2016-05-07 DePy 2016 - pyStan demonstration.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bayesian Inference with Stan\n",
    "\n",
    "This notebook contains examples of Bayesian inference with Stan, using the pyStan interface.\n",
    "\n",
    "Resources:\n",
    "http://mc-stan.org/ : Stan's main website, with lots of documentation and examples\n",
    "http://pystan.readthedocs.io/ : pyStan documentation\n",
    "\n",
    "8-Schools example from Bayesian Data Analysis, by Andrew Gelman et al., http://andrewgelman.com/2014/01/21/everything-need-know-bayesian-statistics-learned-eight-schools/, and http://astrostatistics.psu.edu/su14/lectures/Daniel-Lee-Stan-2.pdf\n",
    "\n",
    "Stephen Hoover<br>\n",
    "Civis Analytics<br>\n",
    "@StephenActual<br>\n",
    "7 May 2016"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pickle\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "import pystan\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Regression\n",
    "\n",
    "Let's start simple, with linear regression. \n",
    "\n",
    "$$ y = \\beta x + \\epsilon$$\n",
    "Here, $y$ are the observed outcomes, $x$ are the features we know about each example, $\\beta$ are our coefficents, and $\\epsilon$ is the noise.\n",
    "\n",
    "We can fit this with ordinary least squares. To do that, we want to pick $\\beta$ such that we minimize\n",
    "$$ \\sum_{i=1}^n (y_i - \\beta x_i)^2 $$\n",
    "We can write down a this linear regression model in Stan code as"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "stan_model = \"\"\"\n",
    "data {\n",
    "    // Define input data in this block\n",
    "    int n;  // Number of samples\n",
    "    int m;  // Number of features\n",
    "    matrix[n, m] features;\n",
    "    vector[n] y;  // outcome\n",
    "}\n",
    "transformed data {\n",
    "    // Modify / transform input data.\n",
    "    // This block runs once.\n",
    "}\n",
    "parameters {\n",
    "    // These are random parameters which we\n",
    "    // want to estimate\n",
    "    vector[m] beta;  // Coefficients\n",
    "    real<lower=0> epsilon;  // Uncertainty / unexplained variance\n",
    "}\n",
    "transformed parameters {\n",
    "    // Create quantities derived from the parameters.\n",
    "    // Runs on every evaluation of log-prob\n",
    "}\n",
    "model {\n",
    "    // Define your model here!\n",
    "    y ~ normal(features * beta, epsilon);\n",
    "    \n",
    "    // Equivalent to:\n",
    "    // increment_log_prob(normal_log(y, features * beta, epsilon));\n",
    "}\n",
    "generated quantities {\n",
    "    // Can use to simulate / predict using parameters\n",
    "    // Runs once per MCMC step after warmup\n",
    "}\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Generate some data for us to fit\n",
    "rng = np.random.RandomState(42)\n",
    "n_samples = 10\n",
    "n_feat = 4\n",
    "\n",
    "feat = rng.normal(0, 1, size=(n_samples, n_feat))\n",
    "tgt = feat @ np.array([-1, 0.4, 0, 0]) + rng.normal(scale=0.2, size=n_samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "lin_reg = pystan.model.StanModel(model_code=stan_model,\n",
    "                                 model_name='linear_regression')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "lin_fit = lin_reg.sampling(data={'n': n_samples, \n",
    "                                 'm': n_feat, \n",
    "                                 'features': feat, \n",
    "                                 'y': tgt}, \n",
    "                           iter=1000, chains=4, \n",
    "                           warmup=500, n_jobs=-1,\n",
    "                           seed=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Inference for Stan model: linear_regression_087f0c0e4eef3ff0be6e63bbe468afe1.\n",
       "4 chains, each with iter=1000; warmup=500; thin=1; \n",
       "post-warmup draws per chain=500, total post-warmup draws=2000.\n",
       "\n",
       "          mean se_mean     sd   2.5%    25%    50%    75%  97.5%  n_eff   Rhat\n",
       "beta[0]  -0.99  5.4e-3   0.11   -1.2  -1.05  -0.99  -0.92  -0.75    449    1.0\n",
       "beta[1]   0.43  4.1e-3   0.08   0.27   0.38   0.43   0.47   0.59    400   1.01\n",
       "beta[2]   0.07  4.0e-3   0.08  -0.09   0.03   0.07   0.11   0.22    355    1.0\n",
       "beta[3]   0.08  3.0e-3   0.06  -0.07   0.04   0.08   0.11    0.2    455    1.0\n",
       "epsilon    0.2  5.3e-3   0.08   0.11   0.14   0.18   0.23   0.42    245   1.02\n",
       "lp__     10.66    0.15    2.3   4.63   9.61  11.16  12.35  13.59    241   1.02\n",
       "\n",
       "Samples were drawn using NUTS(diag_e) at Sat May  7 13:47:55 2016.\n",
       "For each parameter, n_eff is a crude measure of effective sample size,\n",
       "and Rhat is the potential scale reduction factor on split chains (at \n",
       "convergence, Rhat=1)."
