{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "PyMC3 Version 3.7\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/Users/claus/miniconda3/lib/python3.7/site-packages/xarray/core/merge.py:17: FutureWarning: The Panel class is removed from pandas. Accessing it from the top-level namespace will also be removed in the next version\n", " PANDAS_TYPES = (pd.Series, pd.DataFrame, pd.Panel)\n" ] } ], "source": [ "import numpy as np\n", "from scipy import stats\n", "import pandas as pd\n", "\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "\n", "import pymc3 as pm\n", "import theano.tensor as tt\n", "\n", "print(f\"PyMC3 Version {pm.__version__}\")\n", "\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Dice, Polls & Dirichlet Multinomials" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As part of a longer term project to learn Bayesian Statistics, I'm currently reading [Bayesian Data Analysis, 3rd Edition](http://www.stat.columbia.edu/~gelman/book/) by Andrew Gelman, John Carlin, Hal Stern, David Dunson, Aki Vehtari, and Donald Rubin, commonly known as **BDA3**.\n", "Although I've been using Bayesian statistics and probabilistic programming languages, like [PyMC3](https://docs.pymc.io/), in projects for the last year or so, this book forces me to go beyond a pure practioner's approach to modeling, while still delivering very practical value.\n", "\n", "Below are a few take aways from the earlier chapters in the book I found interesting. They are meant to hopefully inspire others to learn about Bayesian statistics, without trying to be overly formal about the math. If something doesn't look 100% to the trained mathematicians in the room, please let me know, or just squint a little harder. ;)\n", "\n", "We'll cover:\n", "- Some common **conjugate distributions**\n", "- An example of the **Dirichlet-Multinomial** distribution using dice rolls\n", "- Two examples involing **polling data** from BDA3\n", "\n", "## Conjugate Distributions\n", "In Chapter 2 of the book, the authors introduce several choices for prior probability distributions, along with the concept of **conjugate distributions** in section 2.4. \n", "\n", "From [Wikipedia](https://en.wikipedia.org/wiki/Conjugate_prior)\n", "> In Bayesian probability theory, if the posterior distributions p(θ | x) are in the same probability distribution family as the prior probability distribution p(θ), the prior and posterior are then called conjugate distributions, and the prior is called a conjugate prior for the likelihood function\n", "\n", "John Cook has this helpful diagram on his [website](https://www.johndcook.com/blog/conjugate_prior_diagram/) that shows some common families of conjugate distributions:\n", "\n", "\n", "\n", "\n", "Conjugate distributions are a very important concept in probability theory, owing to a large degree to some nice mathematical properties that make computing the posteriors more tractable. Even with increasingly better computational tools, such as MCMC, models based on conjugate distributions are advantageous.\n", "\n", "### Beta-Binomial\n", "One of the better known examples of conjugate distributions is the [Beta-Binomial](https://www.statisticshowto.datasciencecentral.com/beta-binomial-distribution/) distribution, which is often used to model series of coin flips (the ever present topic in posts about probability). While the $Binomial$ distribution represents the probability of success in a series of Bernoulli trials, the Beta distribution here represents the prior probability distribtution of the probability of success for each trial. \n", "Thus, the probability $p$ of a coin landing on _head_ is modeled to be $Beta$ distributed (with parameters $\\alpha$ and $\\beta$), while the likelihood of _heads_ and _tails_ is assumed to follow a $Binomial$ distribution with parameters $n$ (representing the number of flips) and the $Beta$ distributed $p$, thus creating the link.