{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hierarchical Partial Pooling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose you are tasked with estimating baseball batting skills for several players. One such performance metric is batting average. Since players play a different number of games and bat in different positions in the order, each player has a different number of at-bats. However, you want to estimate the skill of all players, including those with a relatively small number of batting opportunities.\n",
    "\n",
    "So, suppose a player came to bat only 4 times, and never hit the ball. Are they a bad player?\n",
    "\n",
    "As a disclaimer, the author of this notebook assumes little to non-existant knowledge about baseball and its rules. The number of times at bat in his entire life is around \"4\".\n",
    "\n",
    "\n",
    "## Data\n",
    "\n",
    "We will use the [baseball data for 18 players from Efron and Morris](http://www.swarthmore.edu/NatSci/peverso1/Sports%20Data/JamesSteinData/Efron-Morris%20Baseball/EfronMorrisBB.txt) (1975).\n",
    "\n",
    "\n",
    "## Approach\n",
    "\n",
    "We will use PyMC3 to estimate the batting average for each player. Having estimated the averages across all players in the datasets, we can use this information to inform an estimate of an additional player, for which there is little data (*i.e.* 4 at-bats).\n",
    "\n",
    "In the absence of a Bayesian hierarchical model, there are two approaches for this problem:\n",
    "\n",
    "(1) independently compute batting average for each player (no pooling)\n",
    "(2) compute an overall average, under the assumption that everyone has the same underlying average (complete pooling)\n",
    "\n",
    "Of course, neither approach is realistic. Clearly, all players aren't equally skilled hitters, so the global average is implausible. At the same time, professional baseball players are similar in many ways, so their averages aren't entirely independent either. \n",
    "\n",
    "It may be possible to cluster groups of \"similar\" players, and estimate group averages, but using a hierarchical modeling approach is a natural way of sharing information that does not involve identifying *ad hoc* clusters.\n",
    "\n",
    "The idea of hierarchical partial pooling is to model the global performance, and use that estimate to parameterize a population of players that accounts for differences among the players' performances. This tradeoff between global and individual performance will be automatically tuned by the model. Also, uncertainty due to different number of at bats for each player (*i.e.* informatino) will be automatically accounted for, by shrinking those estimates closer to the global mean.\n",
    "\n",
    "For far more in-depth discussion please refer to Stan [tutorial](http://mc-stan.org/documentation/case-studies/pool-binary-trials.html) on the subject. The model and parameter values were taken from that example.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import pymc3 as pm\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import theano.tensor as tt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can load the dataset using pandas:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data = pd.read_table(pm.get_data('efron-morris-75-data.tsv'), sep=\"\\t\")\n",
    "at_bats, hits = data[['At-Bats', 'Hits']].values.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's develop a generative model for these data.\n",
    "\n",
    "We will assume that there exists a hidden factor (`phi`) related to the expected performance for all players (not limited to our 18). Since the population mean is an unknown value between 0 and 1, it must be bounded from below and above. Also, we assume that nothing is known about global average. Hence, a natural choice for a prior distribution is the uniform distribution.\n",
    "\n",
    "Next, we introduce a hyperparameter `kappa` to account for the variance in the population batting averages, for which we will use a bounded Pareto distribution. This will ensure that the estimated value falls within reasonable bounds. These hyperparameters will be, in turn, used to parameterize a beta distribution, which is ideal for modeling quantities on the unit interval. The beta distribution is typically parameterized via a scale and shape parameter, it may also be parametrized in terms of its mean $\\mu \\in [0,1]$ and sample size (a proxy for variance) $\\nu = \\alpha + \\beta (\\nu > 0)$.\n",
    "\n",
    "The final step is to specify a sampling distribution for the data (hit or miss) for every player, using a Binomial distribution. This is where the data are brought to bear on the model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We could use `pm.Pareto('kappa', m=1.5)`, to define our prior on `kappa`, but the Pareto\n",
