{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Think Bayes\n", "\n", "This notebook presents example code and exercise solutions for Think Bayes.\n", "\n", "Copyright 2018 Allen B. Downey\n", "\n", "MIT License: https://opensource.org/licenses/MIT" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# Configure Jupyter so figures appear in the notebook\n", "%matplotlib inline\n", "\n", "# Configure Jupyter to display the assigned value after an assignment\n", "%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'\n", "\n", "# import classes from thinkbayes2\n", "from thinkbayes2 import Pmf, Suite, Beta\n", "import thinkplot\n", "\n", "import numpy as np" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The social desirability problem\n", "\n", "Whenever you survey people about sensitive issues, you have to deal with [social desirability bias](https://en.wikipedia.org/wiki/Social_desirability_bias), which is the tendency of people to shade their answers in the direction they think shows them in the most positive light.\n", "\n", "One of the ways to improve the quality of the results is to collect responses in indirect ways. For example, [here's a clever way one research group estimated the prevalence of atheists](https://fivethirtyeight.com/features/way-more-americans-may-be-atheists-than-we-thought/).\n", "\n", "Another way is [randomized response](https://en.wikipedia.org/wiki/Randomized_response), as described in [this presentation](http://www.soz.unibe.ch/ueber_uns/personen/jann/presentations_by_ben_jann/e131361/e131381/rrt_online07_kassel08_ger.pdf) or [this video](https://www.youtube.com/watch?v=nwJ0qY_rP0A).\n", "\n", "As an example, suppose you ask 100 people to flip a coin and:\n", "\n", "* If they get heads, they honestly answer the question \"Do you believe in God?\"\n", "\n", "* If they get tails, they flip a second coin and report YES for heads, tails for NO.\n", "\n", "Assume that you cannot observe whether they flip one coin or two.\n", "And suppose you get 55 YESes and 45 NOs.\n", "\n", "1. Estimate the prevalence of believers in the surveyed population (by which, as always, I mean compute a posterior distribution).\n", "\n", "2. How efficient is this method? That is, how does the width of the posterior distribution compare to the distribution you would get if 100 people answered the question honestly?" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# Solution\n", "\n", "class Social(Suite):\n", " \n", " def Likelihood(self, data, hypo):\n", " \"\"\"\n", " data: outcome of unreliable measurement, either 'YES' or 'NO'\n", " hypo: actual proportion of the thing we're measuring\n", " \"\"\"\n", " p = hypo\n", " p_yes = 0.25 + p/2\n", " if data == 'YES':\n", " return p_yes\n", " else:\n", " return 1 - p_yes" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Solution\n", "\n", "prior = np.linspace(0, 1, 101)\n", "suite = Social(prior)\n", "\n", "thinkplot.Pdf(suite, label='Prior')\n", "thinkplot.decorate(xlabel='Fraction of the population',\n", " ylabel='PDF')" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# Solution\n", "\n", "for i in range(55):\n", " suite.Update('YES')\n", " \n", "for i in range(45):\n", " suite.Update('NO')" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Solution\n", "\n", "thinkplot.Pdf(suite, label='Posterior')\n", "thinkplot.decorate(xlabel='Fraction of the population',\n", " ylabel='PDF')" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.5980373585330246, 0.6)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Solution\n", "\n", "suite.Mean(), suite.MAP()" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Solution\n", "\n", "# For comparison, what would we think if we had been able \n", "# to survey 100 people directly?\n", "\n", "beta = Beta(1, 1)\n", "beta.Update((60, 40))\n", "thinkplot.Pdf(beta.MakePmf(), label='Direct', color='gray')\n", "\n", "thinkplot.Pdf(suite, label='Randomized')\n", "thinkplot.decorate(xlabel='Fraction of the population',\n", " ylabel='PDF')" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Solution\n", "\n", "# To see how efficient this method is, we can divide the sample size for\n", "# the direct method by a factor. It looks like we lose a factor of about 4.\n", "\n", "factor = 4\n", "beta = Beta(1, 1)\n", "beta.Update((60/factor, 40/factor))\n", "thinkplot.Pdf(beta.MakePmf(), label='Direct', color='gray')\n", "\n", "thinkplot.Pdf(suite, label='Randomized')\n", "thinkplot.decorate(xlabel='Fraction of the population',\n", " ylabel='PDF')" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "# Solution\n", "\n", "# So the effective sample size is about 25." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "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 }