\n", "\n", "$$p \\sim Beta(\\alpha, \\beta)$$\n", "$$y \\sim Binomial(n, p)$$\n", "\n", "### Gamma-Poisson\n", "Another often-used conjugate distribution is the Gamma-Poisson distribution, so named because the rate parameter $\\lambda$ that parameterizes the Poisson distributed is modeled as a Gamma distribution:\n", "$$\\lambda \\sim Gamma(k, \\theta)$$\n", "$$y \\sim Poisson(\\lambda)$$\n", "\n", "While the discrete $Poisson$ distributed is often used in applications of count data, such as store customers, eCommerce orders, website visits, the $Gamma$ distribution serves as a useful distribution to model the rate at which these events occur ($\\lambda$), since the $Gamma$ distribution models positive continuous values only but is otherwise quite flexible:\n", "\n", "\n", "\n", "### Dirichlet-Multinomial\n", "A perhaps more interesting and seemingly less talked-about example of conjugate distributions is the [Dirichlet-Multinomial](https://en.wikipedia.org/wiki/Dirichlet-multinomial_distribution) distribution, introduced in chapter 3 of BDA3. \n", "\n", "One way of think about the $Dirichlet-Multinomial$ distribution is that while the $Multinomial$ (-> multiple choices) distribution is a generalization of the $Binomial$ distribution (-> binary choice), the $Dirichlet$ distribution is a generalization of the $Beta$ distribution. That is, while the $Beta$ distribution models the probability of a _single_ probability $p$, the $Dirichlet$ models the probabilities of _multiple_, mutually exclusive choices, parameterized by $a$ which is referred to as the _concentration_ parameter and represents the weights for each choice (we'll see more on that later). \n", "\n", "In other words, think **coins** for $Beta-Binomial$ and **dice** for $Dirichlet-Multinomial$.\n", "\n", "$$\\theta \\sim Dirichlet(a)$$\n", "$$y \\sim Multinomial(n, \\theta)$$\n", "\n", "In the wild, we might encounter the Dirichlet distribution these days mostly in the context of topic modeling in natural language processing, where it's commonly used as part of a [Latent Dirichlet Allocation](https://en.wikipedia.org/wiki/Latent_Dirichlet_allocation) (or LDA) model, which is fancy way of saying we're trying to figure out the probability of an article belonging to a certain topic given its text.\n", "\n", "However, for our purposes, let's look at the Dirichlet-Multinomial in the context of multiple choices, and let's start by throwing dice as a motivating example:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Throwing Dice" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's first create some data representing 122 rolls of six-sided die, where $p$ represents the expected probability for each side, $1/6$" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "y = np.asarray([20, 21, 17, 19, 17, 28])\n", "k = len(y)\n", "p = 1/k\n", "n = y.sum()" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(122, 0.16666666666666666)" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n, p" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Just looking at a simple bar plot, we suspect that we might not be dealing with a fair die! \n", "\n", "However, students of Bayesian statistics that we are, we'd like to go further and quantify our uncertainty in the fairness of the die and calculate the probability that someone slipped us loaded dice." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "sns.barplot(x=np.arange(1, k+1), y=y);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's set up a simple model in PyMC3 that not only calculates the posterior probability for $theta$ (i.e. the probability for each side of the die), but also estimates the bias for throwing a $6$. \n", "We will use `Deterministic` variable, in addition to our unobserved (`theta`) and observed (`results`) variables." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the prior on $theta$, we'll use a non-informative uniform distribution, by initializing the $Dirichlet$ prior with a series of 1s for the parameter `a`, one for each of the `k` possible outcomes. This is similar to initializing a $Beta$ distribution as $Beta(1, 1)$, which corresponds to the Uniform distribution." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(122, array([20, 21, 17, 19, 17, 28]))" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n, y" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "with pm.Model() as dice_model:\n", " \n", " # initializes the Dirichlet distribution with a uniform prior:\n", " a = np.ones(k) \n", " \n", " theta = pm.Dirichlet(\"theta\", a=a)\n", " \n", " # Since theta[5] will hold the posterior probability of rolling a 6\n", " # we'll compare this to the reference value p = 1/6\n", "# six_bias = pm.Deterministic(\"six_bias\", theta[k-1] - p)\n", " \n", " results = pm.Multinomial(\"results\", n=n, p=theta, observed=y)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\n", " \\begin{array}{rcl}\n", " theta &\\sim & \\text{Dirichlet}(\\mathit{a}=array)\\\\results &\\sim & \\text{Multinomial}(\\mathit{n}=122, \\mathit{p}=f(\\text{theta},~f(f(\\text{theta}))))\n", " \\end{array}\n", " $$" ], "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dice_model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Starting with version 3.5, PyMC3 includes a handy function to plot models in plate notation:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "%3\n", "\n", "\n", "cluster6\n", "\n", "6\n", "\n", "\n", "\n", "results\n", "\n", "results ~ Multinomial\n", "\n", "\n", "\n", "theta\n", "\n", "theta ~ Dirichlet\n", "\n", "\n", "\n", "theta->results\n", "\n", "\n", "\n", "\n", "\n", "six_bias\n", "\n", "six_bias ~ Deterministic\n", "\n", "\n", "\n", "theta->six_bias\n", "\n", "\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pm.model_to_graphviz(dice_model)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "theta_stickbreaking__ -5.96\n", "results -13.14\n", "Name: Log-probability of test_point, dtype: float64" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dice_model.check_test_point()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's draw 1,000 samples from the joint posterior using the default NUTS sampler:" ] }, { "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 (4 chains in 4 jobs)\n", "NUTS: [theta]\n", "Sampling 4 chains: 100%|██████████| 6000/6000 [00:01<00:00, 4523.78draws/s]\n" ] } ], "source": [ "with dice_model:\n", " dice_trace = pm.sample(draws=1000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From the traceplot, we can already see that one of the $theta$ posteriors isn't in line with the rest:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/claus/.pyenv/versions/3.6.7/lib/python3.6/site-packages/matplotlib/axes/_base.py:3455: MatplotlibDeprecationWarning: \n", "The `ymin` argument was deprecated in Matplotlib 3.0 and will be removed in 3.2. Use `bottom` instead.\n", " alternative='`bottom`', obj_type='argument')\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "with dice_model:\n", " pm.traceplot(dice_trace, combined=True, lines={\"theta\": p})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We'll plot the posterior distributions for each $theta$ and compare it our reference value $p$ to see if the 95% HPD (Highest Posterior Density) interval includes $p = 1/6$." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "axes = pm.plot_posterior(dice_trace, varnames=[\"theta\"], ref_val=np.round(p, 3))\n", "for i, ax in enumerate(axes):\n", " ax.set_title(f\"{i+1}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can clearly see that the HPD for the posterior probability for rolling a $6$ barely includes what we'd expect from a fair die." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To be more precise, let's plot the probability of our die being biased on $6$, by comparing $theta[Six]$ to $p$" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax = pm.plot_posterior(dice_trace, varnames=[\"six_bias\"], ref_val=[0])\n", "ax.set_title(f\"P(Theta[Six] - {p:.2%})\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Lastly, we can calculate the probability that the die is biased on $6$ by calculating the density to the right of our reference line at $0$:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "P(Six is biased) = 95.05%\n" ] } ], "source": [ "six_bias_perc = len(dice_trace[\"six_bias\"][dice_trace[\"six_bias\"]>0])/len(dice_trace[\"six_bias\"])\n", " \n", "print(f'P(Six is biased) = {six_bias_perc:.2%}')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Better get some new dice...!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Polling #1\n", "\n", "Let's turn our review of the Dirichlet-Multinomial distribution to another example, concerning polling data. \n", "\n", "In section 3.4 of BDA3 on multivariate models and, specifically the section on _Multinomial Models for Categorical Data_, the authors include a, little dated, example of polling data in the 1988 Presidential race between George H.W. Bush and Michael Dukakis.\n", "\n", "Here's the setup:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- 1,447 likely voters were surveyed about their preferences in the upcoming presidential election\n", "- Their responses were:\n", " - Bush: 727\n", " - Dukakis: 583\n", " - Other: 137\n", "- What is the probability that more people will vote for Bush over Dukakis?\n", " - i.e. what is the difference in support for the two major candidates?