    "distribution has very long tails. Exploring these properly\n",
    "is difficult for the sampler, so we use an equivalent\n",
    "but faster parametrization using the exponential distribution.\n",
    "We use the fact that the log of a Pareto distributed\n",
    "random variable follows an exponential distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "N = len(hits)\n",
    "\n",
    "with pm.Model() as baseball_model:\n",
    "    \n",
    "    phi = pm.Uniform('phi', lower=0.0, upper=1.0)\n",
    "    \n",
    "    kappa_log = pm.Exponential('kappa_log', lam=1.5)\n",
    "    kappa = pm.Deterministic('kappa', tt.exp(kappa_log))\n",
    "\n",
    "    thetas = pm.Beta('thetas', alpha=phi*kappa, beta=(1.0-phi)*kappa, shape=N)\n",
    "    y = pm.Binomial('y', n=at_bats, p=thetas, observed=hits)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recall our original question was with regard to the true batting average for a player with only 4 at bats and no hits. We can add this as an additional variable in the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with baseball_model:\n",
    "    \n",
    "    theta_new = pm.Beta('theta_new', alpha=phi*kappa, beta=(1.0-phi)*kappa)\n",
    "    y_new = pm.Binomial('y_new', n=4, p=theta_new, observed=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now fit the model using MCMC:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using ADVI...\n",
      "Average Loss = 89.154:   3%|▎         | 6891/200000 [00:02<01:02, 3067.32it/s] \n",
      "Convergence archived at 7100\n",
      "Interrupted at 7,100 [3%]: Average Loss = 229.36\n",
      "100%|██████████| 3000/3000 [00:39<00:00, 76.21it/s]\n"
     ]
    }
   ],
   "source": [
    "with baseball_model:\n",
    "    trace = pm.sample(2000, tune=1000, chains=2,\n",
    "                      nuts_kwargs={'target_accept': 0.95})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can plot the posteriors distribution of the parameters. First, the population hyperparameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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3BdteRH6P9wU5R0SqROTDwN0isk1EtgIXAP89TOIro4hH1x3lyS3H+ewlszl9WonT4jjC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8CPGG665lvcqnrc/b8JuM+NKR/PyW8Ctqlqoxtv3m1LCuRcmuhc6Ta7O+E+3orTp+k0N0ZvM8Kc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\nLGOMMcYYY4zJkv8PkRv/1DjttIUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fef2bd58fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.traceplot(trace, varnames=['phi', 'kappa']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hence, the population mean batting average is in the 0.22-0.31 range, with an expected value of around 0.26.\n",
    "\n",
    "Next, the estimates for all 18 players in the dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.gridspec.GridSpec at 0x7fef282a09b0>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Lmuh/N/X1gyXdJelhSa9IutDXnw+s4COuIb7uFO/XNEkntfeLEupTpICHzqjW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\nQsiN/w/gL2Vqyme5iwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fef2bb57e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "player_names = data.apply(lambda x: x.FirstName + ' ' + x.LastName, axis=1)\n",
    "pm.forestplot(trace, varnames=['thetas'], ylabels=player_names)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, let's get the estimate for our 0-for-4 player:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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F6r164XBzwGGTkZyzD9Y7AIQsahBOoHLVgXrpQs3nNRgGR5xh50pZmY8zkUIh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\nGcBcz99jT2C8J4BSv9u+C3zec/3zwHc8168GHsO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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fef2bba3e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.traceplot(trace, varnames=['theta_new']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that, despite the fact our additional player did not get any hits, the estimate of his average is not zero -- zero is not even a highly-probably value. This is because we are assuming that the player is drawn from a *population* of players with a distribution specified by our estimated hyperparemeters. However, the estimated mean for this player is toward the low end of the means for the players in our dataset, indicating that the 4 at-bats contributed some information toward the estimate."
   ]
  }
 ],
 "metadata": {
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  "gist": {
   "data": {
    "description": "hierarchical_partial_pooling.ipynb",
    "public": true
   },
   "id": "08078792809cc29b522253957464d5b7"
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
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   "pygments_lexer": "ipython3",
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}
