{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Bayesian Statistics - The Challenger Disaster" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This ipynotebook is an excerpt of the excellent 'Bayesian Methods for Hackers'. For the whole book, check out http://camdavidsonpilon.github.io/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/.\n", "\n", "Note that this Notebook requires the package *pymc*.\n", "\n", "author: Thomas Haslwanter, date: Oct-2015\n", "\n", "On January 28, 1986, the twenty-fifth flight of the U.S. space shuttle program ended in disaster when one of the rocket boosters of the Shuttle Challenger exploded shortly after lift-off, killing all seven crew members. The presidential commission on the accident concluded that it was caused by the failure of an O-ring in a field joint on the rocket booster, and that this failure was due to a faulty design that made the O-ring unacceptably sensitive to a number of factors including outside temperature. Of the previous 24 flights, data were available on failures of O-rings on 23, (one was lost at sea), and these data were discussed on the evening preceding the Challenger launch, but unfortunately only the data corresponding to the 7 flights on which there was a damage incident were considered important and these were thought to show no obvious trend. The data are shown below:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Temp (F), O-Ring failure?\n", "[[ 66. 0.]\n", " [ 70. 1.]\n", " [ 69. 0.]\n", " [ 68. 0.]\n", " [ 67. 0.]\n", " [ 72. 0.]\n", " [ 73. 0.]\n", " [ 70. 0.]\n", " [ 57. 1.]\n", " [ 63. 1.]\n", " [ 70. 1.]\n", " [ 78. 0.]\n", " [ 67. 0.]\n", " [ 53. 1.]\n", " [ 67. 0.]\n", " [ 75. 0.]\n", " [ 70. 0.]\n", " [ 81. 0.]\n", " [ 76. 0.]\n", " [ 79. 0.]\n", " [ 75. 1.]\n", " [ 76. 0.]\n", " [ 58. 1.]]\n" ] } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import os\n", "import seaborn as sns\n", "from urllib.request import urlopen\n", "\n", "url_base = 'https://raw.githubusercontent.com/thomas-haslwanter/statsintro_python/master/ipynb/Data/data_bayes/'\n", "inFile = 'challenger_data.csv'\n", "url = url_base + inFile\n", "challenger_data = np.genfromtxt(urlopen(url), skip_header=1, usecols=[1, 2],\n", " missing_values='NA', delimiter=',')\n", "# drop the NA values\n", "challenger_data = challenger_data[~np.isnan(challenger_data[:, 1])]\n", "\n", "# plot it, as a function of tempature (the first column)\n", "print(\"Temp (F), O-Ring failure?\")\n", "print(challenger_data)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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L+PLLL5Geng4hBHQ6HRISEnDs2DFj5CMiolKm9xp/SEgIunfvjqysLAwbNgxO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\nqFGjBk6ePInOnTuXekZ6NSz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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "sns.set_style('darkgrid')\n", "np.set_printoptions(precision=3, suppress=True)\n", "\n", "plt.scatter(challenger_data[:, 0], challenger_data[:, 1], s=75, color=\"k\",\n", " alpha=0.5)\n", "plt.yticks([0, 1])\n", "plt.ylabel(\"Damage Incident?\")\n", "plt.xlabel(\"Outside temperature (Fahrenheit)\")\n", "plt.title(\"Defects of the Space Shuttle O-Rings vs temperature\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It looks clear that the probability of damage incidents occurring increases as the outside temperature decreases. We are interested in modeling the probability here because it does not look like there is a strict cutoff point between temperature and a damage incident occurring. The best we can do is ask \"At temperature t, what is the probability of a damage incident?\". The goal of this example is to answer that question.\n", "\n", "We need a function of temperature, call it p(t), that is bounded between 0 and 1 (so as to model a probability) and changes from 1 to 0 as we increase temperature. There are actually many such functions, but the most popular choice is the *logistic function*.\n", "\n", "\n", "$$p(t) = \\frac{1}{ 1 + e^{ \\;\\beta t + \\alpha } } $$\n", "\n", "In this model, the variable $\\beta$ that describes how quickly the function changes from 1 to 0, and $\\alpha$ indicates the location of this change. For example" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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KwMffZcLU1rNtCXE0KupuJNorgppgeqjh6GFUrF/X4+3uGRsKkYCHrQfpOgZx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\nYbAqFodLug4qRtwXn8fBgqk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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def logistic(x, beta, alpha=0):\n", " return 1.0 / (1.0 + np.exp(np.dot(beta, x) + alpha))\n", "\n", "x = np.linspace(-4, 4, 100)\n", "\n", "plt.plot(x, logistic(x, 1), label=r\"$\\beta = 1, \\alpha = 0$\", ls=\"-\", lw=1)\n", "plt.plot(x, logistic(x, 3, 6), label=r\"$\\beta = 3, \\alpha = 6$\", ls=\"-\", lw=1)\n", "plt.plot(x, logistic(x, -5), label=r\"$\\beta = -5, \\alpha = 0$\", ls=\"--\", lw=1)\n", "\n", "plt.legend(loc='lower left')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Perform the MCMC-simulations" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import pymc as pm\n", "\n", "temperature = challenger_data[:, 0]\n", "D = challenger_data[:, 1] # defect or not?