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "chains = lin_fit.extract()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "OrderedDict([('beta',\n",
       "              array([[-1.01763661,  0.37649818,  0.10570001,  0.05404354],\n",
       "                     [-0.93332508,  0.50234876,  0.17387378, -0.09616874],\n",
       "                     [-0.89627442,  0.47404553,  0.01599869,  0.1143778 ],\n",
       "                     ..., \n",
       "                     [-0.86882841,  0.36307688,  0.02157189,  0.06358885],\n",
       "                     [-0.96600794,  0.51663891,  0.05793773,  0.08761251],\n",
       "                     [-0.99316095,  0.41921682,  0.01724642,  0.0535017 ]])),\n",
       "             ('epsilon',\n",
       "              array([ 0.08935834,  0.33816026,  0.18961911, ...,  0.20131365,\n",
       "                      0.17700009,  0.11271441])),\n",
       "             ('lp__',\n",
       "              array([ 11.35349354,   6.57292638,  12.33864629, ...,  10.52931093,\n",
       "                      12.25936065,  12.17528791]))])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "chains"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2000, 4)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "chains['beta'].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x111fc65f8>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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vztoAALjq9GHC0/f6s7JUTA4LUw4uWBbHWEqHTUYhThBZl6x853bLa/byXZi9fJdxvrat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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a826f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(chains['beta'][:,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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BjtWb7gJuzcwrgNMi4oYS6pMktUErwz6/AXwe+CG1m7hfnJm769Meo/ZtQJLUgwqFf0T8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\n/wPrLb5gHEJlVwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1121959e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "histout = plt.hist(chains['beta'][:,0], bins=50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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BgcDRo3R3e5kc1NA1hQO3jHLDS+4hfPudDI1G6B0IoqpKOQvX71FsCY9JO/tX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\nEDQajUZjoh2CRqPRaAD4/72rcJiADOAkAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112088828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = lin_fit.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interlude: Caching models\n",
    "\n",
    "It can take a long(ish) time to compile these models, so you often want to save them for later. Good news: the models can be pickled!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "with open(os.path.join(os.getenv(\"HOME\"), \"stan_cache\", \n",
    "                       \"linear_regression_stan.pkl\"), 'wb') as fout:\n",
    "    pickle.dump(lin_reg, fout)\n",
    "    \n",
    "# If you want to get fancy, you can write a \n",
    "# function to do this automatically.\n",
    "# This version adapted from the pyStan docs.\n",
    "import os\n",
    "import pystan\n",
    "import pickle\n",
    "from hashlib import md5\n",
    "\n",
    "def stan_cache(model_code, model_name=None, cache_dir=None):\n",
    "    \"\"\"Creates or retrieves a StanModel\"\"\"\n",
    "    if cache_dir is None:\n",
    "        cache_dir = os.path.join(os.getenv(\"HOME\"), \"stan_cache\")\n",
