{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Hierarchical Binomial Model: Rat Tumor Example\n", ":::{post} Jan 10, 2023\n", ":tags: generalized linear model, hierarchical model \n", ":category: intermediate\n", ":author: Demetri Pananos, Junpeng Lao, Raúl Maldonado, Farhan Reynaldo\n", ":::" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import arviz as az\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pandas as pd\n", "import pymc as pm\n", "import pytensor.tensor as pt\n", "\n", "from scipy.special import gammaln" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "%config InlineBackend.figure_format = 'retina'\n", "az.style.use(\"arviz-darkgrid\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This short tutorial demonstrates how to use PyMC to do inference for the rat tumour example found in chapter 5 of *Bayesian Data Analysis 3rd Edition* {cite:p}gelman2013bayesian. Readers should already be familiar with the PyMC API.\n", "\n", "Suppose we are interested in the probability that a lab rat develops endometrial stromal polyps. We have data from 71 previously performed trials and would like to use this data to perform inference.\n", "\n", "The authors of BDA3 choose to model this problem hierarchically. Let $y_i$ be the number of lab rats which develop endometrial stromal polyps out of a possible $n_i$. We model the number rodents which develop endometrial stromal polyps as binomial\n", "\n", "$$y_i \\sim \\operatorname{Bin}(\\theta_i;n_i)$$\n", "\n", "allowing the probability of developing an endometrial stromal polyp (i.e. $\\theta_i$) to be drawn from some population distribution. For analytical tractability, we assume that $\\theta_i$ has Beta distribution\n", "\n", "$$\\theta_i \\sim \\operatorname{Beta}(\\alpha, \\beta)$$\n", "\n", "We are free to specify a prior distribution for $\\alpha, \\beta$. We choose a weakly informative prior distribution to reflect our ignorance about the true values of $\\alpha, \\beta$. The authors of BDA3 choose the joint hyperprior for $\\alpha, \\beta$ to be\n", "\n", "$$p(\\alpha, \\beta) \\propto (\\alpha + \\beta) ^{-5/2}$$\n", "\n", "For more information, please see *Bayesian Data Analysis 3rd Edition* pg. 110." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A Directly Computed Solution\n", "\n", "Our joint posterior distribution is\n", "\n", "$$p(\\alpha,\\beta,\\theta \\lvert y) \n", "\\propto \n", "p(\\alpha, \\beta) \n", "p(\\theta \\lvert \\alpha,\\beta)\n", "p(y \\lvert \\theta)$$\n", "\n", "which can be rewritten in such a way so as to obtain the marginal posterior distribution for $\\alpha$ and $\\beta$, namely\n", "\n", "$$p(\\alpha, \\beta, \\lvert y) = \n", "p(\\alpha, \\beta) \n", "\\prod_{i = 1}^{N} \\dfrac{\\Gamma(\\alpha+\\beta)}{\\Gamma(\\alpha)\\Gamma(\\beta)}\n", "\\dfrac{\\Gamma(\\alpha+y_i)\\Gamma(\\beta+n_i - y_i)}{\\Gamma(\\alpha+\\beta+n_i)}$$\n", "\n", "\n", "See BDA3 pg. 110 for a more information on the deriving the marginal posterior distribution. With a little determination, we can plot the marginal posterior and estimate the means of $\\alpha$ and $\\beta$ without having to resort to MCMC. We will see, however, that this requires considerable effort.\n", "\n", "The authors of BDA3 choose to plot the surface under the parameterization $(\\log(\\alpha/\\beta), \\log(\\alpha+\\beta))$. We do so as well. Through the remainder of the example let $x = \\log(\\alpha/\\beta)$ and $z = \\log(\\alpha+\\beta)$." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# rat data (BDA3, p. 102)\n", "# fmt: off\n", "y = np.array([\n", " 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1,\n", " 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 5, 2,\n", " 5, 3, 2, 7, 7, 3, 3, 2, 9, 10, 4, 4, 4, 4, 4, 4, 4,\n", " 10, 4, 4, 4, 5, 11, 12, 5, 5, 6, 5, 6, 6, 6, 6, 16, 15,\n", " 15, 9, 4\n", "])\n", "n = np.array([\n", " 20, 20, 20, 20, 20, 20, 20, 19, 19, 19, 19, 18, 18, 17, 20, 20, 20,\n", " 20, 19, 19, 18, 18, 25, 24, 23, 20, 20, 20, 20, 20, 20, 10, 49, 19,\n", " 46, 27, 17, 49, 47, 20, 20, 13, 48, 50, 20, 20, 20, 20, 20, 20, 20,\n", " 48, 19, 19, 19, 22, 46, 49, 20, 20, 23, 19, 22, 20, 20, 20, 52, 46,\n", " 47, 24, 14\n", "])\n", "# fmt: on\n", "\n", "N = len(n)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# Compute on log scale because products turn to sums\n", "def log_likelihood(alpha, beta, y, n):\n", " LL = 0\n", "\n", " # Summing over data\n", " for Y, N in zip(y, n):\n", " LL += (\n", " gammaln(alpha + beta)\n", " - gammaln(alpha)\n", " - gammaln(beta)\n", " + gammaln(alpha + Y)\n", " + gammaln(beta + N - Y)\n", " - gammaln(alpha + beta + N)\n", " )\n", "\n", " return LL\n", "\n", "\n", "def log_prior(A, B):\n", " return -5 / 2 * np.log(A + B)\n", "\n", "\n", "def trans_to_beta(x, y):\n", " return np.exp(y) / (np.exp(x) + 1)\n", "\n", "\n", "def trans_to_alpha(x, y):\n", " return np.exp(x) * trans_to_beta(x, y)\n", "\n", "\n", "# Create space for the parameterization in which we wish to plot\n", "X, Z = np.meshgrid(np.arange(-2.3, -1.3, 0.01), np.arange(1, 5, 0.01))\n", "param_space = np.c_[X.ravel(), Z.ravel()]\n", "df = pd.DataFrame(param_space, columns=[\"X\", \"Z\"])\n", "\n", "# Transform the space back to alpha beta to compute the log-posterior\n", "df[\"alpha\"] = trans_to_alpha(df.X, df.Z)\n", "df[\"beta\"] = trans_to_beta(df.X, df.Z)\n", "\n", "df[\"log_posterior\"] = log_prior(df.alpha, df.beta) + log_likelihood(df.alpha, df.beta, y, n)\n", "df[\"log_jacobian\"] = np.log(df.alpha) + np.log(df.beta)\n", "\n", "df[\"transformed\"] = df.log_posterior + df.log_jacobian\n", "df[\"exp_trans\"] = np.exp(df.transformed - df.transformed.max())\n", "\n", "# This will ensure the density is normalized\n", "df[\"normed_exp_trans\"] = df.exp_trans / df.exp_trans.sum()\n", "\n", "\n", "surface = df.set_index([\"X\", \"Z\"]).exp_trans.unstack().values.T" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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