{ "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\n", "\n", "import thinkbayes2\n", "import thinkplot\n", "\n", "import numpy as np\n", "from scipy.special import gamma" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The World Cup Problem, Part One\n", "\n", ">In the 2014 FIFA World Cup, Germany played Brazil in a semifinal match. Germany scored after 11 minutes and again at the 23 minute mark. At that point in the match, how many goals would you expect Germany to score after 90 minutes? What was the probability that they would score 5 more goals (as, in fact, they did)?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's assume that Germany has some hypothetical goal-scoring rate, λ, in goals per game.\n", "\n", "To represent the prior distribution of λ, I'll use a Gamma distribution with mean 1.3, which is the average number of goals per team per game in World Cup play.\n", "\n", "Here's what the prior looks like." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.310359949002256" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from thinkbayes2 import MakeGammaPmf\n", "\n", "xs = np.linspace(0, 8, 101)\n", "pmf = MakeGammaPmf(xs, 1.3)\n", "thinkplot.Pdf(pmf)\n", "thinkplot.decorate(title='Gamma PDF',\n", " xlabel='Goals per game',\n", " ylabel='PDF')\n", "pmf.Mean()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Exercise:** Write a class called `Soccer` that extends `Suite` and defines `Likelihood`, which should compute the probability of the data (the time between goals in minutes) for a hypothetical goal-scoring rate, `lam`, in goals per game.\n", "\n", "Hint: For a given value of `lam`, the time between goals is distributed exponentially.\n", "\n", "Here's an outline to get you started:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "class Soccer(Suite):\n", " \"\"\"Represents hypotheses about goal-scoring rates.\"\"\"\n", "\n", " def Likelihood(self, data, hypo):\n", " \"\"\"Computes the likelihood of the data under the hypothesis.\n", "\n", " hypo: scoring rate in goals per game\n", " data: interarrival time in minutes\n", " \"\"\"\n", " return 1" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# Solution goes here" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can create a `Soccer` object and initialize it with the prior Pmf:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.3103599490022553" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "soccer = Soccer(pmf)\n", "thinkplot.Pdf(soccer)\n", "thinkplot.decorate(title='Gamma prior',\n", " xlabel='Goals per game',\n", " ylabel='PDF')\n", "soccer.Mean()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's the update after first goal at 11 minutes." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.310359949002255" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "thinkplot.Pdf(soccer, color='0.7')\n", "soccer.Update(11)\n", "thinkplot.Pdf(soccer)\n", "thinkplot.decorate(title='Posterior after 1 goal',\n", " xlabel='Goals per game',\n", " ylabel='PDF')\n", "soccer.Mean()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's the update after the second goal at 23 minutes (the time between first and second goals is 12 minutes).