sharanry/8schools.ipynb

## 8schools.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Eight Schools Problem with PyMC4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "import os\n",
    "import tensorflow as tf\n",
    "import pymc4 as pm\n",
    "from tensorflow_probability import edward2 as ed\n",
    "from tensorflow_probability import distributions as tfd\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "from pymc4.inference.sampling.sample import sample\n",
    "os.environ['TF_CPP_MIN_LOG_LEVEL'] = '0' \n",
    "import pymc3 as pm3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Data of the Eight Schools Model\n",
    "J = 8\n",
    "y = np.array([28.,  8., -3.,  7., -1.,  1., 18., 12.])\n",
    "sigma = np.array([15., 10., 16., 11.,  9., 11., 10., 18.])\n",
    "# tau = 25."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Centered Eight Schools"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "with pm3.Model() as Centered_eight:\n",
    "    mu = pm3.Normal('mu', mu=0, sd=5)\n",
    "    tau = pm3.HalfCauchy('tau', beta=5)\n",
    "    theta = pm3.Normal('theta', mu=mu, sd=tau, shape=J)\n",
    "    obs = pm3.Normal('obs', mu=theta, sd=sigma, observed=y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Sequential sampling (1 chains in 1 job)\n",
      "NUTS: [theta, tau_log__, mu]\n",
      "100%|██████████| 1700/1700 [00:05<00:00, 339.76it/s]\n",
      "There were 31 divergences after tuning. Increase `target_accept` or reparameterize.\n",
      "Only one chain was sampled, this makes it impossible to run some convergence checks\n"
     ]
    }
   ],
   "source": [
    "with Centered_eight:\n",
    "    short_trace = pm3.sample(1200, chains=1, random_seed=54)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>mc_error</th>\n",
       "      <th>hpd_2.5</th>\n",
       "      <th>hpd_97.5</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>mu</th>\n",
       "      <td>4.655</td>\n",
       "      <td>3.105</td>\n",
       "      <td>0.162</td>\n",
       "      <td>-1.696</td>\n",
       "      <td>10.520</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>theta__0</th>\n",
       "      <td>6.979</td>\n",
       "      <td>5.885</td>\n",
       "      <td>0.282</td>\n",
       "      <td>-4.199</td>\n",
       "      <td>19.092</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>theta__1</th>\n",
       "      <td>5.248</td>\n",
       "      <td>4.787</td>\n",
       "      <td>0.188</td>\n",
       "      <td>-3.609</td>\n",
       "      <td>16.081</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>theta__2</th>\n",
       "      <td>4.070</td>\n",
       "      <td>5.245</td>\n",
       "      <td>0.234</td>\n",
       "      <td>-6.745</td>\n",
       "      <td>14.749</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>theta__3</th>\n",
       "      <td>5.047</td>\n",
       "      <td>4.795</td>\n",
       "      <td>0.193</td>\n",
       "      <td>-4.795</td>\n",
       "      <td>14.626</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>theta__4</th>\n",
       "      <td>3.979</td>\n",
       "      <td>4.762</td>\n",
       "      <td>0.198</td>\n",
       "      <td>-7.953</td>\n",
       "      <td>12.240</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>theta__5</th>\n",
       "      <td>4.363</td>\n",
       "      <td>4.819</td>\n",
       "      <td>0.196</td>\n",
       "      <td>-5.899</td>\n",
       "      <td>14.258</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>theta__6</th>\n",
       "      <td>6.757</td>\n",
       "      <td>5.000</td>\n",
       "      <td>0.234</td>\n",
       "      <td>-2.017</td>\n",
       "      <td>17.388</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>theta__7</th>\n",
       "      <td>5.094</td>\n",
       "      <td>5.286</td>\n",
       "      <td>0.234</td>\n",
       "      <td>-5.241</td>\n",
       "      <td>15.997</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>tau</th>\n",
       "      <td>3.987</td>\n",
       "      <td>3.110</td>\n",
       "      <td>0.224</td>\n",
       "      <td>0.577</td>\n",
       "      <td>10.037</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           mean     sd  mc_error  hpd_2.5  hpd_97.5\n",
       "mu        4.655  3.105     0.162   -1.696    10.520\n",
       "theta__0  6.979  5.885     0.282   -4.199    19.092\n",
       "theta__1  5.248  4.787     0.188   -3.609    16.081\n",
       "theta__2  4.070  5.245     0.234   -6.745    14.749\n",
       "theta__3  5.047  4.795     0.193   -4.795    14.626\n",
       "theta__4  3.979  4.762     0.198   -7.953    12.240\n",
       "theta__5  4.363  4.819     0.196   -5.899    14.258\n",
       "theta__6  6.757  5.000     0.234   -2.017    17.388\n",
       "theta__7  5.094  5.286     0.234   -5.241    15.997\n",
       "tau       3.987  3.110     0.224    0.577    10.037"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pm3.summary(short_trace).round(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x144 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the trace of log(tau)\n",
    "pm3.traceplot(short_trace, varnames=['tau'], transform=np.log);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 4 jobs)\n",
      "NUTS: [theta, tau_log__, mu]\n",
      "100%|██████████| 5000/5000 [00:11<00:00, 430.94it/s]\n",
      "There were 57 divergences after tuning. Increase `target_accept` or reparameterize.\n",
      "There were 223 divergences after tuning. Increase `target_accept` or reparameterize.\n",