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We set up the data, where $k$ represents the number of choices the respondents had:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(1447, 3)" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "y = np.asarray([727, 583, 137])\n", "n = y.sum()\n", "k = len(y)\n", "n, k" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We, again, set up a simple Dirichlet-Multinomial model and include a `Deterministic` variable that calculates the metric of interest - the difference in probability of respondents for Bush vs. Dukakis." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "with pm.Model() as polling_model:\n", " \n", " # initializes the Dirichlet distribution with a uniform prior:\n", " a = np.ones(k) \n", " \n", " theta = pm.Dirichlet(\"theta\", a=a)\n", " \n", " bush_dukakis_diff = pm.Deterministic(\"bush_dukakis_diff\", theta[0] - theta[1])\n", " \n", " likelihood = pm.Multinomial(\"likelihood\", n=n, p=theta, observed=y)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "%3\n", "\n", "\n", "cluster3\n", "\n", "3\n", "\n", "\n", "\n", "likelihood\n", "\n", "likelihood ~ Multinomial\n", "\n", "\n", "\n", "theta\n", "\n", "theta ~ Dirichlet\n", "\n", "\n", "\n", "theta->likelihood\n", "\n", "\n", "\n", "\n", "\n", "bush_dukakis_diff\n", "\n", "bush_dukakis_diff ~ Deterministic\n", "\n", "\n", "\n", "theta->bush_dukakis_diff\n", "\n", "\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pm.model_to_graphviz(polling_model)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "Multiprocess sampling (4 chains in 4 jobs)\n", "NUTS: [theta]\n", "Sampling 4 chains: 100%|██████████| 6000/6000 [00:01<00:00, 5143.58draws/s]\n", "The acceptance probability does not match the target. It is 0.8821129470305148, but should be close to 0.8. Try to increase the number of tuning steps.\n" ] } ], "source": [ "with polling_model:\n", " polling_trace = pm.sample(draws=1000)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/claus/.pyenv/versions/3.6.7/lib/python3.6/site-packages/matplotlib/axes/_base.py:3455: MatplotlibDeprecationWarning: \n", "The `ymin` argument was deprecated in Matplotlib 3.0 and will be removed in 3.2. Use `bottom` instead.\n", " alternative='`bottom`', obj_type='argument')\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "with polling_model:\n", " pm.traceplot(polling_trace, combined=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Looking at the % difference between respondents for Bush vs Dukakis, we can see that most of the density is greater than 0%, signifying a strong advantage for Bush in this poll.\n", "\n", "We've also fit a $Beta$ distribution to this data via `scipy.stats`, and we can see that posterior of the difference of the 2 $theta$ values is a pretty good match." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_, ax = plt.subplots(1,1, figsize=(10, 6))\n", "sns.distplot(polling_trace[\"bush_dukakis_diff\"], bins=20, ax=ax, kde=False, fit=stats.beta)\n", "ax.axvline(0, c='g', linestyle='dotted')\n", "ax.set_title(\"% Difference Bush vs Dukakis\")\n", "ax.set_xlabel(\"% Difference\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Percentage of samples with `bush_dukakis_diff > 0`:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "P(More Responses for Bush) = 100%\n" ] } ], "source": [ "bush_dukakis_diff_perc = len(polling_trace[\"bush_dukakis_diff\"][polling_trace[\"bush_dukakis_diff\"]>0])/len(polling_trace[\"bush_dukakis_diff\"])\n", " \n", "print(f'P(More Responses for Bush) = {bush_dukakis_diff_perc:.0%}')" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Polling #2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As an extension to the previous model, the authors of BDA include an exercise in chapter 3.10 (Exercise 2) that presents us with polling data from the 1988 Presidential race, taking _before_ and _after_ the one of the debates.\n", "\n", "> Comparison of two multinomial observations: on September 25, 1988, the evening of a\n", "presidential campaign debate, ABC News conducted a survey of registered voters in the\n", "United States; 639 persons were polled before the debate, and 639 different persons were\n", "polled after. The results are displayed in Table 3.2. Assume the surveys are independent\n", "simple random samples from the population of registered voters. Model the data with\n", "two different multinomial distributions. For $j = 1, 2$, let $\\alpha_j$ be the proportion of voters\n", "who preferred Bush, out of those who had a preference for either Bush or Dukakis at\n", "the time of survey $j$. Plot a histogram of the posterior density for $\\alpha_2 − \\alpha_1$. What is the\n", "posterior probability that there was a shift toward Bush?