    "        os.makedirs(cache_dir, exist_ok=True)\n",
    "    code_hash = md5((model_code + pystan.__version__)\n",
    "                    .encode('ascii')).hexdigest()\n",
    "    if model_name is None:\n",
    "        cache_fn = 'cached-model-{}.pkl'.format(code_hash)\n",
    "    else:\n",
    "        cache_fn = 'cached-{}-{}.pkl'.format(model_name, code_hash)\n",
    "    cache_fn = os.path.join(cache_dir, cache_fn)\n",
    "\n",
    "    try:\n",
    "        sm = pickle.load(open(cache_fn, 'rb'))\n",
    "    except:\n",
    "        sm = pystan.StanModel(model_code=model_code)\n",
    "        with open(cache_fn, 'wb') as f:\n",
    "            pickle.dump(sm, f)\n",
    "    else:\n",
    "        print(\"Using cached StanModel\")\n",
    "    return sm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# LASSO Regression\n",
    "\n",
    "We can also get fancier. In LASSO regression, we regularize the model by adding an additional penalty term to our ordinary least squares model:\n",
    "$$ \\sum_{i=1}^n (y_i - \\beta x_i)^2  + \\lambda \\sum_{j=1}^m |\\beta_j|$$\n",
    "\n",
    "You write this in Stan by realizing that it's a prior on your coefficents:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "stan_model_lasso = \"\"\"\n",
    "data {\n",
    "    int n;  // Number of samples\n",
    "    int m;  // Number of features\n",
    "    matrix[n, m] features;\n",
    "    vector[n] y;  // Outcome\n",
    "    real<lower=0> lambda;  // Regularization strength\n",
    "}\n",
    "parameters {\n",
    "    vector[m] beta;  // Coefficients\n",
    "    real<lower=0> epsilon;  // Uncertainty / unexplained variance\n",
    "}\n",
    "model {\n",
    "    beta ~ double_exponential(0, 1 / lambda);  // Laplace prior\n",
    "    y ~ normal(features * beta, epsilon);\n",
    "}\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using cached StanModel\n"
     ]
    }
   ],
   "source": [
    "lasso_reg = stan_cache(model_code=stan_model_lasso,\n",
    "                       model_name='lasso_regression')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "lasso_fit = lasso_reg.sampling(\n",
    "    data={'n': n_samples, 'm': n_feat, \n",
    "          'features': feat, 'y': tgt, 'lambda': 10},\n",
    "    iter=1000, seed=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Inference for Stan model: anon_model_453ed1561ef59806d76edb8b044246f9.\n",
       "4 chains, each with iter=1000; warmup=500; thin=1; \n",
       "post-warmup draws per chain=500, total post-warmup draws=2000.\n",
       "\n",
       "          mean se_mean     sd   2.5%    25%    50%    75%  97.5%  n_eff   Rhat\n",
       "beta[0]  -0.75    0.03    0.3  -1.08  -0.95  -0.86  -0.66 2.0e-3    128   1.03\n",
       "beta[1]   0.36    0.01   0.14-8.1e-3   0.31   0.39   0.45   0.57    153   1.02\n",
       "beta[2]   0.04  3.6e-3   0.07  -0.11-2.3e-3   0.04   0.08   0.18    388   1.01\n",
       "beta[3]   0.06  3.6e-3   0.07  -0.08   0.02   0.06    0.1   0.19    362    1.0\n",
       "epsilon   0.33    0.03   0.27   0.11   0.17   0.22   0.37   1.11    117   1.04\n",
       "lp__     -5.02    0.19   2.32 -10.12  -6.49  -4.64  -3.19  -1.73    142   1.03\n",
       "\n",
       "Samples were drawn using NUTS(diag_e) at Sat May  7 13:52:40 2016.\n",
       "For each parameter, n_eff is a crude measure of effective sample size,\n",
       "and Rhat is the potential scale reduction factor on split chains (at \n",
       "convergence, Rhat=1)."