\n", "\n", "# Define the prior distributions for alpha and beta\n", "# 'value' sets the start parameter for the simulation\n", "# The second parameter for the normal distributions is the \"precision\",\n", "# i.e. the inverse of the standard deviation\n", "\n", "# notice the`value` here. We explain why below.\n", "beta = pm.Normal(\"beta\", 0, 0.001, value=0)\n", "alpha = pm.Normal(\"alpha\", 0, 0.001, value=0)\n", "\n", "\n", "@pm.deterministic\n", "def p(t=temperature, alpha=alpha, beta=beta):\n", " return 1.0 / (1. + np.exp(beta * t + alpha))\n", "\n", "# connect the probabilities in `p` with our observations through a\n", "# Bernoulli random variable.\n", "observed = pm.Bernoulli(\"bernoulli_obs\", p, value=D, observed=True)\n", "\n", "# Combine the values to a model\n", "model = pm.Model([observed, beta, alpha])" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " [-----------------100%-----------------] 120000 of 120000 complete in 11.0 sec" ] } ], "source": [ "# Perform the simulations\n", "map_ = pm.MAP(model)\n", "map_.fit()\n", "mcmc = pm.MCMC(model)\n", "mcmc.sample(120000, 100000, 2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Show the resulting posterior distributions" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Bw4YNAwD069cPly9f1mnPzMxEYmIiioqKEBwcjHnz5jU9UkIIIVZhUeJ/uBCb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\nPawxiV+5NBojwq03YqUxmnI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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "alpha_samples = mcmc.trace('alpha')[:, None] # best to make them 1d\n", "beta_samples = mcmc.trace('beta')[:, None]\n", "\n", "# histogram of the samples:\n", "plt.subplot(211)\n", "plt.title(r\"Posterior distributions of the variables $\\alpha, \\beta$\")\n", "plt.hist(beta_samples, histtype='stepfilled', bins=35, alpha=0.85,\n", " label=r\"posterior of $\\beta$\", color=\"#7A68A6\", normed=True)\n", "plt.legend()\n", "\n", "plt.subplot(212)\n", "plt.hist(alpha_samples, histtype='stepfilled', bins=35, alpha=0.85,\n", " label=r\"posterior of $\\alpha$\", color=\"#A60628\", normed=True)\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Show the probability curve" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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7l8TbvyTe/iXx9p920w1GCNE+GXQGInThPmffOdcfR/+BGoeFMls5JdZSiq2l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\nlwRB6PpEsS4IgiB0efGRftwwpQ9XTExmfdYh1m4v4dBRXWR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a76CO0tXy3d2JfHvPaX+B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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Draw the probability as a function of time\n", "t = np.linspace(temperature.min() - 5, temperature.max() + 5, 50)[:, None]\n", "p_t = logistic(t.T, beta_samples, alpha_samples)\n", "\n", "mean_prob_t = p_t.mean(axis=0)\n", "\n", "plt.figure(figsize=(12.5, 4))\n", "\n", "plt.plot(t, mean_prob_t, lw=3, label=\"average posterior \\nprobability \\\n", "of defect\")\n", "plt.plot(t, p_t[0, :], ls=\"--\", label=\"realization from posterior\")\n", "plt.plot(t, p_t[-2, :], ls=\"--\", label=\"realization from posterior\")\n", "plt.scatter(temperature, D, color=\"k\", s=50, alpha=0.5)\n", "plt.title(\"Posterior expected value of probability of defect; \\\n", "plus realizations\")\n", "plt.legend(loc=\"lower left\")\n", "plt.ylim(-0.1, 1.1)\n", "plt.xlim(t.min(), t.max())\n", "plt.ylabel(\"probability\")\n", "plt.xlabel(\"temperature\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Draw Confidence-Intervals" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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6mXcTGR7Ly28txWazejrSGVEoJI4dKaTaVOPpKIJwVlwWgVtuuYV33nmH7du3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\nKS42k5+fh7e3D/v27SUkJJS9e3fj4+PLO+98wJ9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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.stats.mstats import mquantiles\n", "\n", "# vectorized bottom and top 2.5% quantiles for \"confidence interval\"\n", "qs = mquantiles(p_t, [0.025, 0.975], axis=0)\n", "plt.fill_between(t[:, 0], *qs, alpha=0.7,\n", " color=\"#7A68A6\")\n", "\n", "plt.plot(t[:, 0], qs[0], label=\"95% CI\", color=\"#7A68A6\", alpha=0.7)\n", "\n", "plt.plot(t, mean_prob_t, lw=1, ls=\"--\", color=\"k\",\n", " label=\"average posterior \\nprobability of defect\")\n", "\n", "plt.xlim(t.min(), t.max())\n", "plt.ylim(-0.02, 1.02)\n", "plt.legend(loc=\"lower left\")\n", "plt.scatter(temperature, D, color=\"k\", s=50, alpha=0.5)\n", "plt.xlabel(\"temp, $t$\")\n", "\n", "plt.ylabel(\"probability estimate\")\n", "plt.title(\"Posterior probability estimates given temp. $t$\")" ] } ], "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": "3.4.3" } }, "nbformat": 4, "nbformat_minor": 0 }