\n", "\n", "Let's copy the data from the exercise and model the problem as a probabilistic model, again using PyMC3:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "data = pd.DataFrame([\n", " {\"candidate\": \"bush\", \"pre\": 294, \"post\": 288},\n", " {\"candidate\": \"dukakis\", \"pre\": 307, \"post\": 332},\n", " {\"candidate\": \"other\", \"pre\": 38, \"post\": 10}\n", " ], columns=[\"candidate\", \"pre\", \"post\"])" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " candidate pre post\n", "0 bush 294 288\n", "1 dukakis 307 332\n", "2 other 38 10" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Convert to 2x3 array" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[294, 307, 38],\n", " [288, 332, 10]])" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "y = data[[\"pre\", \"post\"]].T.values\n", "y" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Number of respondents in each survey" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([639, 630])" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n = y.sum(axis=1) \n", "n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Number of respondents for the 2 major candidates in each survey" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([601, 620])" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m = y[:, :2].sum(axis=1) \n", "m" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For this model, we'll need to set up the priors slightly differently. Instead of 1 set of thetas, we need 2, one for each survey (pre/post debate).\n", "To do that without creating specific pre/post versions of each variable, we'll take advantage of PyMC3's `shape` parameter, available for most (all?) distributions.\n", "\n", "In this case, we'll need a 2-dimensional shape parameter, representing the number of debates `n_debates` and the number of choices in candidates `n_candidates`" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(2, 3)" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n_debates, n_candidates = y.shape\n", "n_debates, n_candidates" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Thus, we need to initialize a Dirichlet distribution prior with shape `(2,3)` and then refer to the relevant parameters by index where needed." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/claus/.pyenv/versions/3.6.7/lib/python3.6/site-packages/theano/tensor/subtensor.py:2197: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n", " rval = inputs[0].__getitem__(inputs[1:])\n" ] } ], "source": [ "with pm.Model() as polling_model_debates:\n", " \n", " # initializes the Dirichlet distribution with a uniform prior:\n", " shape = (n_debates, n_candidates)\n", " a = np.ones(shape)\n", " \n", " # This creates a separate Dirichlet distribution for each debate\n", " # where sum of probabilities across candidates = 100% for each debate\n", " theta = pm.Dirichlet(\"theta\", a=a, shape=shape)\n", " \n", " # get the \"Bush\" theta for each debate, at index=0\n", " bush_pref = pm.Deterministic(\"bush_pref\", theta[:, 0] * n / m)\n", " \n", " # to calculate probability that support for Bush shifted from debate 1 [0] to 2 [1]\n", " bush_shift = pm.Deterministic(\"bush_shift\", bush_pref[1]-bush_pref[0])\n", " \n", " # because of the shapes of the inputs, this essentially creates 2 multinomials, \n", " # one for each debate\n", " responses = pm.Multinomial(\"responses\", n=n, p=theta, observed=y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For models with multi-dimensional shapes, it's always good to check the shapes of the various parameters before sampling:" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "theta_stickbreaking__ (2, 2)\n", "theta (2, 3)\n", "bush_pref (2,)\n", "bush_shift ()\n" ] } ], "source": [ "for v in polling_model_debates.unobserved_RVs:\n", " print(v, v.tag.test_value.shape)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The plate notation visual can also help with that:" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "%3\n", "\n", "\n", "cluster2 x 3\n", "\n", "2 x 3\n", "\n", "\n", "cluster2\n", "\n", "2\n", "\n", "\n", "\n", "responses\n", "\n", "responses ~ Multinomial\n", "\n", "\n", "\n", "theta\n", "\n", "theta ~ Dirichlet\n", "\n", "\n", "\n", "theta->responses\n", "\n", "\n", "\n", "\n", "\n", "bush_pref\n", "\n", "bush_pref ~ Deterministic\n", "\n", "\n", "\n", "theta->bush_pref\n", "\n", "\n", "\n", "\n", "\n", "bush_shift\n", "\n", "bush_shift ~ Deterministic\n", "\n", "\n", "\n", "bush_pref->bush_shift\n", "\n", "\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pm.model_to_graphviz(polling_model_debates)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's sample with a slightly higher number of draws and tuning steps:" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "Multiprocess sampling (4 chains in 4 jobs)\n", "NUTS: [theta]\n", "Sampling 4 chains: 100%|██████████| 18000/18000 [00:04<00:00, 4375.96draws/s]\n" ] } ], "source": [ "with polling_model_debates:\n", " polling_trace_debates = pm.sample(draws=3000, tune=1500)" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/claus/.pyenv/versions/3.6.7/lib/python3.6/site-packages/matplotlib/axes/_base.py:3455: MatplotlibDeprecationWarning: \n", "The `ymin` argument was deprecated in Matplotlib 3.0 and will be removed in 3.2. Use `bottom` instead.\n", " alternative='`bottom`', obj_type='argument')\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "with polling_model_debates:\n", " pm.traceplot(polling_trace_debates, combined=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We'll take a look at the means of the posteriors for `theta`, indicating the % of support for each candidate pre & post debate:" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
bushdukakisother
pre0.459540.4797500.060710
post0.456460.5261260.017414
\n", "
" ], "text/plain": [ " bush dukakis other\n", "pre 0.45954 0.479750 0.060710\n", "post 0.45646 0.526126 0.017414" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s = [\"pre\", \"post\"]\n", "candidates = data[\"candidate\"].values\n", "pd.DataFrame(polling_trace_debates[\"theta\"].mean(axis=0), index=s, columns=candidates)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Just from the means, we can see that the number of Bush supporters has likely decreased post debate from 48.8% to 46.3% (as a % of supporters of the 2 major candidates):" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
bush_pref
pre0.488596
post0.463823
\n", "
" ], "text/plain": [ " bush_pref\n", "pre 0.488596\n", "post 0.463823" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pd.DataFrame(polling_trace_debates[\"bush_pref\"].mean(axis=0), index=s, columns=[\"bush_pref\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's compare the results visually, by plotting the posterior distributions of the pre/post debate values for % responses for Bush and the posterior for pre/post difference in Bush supporters:" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/claus/.pyenv/versions/3.6.7/lib/python3.6/site-packages/scipy/stats/stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n", " return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_, ax = plt.subplots(2,1, figsize=(10, 10))\n", "\n", "sns.distplot(polling_trace_debates[\"bush_pref\"][:,0], hist=False, ax=ax[0], label=\"Pre-Debate\")\n", "sns.distplot(polling_trace_debates[\"bush_pref\"][:,1], hist=False, ax=ax[0], label=\"Post-Debate\")\n", "ax[0].set_title(\"% Responses for Bush vs Dukakis\")\n", "ax[0].set_xlabel(\"% Responses\");\n", "\n", "sns.distplot(polling_trace_debates[\"bush_shift\"], hist=True, ax=ax[1], label=\"P(Bush Shift)\")\n", "ax[1].axvline(0, c='g', linestyle='dotted')\n", "ax[1].set_title(\"% Shift Pre/Prior Debate\")\n", "ax[1].set_xlabel(\"% Shift\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From the second plot, we can already see that a large portion of the posterior density is below 0, but let's be precise and actually calculate the probability that support shifted _towards_ Bush after the debate:" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "P(Shift Towards Bush) = 19.7%\n" ] } ], "source": [ "perc_shift = (len(polling_trace_debates[\"bush_shift\"][polling_trace_debates[\"bush_shift\"] > 0])\n", " /len(polling_trace_debates[\"bush_shift\"])\n", " )\n", "print(f'P(Shift Towards Bush) = {perc_shift:.1%}')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "While that was a sort of round-about way to show that Bush lost support during the debate, hopefully this illustrated the flexibility and robustness of probabilistic models (and PyMC3)." ] } ], "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": "3.7.4" } }, "nbformat": 4, "nbformat_minor": 4 }