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lasso_fit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 8 Schools: A Multi-level model\n",
    "\n",
    "Let's look at the \"8 schools\" problem. This example is originally from Rubin 1981, and can be found in Bayesian Data Analysis (Gelman et al.). These are data on the effectiveness of a class designed to prepare students for the SAT. Each row represents all of the students in one school. In each school, Rubin measured the average change in SAT scores, as well as calculating a measurement uncertainty."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           Treatment Effect  Uncertainty\n",
      "School ID                               \n",
      "0                        28           15\n",
      "1                         8           10\n",
      "2                        -3           16\n",
      "3                         7           11\n",
      "4                        -1            9\n",
      "5                         1           11\n",
      "6                        18           10\n",
      "7                        12           18\n"
     ]
    }
   ],
   "source": [
    "schools_dat = {'J': 8,\n",
    "               'y': [28,  8, -3,  7, -1,  1, 18, 12],\n",
    "               'sigma': [15, 10, 16, 11,  9, 11, 10, 18]}\n",
    "schools_df = (pd.DataFrame(schools_dat, columns=['y', 'sigma'])\n",
    "              .rename(columns={'y': 'Treatment Effect', \n",
    "                               'sigma': 'Uncertainty'}))\n",
    "schools_df.index.name = 'School ID'\n",
    "print(schools_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### School-by school effects\n",
    "\n",
    "What can we say about the effectiveness of the training? You might say that the measured effect is our best estimate of how well the class in each school does -- after all, we have a measurement and an uncertainty."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Assume each school is completely independent\n",
    "no_pooling = \"\"\"\n",
    "data {\n",
    "    int<lower=0> J; // # schools\n",
    "    real y[J]; // estimated treatment\n",
    "    real<lower=0> sigma[J]; // std err of effect\n",
    "}\n",
    "parameters {\n",
    "    real theta[J]; // school effect\n",
    "}\n",
    "model {\n",
    "    y ~ normal(theta, sigma);\n",
    "}\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using cached StanModel\n"
     ]
    }
   ],
   "source": [
    "nopool_model = stan_cache(model_code=no_pooling, \n",
    "                          model_name='no_pooling')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "nopool_fit = nopool_model.sampling(data=schools_dat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Inference for Stan model: anon_model_fac03134a8935fb2cffe1e3eb2e31136.\n",
       "4 chains, each with iter=2000; warmup=1000; thin=1; \n",
       "post-warmup draws per chain=1000, total post-warmup draws=4000.\n",
       "\n",
       "           mean se_mean     sd   2.5%    25%    50%    75%  97.5%  n_eff   Rhat\n",
       "theta[0]  28.06    0.42  15.17  -2.08  17.77  27.83  38.14  58.85   1321    1.0\n",
       "theta[1]   8.02    0.27   9.88 -10.72   1.39   7.77  14.75   27.7   1334    1.0\n",
       "theta[2]  -3.23    0.44  16.23 -36.22 -14.03  -3.23   7.53  28.35   1334    1.0\n",
       "theta[3]   7.17    0.31  11.07 -14.71  -0.18   6.99  14.57   28.8   1287    1.0\n",
       "theta[4]  -1.14    0.26   9.28 -19.87  -7.51  -1.08    5.2  16.92   1299    1.0\n",
       "theta[5]   1.05    0.31  11.07  -20.4  -6.61   1.23   8.71  22.59   1290    1.0\n",
       "theta[6]  18.09    0.28   9.96  -1.31  11.23  18.23   24.8  37.82   1305    1.0\n",
       "theta[7]  12.46     0.5   18.3 -22.54   0.26  11.95  24.79   49.2   1319    1.0\n",
       "lp__      -4.07    0.07   2.04  -9.17  -5.16  -3.75   -2.6  -1.14    958    1.0\n",
       "\n",
       "Samples were drawn using NUTS(diag_e) at Sat May  7 13:54:03 2016.\n",
       "For each parameter, n_eff is a crude measure of effective sample size,\n",
       "and Rhat is the potential scale reduction factor on split chains (at \n",
       "convergence, Rhat=1)."
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nopool_fit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pooling\n",
    "\n",
    "But that doesn't seem quite right. Each school was using the same training class, so maybe we should say that there's just one \"effectiveness of training\" parameter, and the result of training in each school is a noisy measurement of this one number."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pooling = \"\"\"\n",
    "data {\n",
    "    int<lower=0> J; // # schools\n",
    "    real y[J]; // estimated treatment\n",
    "    real<lower=0> sigma[J]; // std err of effect\n",
    "}\n",
    "parameters {\n",
    "    real theta; // pooled school effect\n",
    "}\n",
    "model {\n",
    "    y ~ normal(theta, sigma);\n",
    "}\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using cached StanModel\n"
     ]
    }
   ],
   "source": [
    "pool_model = stan_cache(model_code=pooling,\n",
    "                        model_name='pooling')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pool_fit = pool_model.sampling(data=schools_dat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Inference for Stan model: anon_model_78b569a62c9d87b3382fb8822816ffa7.\n",
       "4 chains, each with iter=2000; warmup=1000; thin=1; \n",
       "post-warmup draws per chain=1000, total post-warmup draws=4000.\n",
       "\n",
       "        mean se_mean     sd   2.5%    25%    50%    75%  97.5%  n_eff   Rhat\n",
       "theta    7.7    0.15   3.93   0.11   5.03   7.68  10.35  15.59    717    1.0\n",
       "lp__   -2.82    0.02   0.67  -4.69  -2.96  -2.57   -2.4  -2.35    863    1.0\n",
       "\n",
       "Samples were drawn using NUTS(diag_e) at Sat May  7 13:54:52 2016.\n",
       "For each parameter, n_eff is a crude measure of effective sample size,\n",
       "and Rhat is the potential scale reduction factor on split chains (at \n",
       "convergence, Rhat=1)."
