalue_approx0 (generic function with 1 method)" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function loglikrat_approx(k; λ₀=1, α₀=1, τ₀=α₀/λ₀)\n", " n = length(k)\n", " twologBF(k; λ₀, α₀, τ₀) + log(n) - log(2π*λ₀) - 2logpdf(Gamma(α₀, 1/τ₀), λ₀)\n", "end\n", "\n", "function loglikrat_approx0(k; λ₀=1, α₀=1, τ₀=α₀/λ₀)\n", " n, k̄ = length(k), mean(k)\n", " twologBF(k; λ₀, α₀, τ₀) + log(n) - log(2π*k̄) - 2logpdf(Gamma(α₀, 1/τ₀), k̄)\n", "end\n", "\n", "function pvalue_approx(k; λ₀=1, α₀=1, τ₀=α₀/λ₀)\n", " LLR = loglikrat_approx(k; λ₀)\n", " ccdf(Chisq(1), LLR)\n", "end\n", "\n", "function pvalue_approx0(k; λ₀=1, α₀=1, τ₀=α₀/λ₀)\n", " LLR = loglikrat_approx0(k; λ₀)\n", " ccdf(Chisq(1), LLR)\n", "end" ] }, { "cell_type": "code", "execution_count": 30, "id": "5c4f5f67", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "pvalue(k; λ₀) = 0.44968468284221247\n", "pvalue_approx0(k; λ₀, α₀, τ₀) = 0.45000725446151657\n", "pvalue_approx(k; λ₀, α₀, τ₀) = 0.45981288149077343\n" ] } ], "source": [ "k = rand(Poisson(1), 1000)\n", "λ₀, α₀, τ₀ = 1, 1, 1e-2\n", "@show pvalue(k; λ₀)\n", "@show pvalue_approx0(k; λ₀, α₀, τ₀)\n", "@show pvalue_approx(k; λ₀, α₀, τ₀);" ] }, { "cell_type": "code", "execution_count": 31, "id": "d4af29b9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "plot_pval (generic function with 1 method)" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function sim_pval(; n=100, λ₀=1, α₀=1, τ₀=α₀/λ₀, L=10^5)\n", " pval = Vector{Float64}(undef, L)\n", " pval_approx0 = Vector{Float64}(undef, L)\n", " pval_approx = Vector{Float64}(undef, L)\n", " tmp = [Vector{Int}(undef, n) for _ in 1:Threads.nthreads()]\n", " model0 = Poisson(λ₀)\n", " Threads.@threads for i in 1:L\n", " K = rand!(model0, tmp[Threads.threadid()])\n", " pval[i] = pvalue(K; λ₀)\n", " pval_approx0[i] = pvalue_approx0(K; λ₀, α₀, τ₀)\n", " pval_approx[i] = pvalue_approx(K; λ₀, α₀, τ₀)\n", " end\n", " _pval = ecdf(pval)\n", " _pval_approx0 = ecdf(pval_approx0)\n", " _pval_approx = ecdf(pval_approx)\n", " ecdf_pval(x) = _pval(x)\n", " ecdf_pval_approx0(x) = _pval_approx0(x)\n", " ecdf_pval_approx(x) = _pval_approx(x)\n", " (; ecdf_pval, ecdf_pval_approx0, ecdf_pval_approx, pval, pval_approx0, pval_approx)\n", "end\n", "\n", "function plot_pval(; n=100, λ₀=1, α₀=1, τ₀=α₀/λ₀, L=10^4)\n", " (; ecdf_pval, ecdf_pval_approx0, ecdf_pval_approx, pval, pval_approx0, pval_approx) =\n", " sim_pval(; n, λ₀, α₀, τ₀, L)\n", " lim = [0.0, 1.0]\n", " \n", " P1 = scatter(pval, pval_approx0; ms=1, ma=0.7, msw=0, label=\"\")\n", " plot!(lim, lim; label=\"\", ls=:dash, lw=0.5)\n", " plot!(xguide=\"log likelihood ratio P-value\", yguide=\"approx0\")\n", " \n", " P2 = scatter(pval, pval_approx; ms=1.5, ma=0.7, msw=0, label=\"\")\n", " plot!(lim, lim; label=\"\", ls=:dash, lw=0.7)\n", " plot!(xguide=\"log likelihood ratio P-value\", yguide=\"approx\")\n", " \n", " plot(P1, P2; size=(600, 300))\n", " plot!(plot_title=\"n=$n, λ₀=$λ₀, α₀=$α₀, τ₀=$τ₀\")\n", "end" ] }, { "cell_type": "code", "execution_count": 32, "id": "814f5c01", "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot_pval(n=10)" ] }, { "cell_type": "code", "execution_count": 33, "id": "2e8cb0cb", "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot_pval(n=100)" ] }, { "cell_type": "code", "execution_count": 34, "id": "d4dd0471", "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot_pval(n=1000)" ] }, { "cell_type": "code", "execution_count": 35, "id": "2ad72403", "metadata": {}, "outputs": [ { "data": { "image/png": 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" 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