\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.3103599490022553" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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JuAcFUJCfx2ljBkXL/9QzUSLSAilBxYltQTXnc1DxLj/vuOjy3MVr2VS4o57aIiKZRwkqTo2hjpLUggIY1K87Q/p3BaCy0nl1ytykxSIikgxKUHFqzAeVxBYUwEVnHB1dnjJrSY0u8CIimU4JKk5ZeWq0oADOOWkkbQois+tu37Wff3+wOKnxiIg0JyWoOJWVqdOCys3N5qzjj4qWJ05VZwkRaTmUoOLEjsWXrF58sa44bywWPI718acbWb1uS3IDEhFpJsk/A6eY2NHMs5PcggLo3aMzIwb1iJZfeuuDJEYjItJ8lKDilCdhRt2GXHZO9WSG0z74lOKS0iRGIyLSPJSg4tQcSSI1EtSpxw2lc/t8APbuK+XNfy9IckQiIomnBBUnWRMW1iccDnP+KcOj5X++owQlIplPCSpORQr14ot12bljyQ7mp1q1fjsfLV2d3IBERBJMCSpOeQo9BxWrU4c2HD+yf7T8ikaWEJEMlzpn4BQR24LKyU7OaOZ1ueK8MdHlWR9pMkMRyWxKUHFie/GFQqn18Ywc0pd+PToAUFpWwStTNJmhiGSu1DoDp4DYyQFTrQUVCoVqjM/3xvSPawxuKyKSSZSg4pSn0GCxtbnozGNonZ8DwNad+5g2W+PziUhmUoKKU5mCz0HFysvN4ewThkTLr0z5MInRiIgkjhJUnFQcSSLeledXj8+3eMUmPlu9MbkBiYgkgBJUjMrKSrz6Ch+hkCUvmHr06t6ZY4f1jpZfeHN2EqMREUkMJagYZWWxz0BZyvXii3V5TJfz6XOXs2tPURKjERFpegk9A5vZODP7xMyWm9l3a9mea2bPBdtnm1m/YP1YM1sQvD4ys8sTGWeV2Kk2Ujk5ARx/9CB6HdEOgJLScl79lx7cFZHMkrCzsJmFgQeBC4BhwHVmNiyu2peBHe4+ELgfuC9YvwgY4+6jgHHAn80s4X2+U2k23YaEQiEujuly/tq0hepyLiIZJZFn4bHAcndf6e6lwLPA+Lg644EnguUXgLPNzNx9n7uXB+vzAKcZ1GxBpeb9p1gXn3UsBa2yAdi6o4ipsxYlOSIRkaaTyATVE1gbU14XrKu1TpCQdgGdAMzseDNbDHwMfDUmYUWZ2W1mNtfM5hYWFh52wDXH4UvNHnyx8lvlcs6JQ6Pll6fMS2I0IiJNK5EJqrYmSHxLqM467j7b3YcDxwHfM7O8Ayq6/8Xdx7j7mC5duhx2wLEJKhxO/RYUwLUXnUg4aO0tW7WFRZ9+nuSIRESaRiIT1Dqgd0y5F7ChrjrBPaZ2wPbYCu6+FCgCvpCwSAOx96DCKd5Jokq3Lh04fmS/aPn5SepyLiKZIZFn4TnAIDPrb2Y5wARgYlydicDNwfJVwFR39+A9WQBm1hc4ClidwFiB+Id00yNBAVx9wfHR5VkLVrKpcEcSoxERaRoJOwsH94zuAiYDS4Hn3X2xmd1rZpcG1R4FOpnZcuAbQFVX9FOAj8xsAfAy8DV335qoWKvUvMSXPgnq6KH9GNSnMxCZLuSFN9SKEpH0l9CzsLtPcvfB7j7A3X8erLvH3ScGy8XufrW7D3T3se6+Mlj/lLsPd/dR7n6Mu7+SyDirlJZV98NIpwQFcMX51Q/uvjVzCUX7ipMYjYjI4Uuvs3CC1WhBpUE381jnnDSCzh0KANi7r5SJenBXRNKcElSM2Oeg0qGbeaxwOMz4s0ZFy6+8PV8P7opIWlOCipGO3cxjXXbucdG5ogp3FDHl3YVJjkhE5NApQcWI7cWXbvegAAry8zj/5OrRpP7x5pwa81uJiKST9DsLJ1DsJb50eQ4q3jUXnUR2ViT2Veu3M2fh8iRHJCJyaNLzLJwg6focVKwuHdty2phB0fJzenBXRNJUep6FEyRdn4OKN+HiE6Mz7i5Ytp5PVq5PbkAiIocgfc/CCVCRBtO9N8aAPt04JmbG3acnzkxiNCIih0YJKkZZhrSgAG645KTo8swFK1mzfksSoxEROXjpfRZuYhUZcA+qyqhh/Rk+oBsAlZXO0xPfS3JEIiIHJ73Pwk2sRi++NE9QANdfemJ0edoHn2oQWRFJK+l/Fm5CmdCLL9bxRw9iQO9OAJRXOH//p1pRIpI+0v8s3ITKy9P7Qd14oVCICRdVT8UxZeYyduzam8SIREQaL/3Pwk2oorL6El92Vvr24ot15glfoNcR7QAoKS1XK0pE0oYSVIzYFlQ6dzOPFQqFuOaCsdHyG9MXsWtPURIjEhFpHCWoGDV68WVlzkdzwemj6Na5DQD7isv4u3r0iUgayJyzcBMoLY+ZsDCUGS0oiEzFMeHC6lbU6//+WK0oEUl59SYoM3srZvl7iQ8nuTK1BQVw4RnH1GhFPaN7USKS4ho6C3eJWb46kYGkgkzrZh4rK6tmK+q1aWpFiUhqa+gs7M0SRYrIlLH46nLhGcdwRKfWgFpRIpL6GkpQR5rZRDP7Z8xy9NUcATandJ+wsCFZWWGui3ku6rVpH+u5KBFJWVkNbB8fs/zrRAaSCmJbUJnyHFS8C884hmcnfcCmrXvYV1zGky9P5+u3XJjssEREDlBvM8Hd/131ApYAS+LWZZRMG4uvNllZYW4aXz3S+RszFmuMPhFJSQ314jMz+5GZbQWWAZ+aWaGZ3dM84TWvmr34MrMFBXDeqUfTp3t7AErLKnjipelJjkhE5EANNRPuBk4BjnP3Tu7eATgeONnM/jvh0TWzTO7FFysUCnHLFadGy2+/v4y1G7YmMSIRkQM1dBa+CbjO3VdVrXD3lcCNwbaMUlGZ2b34Yp123FAG9ekMREY6f/SFackNSEQkTkMJKtvdD/hq7e6FQHZiQkqeTJqwsCGhUIhbrzotWp4xbzmfrFyfxIhERGpq6Cxceojb0lJFRfVjX5l8D6rK8aMGM3JwDwDc4c/PTE1yRCIi1RpKUEeb2W4z2xO8dleVgRHNEWBziu3Fl+mX+Kp89bqzMIssL/hkPbPmf5LcgEREAg11Mw+7e1t3bxO82saUM+8SX2XLakEBDBnQi1OPHRgt//nZd6iMuRcnIpIsDXUzzzOzu83sATO7zcwaerA3rbWke1Cxbp9wFjnZkYT8+cadvDZ1XpIjEhFp+BLfE8AY4GPgQuA3CY8oiWITVE52RufiGrp37cjFp1dfsX1q4iyKSzLuFqOIpJmGEtQwd7/R3f8MXAWc2kD9tFbeQh7Urc3NV55Om4JcALbt3MffXpmR5IhEpKVrKEGVVS24e3l9FTNB7HNQmToWX13aFLTiuguPi5ZfnDJfQyCJSFI1thdfVc+9kTG9+nY3tHMzG2dmn5jZcjP7bi3bc83suWD7bDPrF6w/18zmmdnHwc+zDuWXO1gtrZt5vKsuOJFeR7QDoKS0nIee/leSIxKRlqyxvfiqeu5lxSy3re+9ZhYGHgQuAIYB15nZsLhqXwZ2uPtA4H7gvmD9VuASdx8B3Aw8dfC/2sGr0c28BSaorKwwd1xf/V3g3Q9XsGDJqnreISKSOInsqjYWWO7uK929FHiWmtN3EJSfCJZfAM42M3P3+e6+IVi/GMgzs9wExgpAZWw38xbyHFS8E0cfxdgRfaLlPz41Rd3ORSQpEpmgegJrY8rrgnW11gnuce0COsXVuRKY7+4l8QcIur7PNbO5hYWFhx1weQuYD6ox7rzhPLKzIv80Vq3fzitT5iQ5IhFpiRKZoKyWdfFTyNdbx8yGE7nsd3ttB3D3v7j7GHcf06VLl0MOtEplCxostj69e3Tm0jNHRstPvDJTM++KSLNLZIJaB/SOKfcCNtRVJ3gIuB2wPSj3Al4GbnL3FQmME4gkp/KYThLZ2S03QQHccuUZdGzXCoA9RSU89PSUJEckIi1NIhPUHGCQmfU3sxxgAjAxrs5EIp0gIPKc1VR3dzNrD7wOfM/d30tgjFGx95/MIqN9t2QF+Xl8dcKZ0fLb73+iDhMi0qwSdhYO7indBUwGlgLPu/tiM7vXzC4Nqj0KdDKz5cA3gKqu6HcBA4EfmtmC4NU1UbFC/ECxLTs5VTnrxC8wakj1bcPfPT6Z8vKKet4hItJ0EnomdvdJ7j7Y3Qe4+8+Ddfe4+8Rgudjdr3b3ge4+NpgMEXf/mbsXuPuomNeWRMZaFnPibemtpyqhUIhvfOmC6nH6Nu3k7/98N8lRiUhLoTNxILZlkBWure9Gy9Sre2euPv+YaPmZ1+ewbqOmhxeRxFOCCpSWVY/kpBZUTV+87DR6dIk8l11SWs6vH52kZ6NEJOF0Jg7U7GKujyVWTk42/3PruOjEhgs/3cA/356b3KBEJOPpTByIbUGFQ7rEF2/08CMZd0r1SFWPvDCDzVt3JjEiEcl0SlCB2FEkwmpB1eprN5xH5/b5ABTtL+P+x95IckQiksl0Jg7EdpII6x5UrQry8/j6TedGyx98vIY3/z0/iRGJSCbTmTgQ2808K0sfS11OHjOUM8YOipYfeuYdzRslIgmhM3FALajG+/rN46LDIO3dV8qv/vKaevWJSJPTmTigkSQar12bAv7n1nHR8oJP1vPCG+8nMSIRyUQ6EwdiL/Gpk0TDThx9FBedNjxafuzlmaxel9DBPkSkhdGZOFBRoak2DtadXzy/xgO8P3/4VUpLy5IclYhkCiWoQHmNsfj0HFRj5OXm8J3bLoo+N7Zi7TYe/rum5RCRpqEEFdBsuodmxFF9uf7isdHyq1MX8u7cpUmMSEQyhRJUoEYvPg0We1BuvuJ0RgzuHi3/+q9vUrh9dxIjEpFMoAQVqDmShFpQByMUCvGDr11O29a5AOzeW8JPH3iZigrNHSUih04JKqDnoA5Pl45t+VZM1/NFyzfyp2f+lcSIRCTd6UwcqNGLTyNJHJKTxwzlinNGRcsvvjWfae8vSmJEIpLOdCYOlJXHjmauj+VQ3XHDuXxhYOz9qMmsWa/no0Tk4OlMHKio9OiyWlCHLhwOc89/Xh4dCmlfcRk/+sNLFJeUJjkyEUk3OhMHYltQWWpBHZbOHdrygzsuJSvoDfn5xp389MGXNV6fiBwUnYkDNe9BqRff4Ro1rD9fuerUaHnWglU8+o+pSYxIRNKNElSgvDymm7laUE3imotO4tyThkTLz7w+lynvfpTEiEQknehMHCivVC++RPifWy9i2IAjouXfPPYWiz/9PIkRiUi60Jk4UK7RzBMiJyebn959NV07tgagtKyCH/7+ZdZv2pbkyEQk1elMHNBYfInToV1rfnr3leTnZQOwc89+vvN/z7Fzd1GSIxORVKYEFajQUEcJNahfd35wxyXRnn0bCnfz/d88R0mJpucQkdopQQViZ9TN1iW+hDhh9GC+ftM50fKyVVv48R9f0Jh9IlIrnYkDNQeL1ceSKBedeSw3XnJ8tDx74Rp+8fArekZKRA6gM3GgosY9qKwkRpL5brnydMadMixafueDz/jd45OUpESkBiWoQM0WlOaDSqRQKMQ3v3Ixpx47ILrutWmLeOR5PcgrItWUoAJqQTWvUCjED++8gmOH946ue3bSXB59/u0kRiUiqUQJKlChe1DNLisrzM/uvqbG6OdPvzZHSUpEACWoqAo9B5UUubnZ/PKb19YYbeLp1+bwyHNKUiItnRJUQL34kqcgP49fffv6Gknq76/P4eGn31LHCZEWLKFnYjMbZ2afmNlyM/tuLdtzzey5YPtsM+sXrO9kZu+Y2V4zeyCRMVapqNRo5smU3yr3gCT1j8kf8utHXlOSEmmhEpagzCwMPAhcAAwDrjOzYXHVvgzscPeBwP3AfcH6YuCHwDcTFV+82LH4sjSSRFJUJakRg6vvSb357hLufeClGn8fEWkZEtmCGgssd/eV7l4KPAuMj6szHngiWH4BONvMzN2L3P1dIomqWcTOqKt7UMmT3yqX//v29Rw/sm903fS5y/nO/z1D0b5m++cgIikgkQmqJ7A2prwuWFdrHXcvB3YBnRp7ADO7zczmmtncwsLCwwo2dqgj3YNKrpycbH7239dwxthB0XXzl67jv376JIXbdycxMhFpTok8E9f2tKsfQp06uftf3H2Mu4/p0qXLQQUXr1ItqJQSDof5wdcuZ/xZI6PrVq3fzp0/eYIVn29KYmQi0lwSmaDWAb1jyr2ADXXVMbMsoB2wPYEx1amyFko7AAAVqElEQVRco5mnnFAoxNdvuZDbrj4FC77KbN1RxN0/f5r35i5NbnAiknCJTFBzgEFm1t/McoAJwMS4OhOBm4Plq4Cp7t7oFlRT0nxQqWvCJafwv7dfRE525O9StL+Me/74Kk+9Ml09/EQyWMISVHBP6S5gMrAUeN7dF5vZvWZ2aVDtUaCTmS0HvgFEu6Kb2Wrgt8AtZraulh6ATSr2RJele1Ap56yTRnDfN6+mfZtWALjDYy/N5KcPvERxSWmSoxORREjomdjdJ7n7YHcf4O4/D9bd4+4Tg+Vid7/a3Qe6+1h3Xxnz3n7u3tHdW7t7L3dfkshYY1tQeg4qNR09tB8P/fgmBvSu7kfz77nL+dqPH2fthq1JjExEEkFNhUDNThIaLDZVdevSgT/eczOnjRkYXbd6/Xbu+PETTJ35cRIjE5GmpgQVqNmC0seSyvJyc7jnriv4ylUnR6eQ31dcxs/+9Dq//etrlJZqGnmRTKAzcUAtqPQSCoW4/tJT+dW3rqFju1bR9a9NW8RtP3yU5Ws2JjE6EWkKSlCBGi0odZJIG6OG9ef//ezLjBzcI7ru8407uevev/Hc6++pl59IGtOZmEgPvtgWlDpJpJcO7Vrz2+/fyJeuOCl6ya+0rII/PzeDu3/2FOs3bUtyhCJyKJSgqDlQbDhkhEL6WNJNKBTii5edxh9+cAM9urSNrl+0fCP/8cPH+MekmWpNiaQZnYmBsnKNw5cphgzoxSO/+AoXn/GF6OgTxSXlPPzsdO76yeN8tlr3pkTShc7GxA0UG6pteEBJJ3m5OXzj1ov59bevoVvnNtH1y1Zt4c6fPMmDT72ph3tF0oASFGpBZarRw4/kr7/8D8afNTL6xaO8wnlxygJu+tafmDx9vi77iaQwnY2JvweljyST5OXm8PVbLuSPP7yBgX06R9dv3bmP+x6ZzH/99AmWLl+XxAhFpC46GxOXoMK6xJeJhgzoxZ/uvZWvXnsarfNzouuXrNjMXT/9Gz/6/T/U208kxShBETfVhlpQGSsUCnHNRSfx5K9uZ9wpwwgFl/3cYca8Fdz6/Uf57V9fY9uOPUmOVERACQrQPaiWpn3bAr5926U8/KMvMmpI9STPZeWVvDZtETd+68888OSb7Ni1N4lRiojOxtS8xKdRJFqOQf178Nvvf5Ff/PcV9O/ZMbq+pLScl/61gBu++Sd+//gkNm/dmcQoRVouDToHlJaVR5dD6mbe4pwwejBjjx7IlPcW8vTEWazbvAuIPD/16tSFTJq+iDPGDua6i0+iX6+uSY5WpOVQgiJ+skINc9QShUIhzj91FOeePJK3ZnzE3ybOYkPhbiBy6W/KzGX8a9Yyjhnam6vGHcdxIwdqxBGRBFOComYLSlNttGyhUIhxp4/mvFOPZsp7C3l+0gesWr8diHSmmLdkLfOWrKVPt/ZcePpILjrzGAry85IctUhmUoKi5lQbugclULNFNevDT/jHm3NY+OmG6PbPN+3kT89N5/FXZnL6mEFcfOZohg/uk8SIRTKPEhQ1W1DqZi6xQqEQJ48ZysljhvLZ6o08P+l9ZsxbTmlZpGNNcUk5k99byuT3ltKne3vOPWk4404bRacObRrYs4g0RAkKqIh9DkotKKnDoH7d+d+vXc7O3UVMfHsub85YxKat1c9Mfb5xJ4+++B6PvzyTEYN7cPaJwzjzhC+Q3yo3iVGLpC8lKKCsQs9BSeO1b1vATZefzo3jT2X2R58xadpHzFm0Jtqqqqh0Fixbz4Jl6/nj36YyemgvTj9uCKceN1T3q0QOghIUNVtQugcljRUKhThx9FGcOPoodu0p4o1p85k6exnLP98arVNaVsHshWuYvXANv3vyX4wY1IMTRg3g9OOH0blD23r2LiJKUGiwWDl87doUMOGSU5hwySmsWb+FyTMWMn3Op9Gu6hBJVlW9AB96ZhpH9urEmOH9OGH0IEYc1Ufd1kXiKEFRcyw+Tfcuh6tvz67cNuEcbptwDp+t2sC/Zi5i5vzlrN9SnazcYcXabaxYu43n3pxH6/wchg/szpjh/Rl79EB69+hczxFEWgYlKA6c8l2kqQzq34NB/Xtwxw3nsXrdFqbNXszsj1bx6ZotePXTDezdVxq9FPjgM9Po1D6fYQO6M/Ko3owa1o/+vbqqhSUtjhIUcfeg1IKSBOnXqyu39OrKLVeeyY5de5n54Sd8sHAlC5atY09RSY2623buY8a8FcyYtwKANgW5DO7blSFHdmP4oN6MOKqPOlxIxlOCIq4Xn76lSjPo0K41F515LBedeSyVlZV8umoDH3y0gg+XrOGT1VsoKS2vUX9PUUn0/hXMwQx6dm3Hkb27MKjvEQw5sgdDBvRU0pKMogRFfAtKCUqaVygUYsiAXgwZ0Iubrohccl786efMXbSSxcs38NmaLRTtL6vxHndYt3kX6zbvYvrc5QCYQdeOrenboxP9e3bmyD5dGdi3G316dCasMSYlDSlBAeVqQUkKycoKc/Sw/hw9rD8QGcx4xeebWbh0DUtWrGf554Ws27yzxj0siCStzdv2snnbXj74eE10fXZWiG6d29LziPb07taRPj060adHZ/r36krrglbN+auJHBQlKHQPSlJbKBRiUL/uDOrXnSuDdXuL9rN0xXqWrljP8jVbWLWukI1b99QYV7JKWXklazftZO2mnbz/0eoa29oU5NKtUxuO6NyO7l3a0b1Le7p3bU+fHp3p0rGd/j9IUilBAeXlMQlKLShJA60LWnHcyIEcN3JgdF1xSSmfrd7Ip6s2snpdIWs2bGftph3s2ltc5372FJWwp6iEz2IeLq4SChkd27aiU/vWdGpfQJeObYJXW7p2bMsRXdrTuUNbJTFJGCUoal7i0z0oSVd5uTmMOKovI47qW2P9zt1FrFq7mZVrt7Bu03bWbdrBxsJdbNm+h/KKA1tcVSorna0797F1574665hB6/xc2rdpRfu2rWjXOp/2bVvRsV0B7dsU0KFdAe3bFtCpfWs6tGtNq7wcdZeXRlOCQoPFSmZr37aA0cOPZPTwI2usr6ioYOOWHazduI21G7exsXAnm7buYsu2PWzdWXRA1/fauFe3wtZu2tlg/eysEAWtcmmdn0Pr/FwK8nNp3SqX1gV5tCnIo01+Hq0LcmlT0IqC/Mi61vl5tC5oRev8PLXWWhglKGqOJJGdpY9EWoZwOEyv7p3p1b0zJ9ayvbiklPWbt7Npyw42b9tN4bbdFO7Yw/ZdRWzfVcSO3fvZu6/kgM4a9Skrr2Tnnv3s3LP/kGLOyQ6Tm5NFq9xs8nKzyMvNJi8nO/IzNztYH1mXm5sVbMuJbs8NtuVkZ5GXl0Nu1c+cbHKzs8jKCquFl0ISejY2s3HA74Ew8Ii7/39x23OBJ4FjgW3Ate6+Otj2PeDLQAXwX+4+OVFxlqubucgB8nJzGNCnGwP6dKuzTmlpGdt37aVw+2627djDtp172bGriB27i9i1Zz+79xazuyiSyPbuK42O+H6oSssqKC2raFTr7lCYQXZWmKxwiKysUHQ5OytMVlaY7HCIrKwwWVkhssJhsrNChMNB/apt4RDhcIhwKCiHIvsKh0NkZ2URDhmhUFU5HK0bDocIhYxwOEw4ZGSFw0E5sj1kRigc+RkOR44bChnhUAgzovswi+wjZEYoZDF1Iu8zLHosIKUTcsISlJmFgQeBc4F1wBwzm+juS2KqfRnY4e4DzWwCcB9wrZkNAyYAw4EewL/MbLC7H96/7jrEDnWUpedFRBotJyebbl060K1Lh0bV37e/hF17iti5ex879xSxe88+du/dH1wm3M++4lL27iuhaF8J+4tL2Vdcyv6SMvYXl1FcWn5QrbVD4V6dBFsKC0Z3C5lhVp2wLChb7HJQ2cx44r7baN+2IKGxJbIFNRZY7u4rAczsWWA8EJugxgM/DpZfAB6wyCcwHnjW3UuAVWa2PNjfrEQEWqEp30WaRX6rXPJb5dK9a8eDfm9lZSX7i0vZU7Sf/cWlFO0voWhfMfuLSykuKaNofwnFJWUUl5QGPyNJraS0nNKyMopLyikrr6C0rDxIQlXlCsrKKykvr6hxLmgpqpJ+RXShccnZmmHY0kQmqJ7A2pjyOuD4uuq4e7mZ7QI6Bevfj3tvz/gDmNltwG0Affr0OeRAa/biUwtKJBWFQiEK8vMSOpxTRUUFJaXllJSWUVJaRllZBSVlkZ+lpWWUVVREklppOeUVFZSXVye3svJyKioqKS2voKKikvKK4Gd5JRWV1QmworIy2F5JZbQcbAvWVVY6lR5sr6ik0j1a1z2SrCurflY67h7UIbrswSuyr8h6iLzHnaBOwj7KJpHIBFVbfo3/OOqq05j34u5/Af4CMGbMmEP+qK+98AROHzuEiopKRh516IlORNJbOBwmv1WY/Fa5yQ6l2UQSViQRuoNTtew41UkwUtdxIomtTTOMQpLIBLUO6B1T7gVsqKPOOjPLAtoB2xv53iZz9NB+HJ2onYuIpLCqe06pOF5jIm+4zAEGmVl/M8sh0ulhYlydicDNwfJVwFSPtEMnAhPMLNfM+gODgA8SGKuIiKSYhLWggntKdwGTiXQz/6u7Lzaze4G57j4ReBR4KugEsZ1IEiOo9zyRDhXlwJ2J6sEnIiKpyTzV75I10pgxY3zu3LnJDkNERBpgZvPcfUxD9dSnWkREUpISlIiIpCQlKBERSUlKUCIikpIyppOEmRUCaxqsWL/OwIEzt6WWdIgR0iNOxdh00iFOxdh0DjfOvu7epaFKGZOgmoKZzW1Mz5JkSocYIT3iVIxNJx3iVIxNp7ni1CU+ERFJSUpQIiKSkpSgavpLsgNohHSIEdIjTsXYdNIhTsXYdJolTt2DEhGRlKQWlIiIpCQlKBERSUlKUICZjTOzT8xsuZl9N9nx1MbM/mpmW8xsUbJjqYuZ9Tazd8xsqZktNrOvJzumeGaWZ2YfmNlHQYw/SXZM9TGzsJnNN7PXkh1LbcxstZl9bGYLzCwlR2s2s/Zm9oKZLQv+bZ6Y7JjimdlRwWdY9dptZncnO654Zvbfwf+bRWb2jJklbnpjdA8KMwsDnwLnEpkocQ5wnbsvSWpgcczsNGAv8KS7fyHZ8dTGzLoD3d39QzNrA8wDLkulz9LMDChw971mlg28C3zd3d9Pcmi1MrNvAGOAtu5+cbLjiWdmq4Ex7p6yD5ea2RPADHd/JJibLt/ddyY7rroE56T1wPHufriDDzQZM+tJ5P/LMHffH0yJNMndH0/UMdWCgrHAcndf6e6lwLPA+CTHdAB3n05kzqyU5e4b3f3DYHkPsBTomdyoavKIvUExO3il5Lc0M+sFXAQ8kuxY0pWZtQVOIzL3HO5emsrJKXA2sCKVklOMLKBVMAN6Pgmc6RyUoCByAl0bU15Hip1U05GZ9QNGA7OTG8mBgstmC4AtwBR3T7kYA78Dvg1UJjuQejjwlpnNM7Pbkh1MLY4ECoHHgkulj5hZQbKDasAE4JlkBxHP3dcDvwY+BzYCu9z9rUQeUwkKrJZ1KfmNOl2YWWvgReBud9+d7HjiuXuFu48CegFjzSzlLpma2cXAFnefl+xYGnCyux8DXADcGVyKTiVZwDHAw+4+GigCUvI+M0BwCfJS4B/JjiWemXUgcnWpP9ADKDCzGxN5TCWoSIupd0y5Fwlutmay4L7Oi8DT7v5SsuOpT3CpZxowLsmh1OZk4NLgHs+zwFlm9rfkhnQgd98Q/NwCvEzkknkqWQesi2klv0AkYaWqC4AP3X1zsgOpxTnAKncvdPcy4CXgpEQeUAkq0ilikJn1D769TAAmJjmmtBR0QHgUWOruv012PLUxsy5m1j5YbkXkP92y5EZ1IHf/nrv3cvd+RP5NTnX3hH5bPVhmVhB0hiG4bHYekFK9TN19E7DWzI4KVp0NpEynnVpcRwpe3gt8DpxgZvnB//WzidxnTpisRO48Hbh7uZndBUwGwsBf3X1xksM6gJk9A5wBdDazdcCP3P3R5EZ1gJOBLwIfB/d4AL7v7pOSGFO87sATQU+pEPC8u6dkF+40cATwcuRcRRbwd3d/M7kh1eo/gaeDL6ArgS8lOZ5amVk+kd7Etyc7ltq4+2wzewH4ECgH5pPgIY9afDdzERFJTbrEJyIiKUkJSkREUpISlIiIpCQlKBERSUlKUCIikpKUoEQAMzvCzP5uZiuDYXtmmdnlh7ivfqk86rxIulCCkhYveOjwFWC6ux/p7scSeTi2V3Ija1gwaKdIRlKCEoGzgFJ3/1PVCndf4+5/hOgcUo8F8x7NN7Mzg/X9zGyGmX0YvA4Y9sXMhgfzTy0ws4VmNqiWOnvN7DfBPt42sy7B+gFm9mbQopthZkOC9Y+b2W/N7B3gvrh95ZvZ88GxnjOz2WY2Jtj2sJnNtbh5sCwyp9MvglbjXDM7xswmm9kKM/tqTL1vmdmcYN8pPY+WZAZ9+xKB4USejq/LnQDuPiJIEm+Z2WAio6Gf6+7FQeJ5hsjcTbG+Cvze3atGMgjXsv8CIuOv/Y+Z3QP8CLiLyFP6X3X3z8zseOAhIskUYDBwjrtXxO3ra8AOdx8ZDIK7IGbb/7r79mAUjbfNbKS7Lwy2rXX3E83sfuBxIqOC5AGLgT+Z2XnAICJj7Rkw0cxOC6aBEUkIJSiROGb2IHAKkVbVccHyHwHcfZmZrSGSINYAD5jZKKAiWBdvFvC/wdxOL7n7Z7XUqQSeC5b/BrwUjAh/EvCPYCghgNyY9/yjluREEOvvg1gXmdnCmG3XBFNiZBEZ8mkYULW9avzJj4HWwXxee8ysOBi78LzgNT+o15pIwlKCkoRRghKJtBKurCq4+51m1hmomsK8tilZAP4b2AwcTeRyeXF8BXf/u5nNJjLx4GQz+4q7T20gHg/2tzOYFqQ2RXWsrzVWM+sPfBM4zt13mNnjRFpIVUqCn5Uxy1XlrGC/v3T3PzcQu0iT0T0oEZgK5JnZHTHr8mOWpwM3AASX9voAnwDtgI3uXklkkNwDLt+Z2ZHASnf/A5FWyshajh8CrgqWrwfeDebRWmVmVwf7MTM7uhG/y7vANcF7hgEjgvVtiSS1XWZ2BJFpHQ7GZODWoGWHmfU0s64HuQ+Rg6IWlLR47u5mdhlwv5l9m8gMrEXAd4IqDxG5D/MxkVGcb3H3EjN7CHgxSCLvUHur5lrgRjMrAzYB99ZSpwgYbmbzgF3BeyCSFB82sx8QmZr+WeCjBn6dh4iM1r6QyOW4hURmPv3MzOYTaS2uBN5rYD81uPtbZjYUmBVcctwL3EjkPpxIQmg0c5EkM7O97t66ifYVBrKDjhsDgLeBwe5e2hT7F2lOakGJZJZ84B2LzGxswB1KTpKu1IISEZGUpE4SIiKSkpSgREQkJSlBiYhISlKCEhGRlKQEJSIiKen/B1TQyjy3+9ppAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "thinkplot.Pdf(soccer, color='0.7')\n", "soccer.Update(12)\n", "thinkplot.Pdf(soccer)\n", "thinkplot.decorate(title='Posterior after 2 goals',\n", " xlabel='Goals per game',\n", " ylabel='PDF')\n", "soccer.Mean()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This distribution represents our belief about `lam` after two goals.\n", "\n", "## Estimating the predictive distribution\n", "\n", "Now to predict the number of goals in the remaining 67 minutes. There are two sources of uncertainty:\n", "\n", "1. We don't know the true value of λ.\n", "\n", "2. Even if we did we wouldn't know how many goals would be scored.\n", "\n", "We can quantify both sources of uncertainty at the same time, like this:\n", "\n", "1. Choose a random value from the posterior distribution of λ.\n", "\n", "2. Use the chosen value to generate a random number of goals.\n", "\n", "If we run these steps many times, we can estimate the distribution of goals scored.\n", "\n", "We can sample a value from the posterior like this:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.48" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lam = soccer.Random()\n", "lam" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Given `lam`, the number of goals scored in the remaining 67 minutes comes from the Poisson distribution with parameter `lam * t`, with `t` in units of goals.