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pool_fit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Partial Pooling\n",
    "\n",
    "Our data are consistent with all the training programs creating a treatment effect of 8 points. But that doesn't seem right either. There's different teachers in each school, teaching the classes in different ways. What if there's some average effect of the program, but different schools do a better or worse job of teaching it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "part_pool = \"\"\"\n",
    "data {\n",
    "    int<lower=0> J; // # schools\n",
    "    real y[J]; // estimated treatment\n",
    "    real<lower=0> sigma[J]; // std err of effect\n",
    "    real<lower=0> tau;  // Width of school effect distribution\n",
    "}\n",
    "parameters {\n",
    "    real theta[J]; // school effect\n",
    "    real mu; // Average treatment effect\n",
    "}\n",
    "model {\n",
    "    theta ~ normal(mu, tau);\n",
    "    y ~ normal(theta, sigma);\n",
    "}\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using cached StanModel\n"
     ]
    }
   ],
   "source": [
    "part_model = stan_cache(model_code=part_pool, \n",
    "                        model_name='partial_pooling')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "part_fit = part_model.sampling(data={**schools_dat, 'tau': 25})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Inference for Stan model: anon_model_54826fd87a6d262851a3832021fc15d0.\n",
       "4 chains, each with iter=2000; warmup=1000; thin=1; \n",
       "post-warmup draws per chain=1000, total post-warmup draws=4000.\n",
       "\n",
       "           mean se_mean     sd   2.5%    25%    50%    75%  97.5%  n_eff   Rhat\n",
       "theta[0]  22.73    0.37  13.26  -3.56  13.74  22.74  31.59  49.47   1280    1.0\n",
       "theta[1]   8.03    0.26   9.35 -10.48   1.58   7.92  14.25  26.87   1296    1.0\n",
       "theta[2]   0.56    0.39  13.97 -26.49  -9.03   0.57  10.23  28.02   1272    1.0\n",
       "theta[3]   7.14    0.28  10.06 -12.26   0.39   6.88   13.8  27.28   1309    1.0\n",
       "theta[4]    0.2    0.25   8.74 -16.96   -5.9    0.3   6.01  17.26   1261    1.0\n",
       "theta[5]   2.05    0.29  10.46 -18.58   -4.9   1.99   9.13  22.04   1285    1.0\n",
       "theta[6]  16.75    0.27   9.62  -2.46  10.33  16.68  23.33  35.36   1265    1.0\n",
       "theta[7]  11.32    0.42  15.18 -18.53   0.85  11.03  21.75  40.65   1305    1.0\n",
       "mu         9.01    0.28   9.92 -10.63   2.25    9.1  15.81  28.13   1235    1.0\n",
       "lp__      -5.09    0.07   2.14 -10.14  -6.32   -4.8  -3.54  -1.83    969    1.0\n",
       "\n",
       "Samples were drawn using NUTS(diag_e) at Sat May  7 13:56:33 2016.\n",
       "For each parameter, n_eff is a crude measure of effective sample size,\n",
       "and Rhat is the potential scale reduction factor on split chains (at \n",
       "convergence, Rhat=1)."
