diff --git a/docs/source/examples.rst b/docs/source/examples.rst index 3bde0df13d..e0c9d76201 100644 --- a/docs/source/examples.rst +++ b/docs/source/examples.rst @@ -44,6 +44,7 @@ GLM notebooks/GLM-poisson-regression.ipynb notebooks/hierarchical_partial_pooling.ipynb notebooks/GLM-negative-binomial-regression.ipynb + notebooks/GLM-hierarchical-binominal-model.ipynb Gaussian Processes ================== @@ -78,7 +79,7 @@ Variational Inference notebooks/convolutional_vae_keras_advi.ipynb notebooks/empirical-approx-overview.ipynb notebooks/normalizing_flows_overview.ipynb - + Stochastic Gradient =================== diff --git a/docs/source/notebooks/GLM-hierarchical-binominal-model.ipynb b/docs/source/notebooks/GLM-hierarchical-binominal-model.ipynb new file mode 100644 index 0000000000..ebb3d16f03 --- /dev/null +++ b/docs/source/notebooks/GLM-hierarchical-binominal-model.ipynb @@ -0,0 +1,461 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Hierarchical Binominal Model: Rat Tumor Example" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Running on PyMC3 v3.4.1\n" + ] + } + ], + "source": [ + "%matplotlib inline\n", + "import pymc3 as pm\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import seaborn as sns\n", + "import pandas as pd\n", + "import pymc3.distributions.transforms as tr\n", + "import theano.tensor as tt\n", + "from scipy.special import gammaln\n", + "\n", + "\n", + "\n", + "plt.style.use('seaborn-darkgrid')\n", + "print('Running on PyMC3 v{}'.format(pm.__version__))\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This short tutorial demonstrates how to use pymc3 to do inference for the rat tumour example found in chapter 5 of *Bayesian Data Analysis 3rd Edition*. Readers should already be familliar with the pymc3 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 heirarchically. 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 surfce under the paramterization $(\\log(\\alpha/\\beta), \\log(\\alpha+\\beta))$. We do so as well. Through the remainder of the example let $x = \\log(\\alpha/\\beta)$ and $z = \\log(\\alpha+\\beta)$.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# rat data (BDA3, p. 102)\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", + "\n", + "N = len(n)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "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+= gammaln(alpha+beta) - gammaln(alpha) - gammaln(beta) + gammaln(alpha+Y) +gammaln(beta+N-Y) - gammaln(alpha+beta+N)\n", + " \n", + " return LL\n", + "\n", + "def log_prior(A,B):\n", + " \n", + " return -5/2*np.log(A+B)\n", + "\n", + "def trans_to_beta(x,y):\n", + " \n", + " return np.exp(y)/(np.exp(x)+1)\n", + "\n", + "def trans_to_alpha(x,y):\n", + " \n", + " return np.exp(x)*trans_to_beta(x,y)\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": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(figsize = (8,8))\n", + "ax.contourf(X,Z, surface)\n", + "ax.set_xlabel(r'$\\log(\\alpha/\\beta)$', fontsize = 16)\n", + "ax.set_ylabel(r'$\\log(\\alpha+\\beta)$', fontsize = 16)\n", + "\n", + "ix_z,ix_x = np.unravel_index(np.argmax(surface, axis=None), surface.shape)\n", + "ax.scatter([X[0,ix_x]], [Z[ix_z,0]], color = 'red')\n", + "\n", + "text= r\"$({a},{b})$\".format(a = np.round(X[0,ix_x],2), b = np.round(Z[ix_z,0],2))\n", + "\n", + "ax.annotate(text, \n", + " xy = (X[0,ix_x],Z[ix_z,0]), \n", + " xytext=(-1.6, 3.5), \n", + " ha = 'center',\n", + " fontsize = 16,\n", + " color = 'black',\n", + " arrowprops=dict(\n", + " facecolor='white',\n", + " \n", + " )\n", + " );" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The plot shows that the posterior is roughly symetric about the mode (-1.79, 2.74). This corresponds to $\\alpha = 2.21$ and $\\beta = 13.27$. We can compute the marginal means as the authors of BDA3 do, using\n", + "\n", + "$$ \\operatorname{E}(\\alpha \\lvert y) \\mbox{ is