\n", "\n", "So we can generate a random value like this:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t = 67 / 90\n", "np.random.poisson(lam * t)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we generate a large sample, we can see the shape of the distribution:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.8335" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sample = np.random.poisson(lam * t, size=10000)\n", "pmf = Pmf(sample)\n", "thinkplot.Hist(pmf)\n", "thinkplot.decorate(title='Distribution of goals, known lambda',\n", " xlabel='Goals scored', \n", " ylabel='PMF')\n", "pmf.Mean()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "But that's based on a single value of `lam`, so it doesn't take into account both sources of uncertainty. Instead, we should sample values from the posterior distribution and generate one prediction for each.\n", "\n", "**Exercise:** Write a few lines of code to\n", "\n", "1. Use `Pmf.Sample` to generate a sample with `n=10000` from the posterior distribution `soccer`.\n", "\n", "2. Use `np.random.poisson` to generate a random number of goals from the Poisson distribution with parameter $\\lambda t$, where `t` is the remaining time in the game (in units of games).\n", "\n", "3. Plot the distribution of the predicted number of goals, and print its mean.\n", "\n", "4. What is the probability of scoring 5 or more goals in the remainder of the game?" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "# Solution goes here" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "# Solution goes here" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Computing the predictive distribution\n", "\n", "Alternatively, we can compute the predictive distribution by making a mixture of Poisson distributions.\n", "\n", "`MakePoissonPmf` makes a Pmf that represents a Poisson distribution." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "from thinkbayes2 import MakePoissonPmf" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we assume that `lam` is the mean of the posterior, we can generate a predictive distribution for the number of goals in the remainder of the game." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lam = soccer.Mean()\n", "rem_time = 90 - 23\n", "lt = lam * rem_time / 90\n", "pred = MakePoissonPmf(lt, 10)\n", "thinkplot.Hist(pred)\n", "thinkplot.decorate(title='Distribution of goals, known lambda',\n", " xlabel='Goals scored', \n", " ylabel='PMF')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The predictive mean is about 2 goals." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.9754901051822877" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pred.Mean()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And the chance of scoring 5 more goals is still small." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.003297768976804021" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pred.ProbGreater(4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "But that answer is only approximate because it does not take into account our uncertainty about `lam`.\n", "\n", "The correct method is to compute a weighted mixture of Poisson distributions, one for each possible value of `lam`.\n", "\n", "The following figure shows the different predictive distributions for the different values of `lam`." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for lam, prob in soccer.Items():\n", " lt = lam * rem_time / 90\n", " pred = MakePoissonPmf(lt, 14)\n", " thinkplot.Pdf(pred, color='gray', alpha=0.3, linewidth=0.5)\n", "\n", "thinkplot.decorate(title='Distribution of goals, all lambda',\n", " xlabel='Goals scored', \n", " ylabel='PMF')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can compute the mixture of these distributions by making a Meta-Pmf that maps from each Poisson Pmf to its probability." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "metapmf = Pmf()\n", "\n", "for lam, prob in soccer.Items():\n", " lt = lam * rem_time / 90\n", " pred = MakePoissonPmf(lt, 15)\n", " metapmf[pred] = prob" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`MakeMixture` takes a Meta-Pmf (a Pmf that contains Pmfs) and returns a single Pmf that represents the weighted mixture of distributions:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "def MakeMixture(metapmf, label='mix'):\n", " \"\"\"Make a mixture distribution.\n", "\n", " Args:\n", " metapmf: Pmf that maps from Pmfs to probs.\n", " label: string label for the new Pmf.\n", "\n", " Returns: Pmf object.\n", " \"\"\"\n", " mix = Pmf(label=label)\n", " for pmf, p1 in metapmf.Items():\n", " for x, p2 in pmf.Items():\n", " mix[x] += p1 * p2\n", " return mix" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's the result for the World Cup problem." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0 0.47924077724207537\n", "1 0.2725094835016371\n", "2 0.133775655946909\n", "3 0.06276271009361287\n", "4 0.028740536131222984\n", "5 0.01293828440488025\n", "6 0.005734953182524395\n", "7 0.002498793148679157\n", "8 0.001066322124209203\n", "9 0.00044359776122528073\n", "10 0.00017904726009230283\n", "11 6.981959531261281e-05\n", "12 2.62143057581813e-05\n", "13 9.453212961538524e-06\n", "14 3.268979546003684e-06\n", "15 1.0831093530869543e-06\n" ] } ], "source": [ "mix = MakeMixture(metapmf)\n", "mix.Print()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And here's what the mixture looks like." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "thinkplot.Hist(mix)\n", "thinkplot.decorate(title='Posterior predictive distribution',\n", " xlabel='Goals scored', \n", " ylabel='PMF')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Exercise:** Compute the predictive mean and the probability of scoring 5 or more additional goals." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "# Solution goes here" ] }, { "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": 1 }