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "part_fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           Treatment Effect  Uncertainty\n",
      "School ID                               \n",
      "0                        28           15\n",
      "1                         8           10\n",
      "2                        -3           16\n",
      "3                         7           11\n",
      "4                        -1            9\n",
      "5                         1           11\n",
      "6                        18           10\n",
      "7                        12           18\n"
     ]
    }
   ],
   "source": [
    "# Compare to input data\n",
    "print(schools_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hierarchical Model\n",
    "\n",
    "But we can still do one better. I picked that \"tau\" pretty arbitrarily. What if I don't know how much the schools can vary from the overall class treatment effect? We can estimate that from the data too!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "schools_hier = \"\"\"\n",
    "data {\n",
    "    int<lower=0> J; // # schools\n",
    "    real y[J]; // estimated treatment\n",
    "    real<lower=0> sigma[J]; // std err of effect\n",
    "}\n",
    "parameters {\n",
    "    real theta[J]; // school effect\n",
    "    real mu; // mean for schools\n",
    "    real<lower=0> tau; // variance between schools\n",
    "}\n",
    "model {\n",
    "    theta ~ normal(mu, tau);\n",
    "    y ~ normal(theta, sigma);\n",
    "}\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using cached StanModel\n"
     ]
    }
   ],
   "source": [
    "hier_model = stan_cache(model_code=schools_hier, \n",
    "                        model_name='hierarchical_model')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "hier_fit = hier_model.sampling(data=schools_dat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Inference for Stan model: anon_model_bb61d0eae3d6ef378c04e5c9a4c3d37a.\n",
       "4 chains, each with iter=2000; warmup=1000; thin=1; \n",
       "post-warmup draws per chain=1000, total post-warmup draws=4000.\n",
       "\n",
       "           mean se_mean     sd   2.5%    25%    50%    75%  97.5%  n_eff   Rhat\n",
       "theta[0]  12.24    0.36   8.45  -1.52   6.87  11.45   15.7  33.36    542    1.0\n",
       "theta[1]   8.54    0.25   6.38  -4.79   4.63   8.64  12.79   20.9    631    1.0\n",
       "theta[2]    6.7    0.37   7.96 -12.18    2.7   7.29  11.92  20.47    465    1.0\n",
       "theta[3]   8.03    0.28   6.36  -5.53   4.25   8.13  12.14  20.26    517    1.0\n",
       "theta[4]   5.36    0.41   6.56  -9.19   1.49   6.02   9.91  16.01    254   1.01\n",
       "theta[5]   6.71    0.33   6.75  -8.97   3.05   7.31  11.37  18.67    415    1.0\n",
       "theta[6]   11.5    0.29   6.72  -0.17   7.18  10.91  15.18  26.49    547    1.0\n",
       "theta[7]   9.08    0.29   8.08  -7.23   4.57   8.99   13.6  26.17    803    1.0\n",
       "mu          8.5    0.26   5.19  -2.17   5.42    8.5  11.96  18.71    384    1.0\n",
       "tau        7.14    0.46   6.08   0.86    2.8   5.46   9.54  23.11    173   1.01\n",
       "lp__     -17.67    0.69   5.85 -28.12 -21.85 -18.22 -13.65  -4.52     71   1.04\n",
       "\n",
       "Samples were drawn using NUTS(diag_e) at Sat May  7 13:59:19 2016.\n",
       "For each parameter, n_eff is a crude measure of effective sample size,\n",
       "and Rhat is the potential scale reduction factor on split chains (at \n",
       "convergence, Rhat=1)."
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hier_fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Treatment Effect</th>\n",
       "      <th>Uncertainty</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>School ID</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>28</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>8</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-3</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-1</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>18</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>12</td>\n",
       "      <td>18</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           Treatment Effect  Uncertainty\n",
       "School ID                               \n",
       "0                        28           15\n",
       "1                         8           10\n",
       "2                        -3           16\n",
       "3                         7           11\n",
       "4                        -1            9\n",
       "5                         1           11\n",
       "6                        18           10\n",
       "7                        12           18"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "schools_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AGiMiSaPRRuCgbaNx10rRChtYUUzTtoiDEwghiJPVxvRWWl9KT5PN1RmaijqF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IQrY5udNSbkt/+P+JmDJ/L3N7fy9uoqpyNxsMWNN/4MgDvvvCOumxkAVfUCF4T5alFyXjk4ZB52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\njs3vD9DS0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I+Yle7WqOrlSdrOAh7CLBqWA9wKrEtlHVY9buB+QCy7l2LWmUlpPVZd44Dl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\nJIXTkTg4ODg4JMX/B6kSuewlM7zPAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1116a9cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pp = hier_fit.plot()"
   ]
  }
 ],
 "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": "3.5.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}