Estimated By }\n", + "\\sum_{x,z} \\alpha p(x,z\\lvert y) $$\n", + "\n", + "$$ \\operatorname{E}(\\beta \\lvert y) \\mbox{ is Estimated By }\n", + "\\sum_{x,z} \\beta p(x,z\\lvert y) $$" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "2.403" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "#Estimated mean of alpha\n", + "(df.alpha*df.normed_exp_trans).sum().round(3)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "14.319" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "#Estimated mean of beta\n", + "(df.beta*df.normed_exp_trans).sum().round(3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Computing the Posterior using PyMC3\n", + "\n", + "Computing the marginal posterior directly is a lot of work, and is not always possible for sufficiently complex models. \n", + "\n", + "On the other hand, creating heirarchichal models in pymc3 is simple. We can use the samples obtained from the posterior to estimate the means of $\\alpha$ and $\\beta$.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Auto-assigning NUTS sampler...\n", + "Initializing NUTS using jitter+adapt_diag...\n", + "Multiprocess sampling (2 chains in 2 jobs)\n", + "NUTS: [theta, ab]\n", + "Sampling 2 chains: 100%|██████████| 6000/6000 [00:19<00:00, 314.49draws/s]\n", + "The number of effective samples is smaller than 25% for some parameters.\n" + ] + } + ], + "source": [ + "def logp_ab(value):\n", + " ''' prior density'''\n", + " return tt.log(tt.pow(tt.sum(value), -5/2))\n", + "\n", + "\n", + " \n", + "with pm.Model() as model:\n", + " # Uninformative prior for alpha and beta\n", + " ab = pm.HalfFlat('ab', \n", + " shape=2, \n", + " testval=np.asarray([1., 1.]))\n", + " pm.Potential('p(a, b)', logp_ab(ab))\n", + " \n", + " X = pm.Deterministic('X',tt.log(ab[0]/ab[1]))\n", + " Z = pm.Deterministic('Z',tt.log(tt.sum(ab)))\n", + " \n", + " theta = pm.Beta('theta', alpha=ab[0], beta=ab[1], shape=N)\n", + "\n", + " p = pm.Binomial('y', p=theta, observed=y, n=n)\n", + " trace = pm.sample(1000, tune=2000, nuts_kwargs={'target_accept': .95})\n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#Check the trace. Looks good!\n", + "pm.traceplot(trace, varnames=['ab','X','Z']);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can plot a kernel density estimate for $x$ and $y$. It looks rather similar to our countour plot made from the analytic marginal posterior density. That's a good sign, and required far less effort." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "sns.kdeplot(trace['X'], trace['Z'],shade = True, cmap = 'viridis');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "From here, we could use the trace to compute the mean of the distribution." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "pm.posteriorplot.plot_posterior(trace, varnames = ['ab']);" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 2.44039844, 14.56745196])" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "#estimate the means from the samples\n", + "trace['ab'].mean(axis = 0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Conclusion\n", + "\n", + "Analytically calculating statistics for posterior distributions is difficult if not impossible for some models. Pymc3 provides an easy way drawing samples from your model's posterior with only a few lines of code. Here, we used pymc3 to obtain estimates of the posterior mean for the rat tumor example in chapter 5 of BDA3. The estimates obtained from pymc3 are encouragingly close to the estimates obtained from the analytical posterior density." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# References\n", + "\n", + "1. Gelman, Andrew, et al. *Bayesian Data Analysis*. CRC Press, 2013." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Authors: Demetri Pananos, Junpeng Lao" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.5" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +}