09_predict_soln.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bite Size Bayes\n",
    "\n",
    "Copyright 2020 Allen B. Downey\n",
    "\n",
    "License: [Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)](https://creativecommons.org/licenses/by-nc-sa/4.0/)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Review\n",
    "\n",
    "[In the previous notebook](https://colab.research.google.com/github/AllenDowney/BiteSizeBayes/blob/master/08_soccer.ipynb) I introduced the World Cup problem:\n",
    "\n",
    ">In the 2018 FIFA World Cup final, France defeated Croatia 4 goals to 2.  Based on this outcome:\n",
    ">\n",
    ">1. How confident should we be that France is the better team?\n",
    ">\n",
    ">2. If the same teams played again, what is the chance Croatia would win?\n",
    "\n",
    "I started with the assumption that for any team against any other team there is some unknown goal-scoring rate, λ.\n",
    "\n",
    "And I showed that if we know λ, we can compute the probability of scoring $k$ goals in a game:\n",
    "\n",
    "$f(k; λ) = λ^k exp(-λ) ~/~ k!$\n",
    "\n",
    "This function is the [Poisson distribution](https://en.wikipedia.org/wiki/Poisson_distribution), and we can use SciPy to compute it.\n",
    "\n",
    "For example, if we know that λ is 1.4, we can compute the distribution of $k$ like this:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0     0.246597\n",
       "1     0.345236\n",
       "2     0.241665\n",
       "3     0.112777\n",
       "4     0.039472\n",
       "5     0.011052\n",
       "6     0.002579\n",
       "7     0.000516\n",
       "8     0.000090\n",
       "9     0.000014\n",
       "10    0.000002\n",
       "dtype: float64"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats import poisson\n",
    "\n",
    "λ = 1.4\n",
    "xs = np.arange(11)\n",
    "ys = poisson.pmf(xs, λ)\n",
    "pmf_goals = pd.Series(ys, index=xs)\n",
    "\n",
    "pmf_goals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In theory, the values of $k$ go to infinity, but I cut it off at 10 because higher values have very low probability.\n",
    "\n",
    "Here's what the distribution of $k$ looks like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pmf_goals.plot.bar(color='C0', alpha=0.5, label='Poisson distribution')\n",
    "\n",
    "plt.xlabel('Number of goals')\n",
    "plt.ylabel('Probability')\n",
    "plt.title('Distribution of goals scored')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because the values of $k$ are discrete integers, I use a bar chart to plot the distribution.\n",
    "\n",
    "Next I used a gamma distributon to represent the prior distribution of λ.  I set the parameter of the gamma distribution, α, to 1.4, which is the average number of goals each team score in World Cup play.\n",
    "\n",
    "I broke the range of values for λ into 101 discrete possibilities and used SciPy to compute the prior probabilities:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import gamma\n",
    "\n",
    "α = 1.4\n",
    "qs = np.linspace(0, 10, 101)\n",
    "ps = gamma.pdf(qs, α)\n",
    "\n",
    "prior = pd.Series(ps, index=qs)\n",
    "prior /= prior.sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's what the prior distribution looks like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "prior.plot(label='prior', color='gray')\n",
    "\n",
    "plt.xlabel('Goal scoring rate')\n",
    "plt.ylabel('Probability')\n",
    "plt.title('Prior distribution')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because the values of $λ$ are continuous, I use a line chart to plot the distribution.\n",
    "\n",
    "Next we did a Bayesian update, using the Poisson distribution to compute the likelihood of the data, $k$, for each possible goal scoring rate, $λ$\n",
    "\n",
    "$ f(k; λ) = λ^k \\exp(-λ) ~/~ k! $\n",
    "\n",
    "Since France scored 4 goals, the likelihood of the data is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "λs = prior.index\n",
    "k = 4\n",
    "likelihood = poisson.pmf(k, λs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we can use the following function to do the update:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bayes_update(pmf, likelihood):\n",
    "    \"\"\"Do a Bayesian update.\n",
    "    \n",
    "    pmf: Series that represents the prior\n",
    "    likelihood: sequence of likelihoods\n",
    "    \n",
    "    returns: float probability of the data\n",
    "    \"\"\"\n",
    "    pmf *= likelihood\n",
    "    prob_data = pmf.sum()\n",
    "    pmf /= prob_data\n",
    "    return prob_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.05015532557804499"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "france = prior.copy()\n",
    "bayes_update(france, likelihood)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we can do the same thing for Croatia, given that they scored 2 goals:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1609321178598705"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k = 2\n",
    "λs = prior.index\n",
    "likelihood = poisson.pmf(k, λs)\n",
    "\n",
    "croatia = prior.copy()\n",
    "bayes_update(croatia, likelihood)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's what the results look like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "prior.plot(label='prior', color='gray')\n",
    "france.plot(label='France', color='C0')\n",
    "croatia.plot(label='Croatia', color='C3')\n",
    "\n",
    "plt.xlabel('Goal scoring rate')\n",
    "plt.ylabel('Probability')\n",
    "plt.title('Posterior distributions for France and Croatia')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the previous notebook, I introduces this function, which computes the mean of a PMF."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pmf_mean(pmf):\n",
    "    \"\"\"Compute the mean of a PMF.\n",
    "    \n",
    "    pmf: Series representing a PMF\n",
    "    \n",
    "    return: float\n",
    "    \"\"\"\n",
    "    return np.sum(pmf.index * pmf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use it to compute the posterior means for France and Croatia."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.699772393342308, 1.6999765866755225)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pmf_mean(france), pmf_mean(croatia)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Based on the outcome of the game, we have some reason to think France is the better team.\n",
    "\n",
    "But if we look at the posterior distribution of λ for France and Croatia, there is still a lot of overlap, which means we are still not certain which is the better team.\n",
    "\n",
    "In the next section, we'll use the posterior distributions to compute the \"probability of superiority\"."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Probability of superiority\n",
    "\n",
    "Now that we have a posterior distribution for each team, we can answer the first question: How confident should we be that France is the better team?\n",
    "\n",
    "In the model, \"better\" means having a higher goal-scoring rate against the opponent.  We can use the posterior distributions to compute the probability that a random value drawn from France's distribution exceeds a value drawn from Croatia's.\n",
    "\n",
    "The following function takes a Series that represents a PMF and draws a sample from it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pmf_choice(pmf, n):\n",
    "    \"\"\"Draw a random sample from a PMF.\n",
    "    \n",
    "    pmf: Series representing a PMF\n",
    "    n: number of values to draw\n",
    "    \n",
    "    returns: NumPy array\n",
    "    \"\"\"\n",
    "    return np.random.choice(pmf.index,\n",
    "                            size=n, \n",
    "                            replace=True, \n",
    "                            p=pmf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`pmf_choice` uses `np.random.choice`, which chooses `n` values from the PMF with replacement, so the same value can appear more than once.  It uses the probabilities from the PMF as weights, so the number of times each value appears is proportional to its probability.\n",
    "\n",
    "Here's a sample from the posterior distribution for France."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.6139"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample_france = pmf_choice(france, 1000)\n",
    "sample_france.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here's a sample for Croatia."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.6958"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "sample_croatia = pmf_choice(croatia, 1000)\n",
    "sample_croatia.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To estimate the probability of superiority, we can count the number of times the value from France's distribution exceeds the value from Croatia's distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.733"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "np.mean(sample_france > sample_croatia)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On the basis of one game, we have moderate confidence that France is actually the better team."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Predicting the rematch\n",
    "\n",
    "Now we can take on the second question: If the same teams played again, what is the chance Croatia would win?\n",
    "\n",
    "To answer this question, we'll generate a sample from the \"posterior predictive distribution\", which is the number of goals we expect a team to score.\n",
    "\n",
    "If we knew the goal scoring rate, λ, the distribution of goals would be a Poisson distributon with parameter λ.\n",
    "\n",
    "Since we don't know λ, we can use the sample we generated in the previous section to generate a sample of goals, like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "goals_france = np.random.poisson(sample_france)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`np.random.poisson` uses each element of `sample_france` to generate a random value; that is, each value in the result is based on a different value of λ.\n",
    "\n",
    "To see what the resulting distribution looks like, we'll use this function from a previous notebook:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pmf_from_seq(seq):\n",
    "    \"\"\"Make a PMF from a sequence of values.\n",
    "    \n",
    "    seq: sequence\n",
    "    \n",
    "    returns: Series representing a PMF\n",
    "    \"\"\"\n",
    "    pmf = pd.Series(seq).value_counts(sort=False).sort_index()\n",
    "    pmf /= pmf.sum()\n",
    "    return pmf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.559"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pmf_france = pmf_from_seq(goals_france)\n",
    "pmf_france.plot.bar(color='C0', label='France')\n",
    "\n",
    "plt.xlabel('Goals scored')\n",
    "plt.ylabel('Probability')\n",
    "plt.title('Predictive distribution')\n",
    "plt.legend()\n",
    "\n",
    "goals_france.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This distribution represents two sources of uncertainty: we don't know the actual value of λ, and even if we did, we would not know the number of goals in the next game."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Generate and plot the predictive distribution for Croatia."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.786"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "goals_croatia = np.random.poisson(sample_croatia)\n",
    "\n",
    "pmf_croatia = pmf_from_seq(goals_croatia)\n",
    "pmf_croatia.plot.bar(label='Croatia', color='C3')\n",
    "\n",
    "plt.xlabel('Goals scored')\n",
    "plt.ylabel('Probability')\n",
    "plt.title('Predictive distribution')\n",
    "plt.legend()\n",
    "\n",
    "goals_croatia.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In a sense, these distributions represent the outcomes of 1000 simulated games."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Compute the fraction of simulated rematches Croatia would win, how many France would win, and how many would end in a tie."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.28"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "np.mean(goals_croatia > goals_france)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.549"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "np.mean(goals_france > goals_croatia)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.171"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "np.mean(goals_france == goals_croatia)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Assuming that Croatia wins half of the ties, their chance of winning the rematch is about 33%."
   ]
  }
 ],
 "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": "3.6.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}