      "The acceptance probability does not match the target. It is 0.6796303528986296, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "The estimated number of effective samples is smaller than 200 for some parameters.\n"
     ]
    }
   ],
   "source": [
    "with Centered_eight:\n",
    "    longer_trace = pm3.sample(4000, chains=2, tune=1000, random_seed=54)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>mc_error</th>\n",
       "      <th>hpd_2.5</th>\n",
       "      <th>hpd_97.5</th>\n",
       "      <th>n_eff</th>\n",
       "      <th>Rhat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>mu</th>\n",
       "      <td>4.772</td>\n",
       "      <td>3.927</td>\n",
       "      <td>0.219</td>\n",
       "      <td>-1.150</td>\n",
       "      <td>14.901</td>\n",
       "      <td>83.503</td>\n",
       "      <td>1.004</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>theta__0</th>\n",
       "      <td>7.016</td>\n",
       "      <td>5.970</td>\n",
       "      <td>0.194</td>\n",
       "      <td>-3.777</td>\n",
       "      <td>19.157</td>\n",
       "      <td>381.389</td>\n",
       "      <td>1.003</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>theta__1</th>\n",
       "      <td>5.486</td>\n",
       "      <td>5.289</td>\n",
       "      <td>0.204</td>\n",
       "      <td>-4.370</td>\n",
       "      <td>15.699</td>\n",
       "      <td>198.925</td>\n",
       "      <td>1.002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>theta__2</th>\n",
       "      <td>4.193</td>\n",
       "      <td>5.977</td>\n",
       "      <td>0.226</td>\n",
       "      <td>-7.922</td>\n",
       "      <td>14.893</td>\n",
       "      <td>204.378</td>\n",
       "      <td>1.002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>theta__3</th>\n",
       "      <td>5.205</td>\n",
       "      <td>5.478</td>\n",
       "      <td>0.213</td>\n",
       "      <td>-5.477</td>\n",
       "      <td>15.322</td>\n",
       "      <td>212.728</td>\n",
       "      <td>1.002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>theta__4</th>\n",
       "      <td>3.823</td>\n",
       "      <td>5.303</td>\n",
       "      <td>0.238</td>\n",
       "      <td>-5.524</td>\n",
       "      <td>15.036</td>\n",
       "      <td>134.126</td>\n",
       "      <td>1.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>theta__5</th>\n",
       "      <td>4.341</td>\n",
       "      <td>5.650</td>\n",
       "      <td>0.237</td>\n",
       "      <td>-5.801</td>\n",
       "      <td>15.531</td>\n",
       "      <td>157.387</td>\n",
       "      <td>1.003</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>theta__6</th>\n",
       "      <td>7.103</td>\n",
       "      <td>5.472</td>\n",
       "      <td>0.181</td>\n",
       "      <td>-3.481</td>\n",
       "      <td>17.450</td>\n",
       "      <td>374.376</td>\n",
       "      <td>1.002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>theta__7</th>\n",
       "      <td>5.384</td>\n",
       "      <td>5.960</td>\n",
       "      <td>0.217</td>\n",
       "      <td>-7.348</td>\n",
       "      <td>15.561</td>\n",
       "      <td>213.063</td>\n",
       "      <td>1.004</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>tau</th>\n",
       "      <td>4.382</td>\n",
       "      <td>3.269</td>\n",
       "      <td>0.134</td>\n",
       "      <td>0.878</td>\n",
       "      <td>10.661</td>\n",
       "      <td>323.020</td>\n",
       "      <td>1.001</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           mean     sd  mc_error  hpd_2.5  hpd_97.5    n_eff   Rhat\n",
       "mu        4.772  3.927     0.219   -1.150    14.901   83.503  1.004\n",
       "theta__0  7.016  5.970     0.194   -3.777    19.157  381.389  1.003\n",
       "theta__1  5.486  5.289     0.204   -4.370    15.699  198.925  1.002\n",
       "theta__2  4.193  5.977     0.226   -7.922    14.893  204.378  1.002\n",
       "theta__3  5.205  5.478     0.213   -5.477    15.322  212.728  1.002\n",
       "theta__4  3.823  5.303     0.238   -5.524    15.036  134.126  1.000\n",
       "theta__5  4.341  5.650     0.237   -5.801    15.531  157.387  1.003\n",
       "theta__6  7.103  5.472     0.181   -3.481    17.450  374.376  1.002\n",
       "theta__7  5.384  5.960     0.217   -7.348    15.561  213.063  1.004\n",
       "tau       4.382  3.269     0.134    0.878    10.661  323.020  1.001"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pm3.summary(longer_trace).round(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x144 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the trace of log(tau)\n",
    "pm3.traceplot(longer_trace, varnames=['tau'], transform=np.log);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('float32')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.float32(y).dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = pm.Model(num_schools=J, y=y, sigma=sigma )\n",
    "@model.define\n",
    "def process(cfg):\n",
    "    mu = ed.Normal(loc=0., scale=5., name=\"mu\")  # `mu` above\n",
    "    # Due to the lack of HalfCauchy distribution.\n",
    "    log_tau = ed.Normal(\n",
    "        loc=5., scale=1., name=\"log_tau\")  # `log(tau)` above\n",
    "    theta_prime = ed.Normal(\n",
    "        loc=tf.zeros(cfg.num_schools),\n",
    "        scale=tf.ones(cfg.num_schools),\n",
    "        name=\"theta_prime\")  # `theta_prime` above\n",
    "    theta = mu + tf.exp(\n",
    "        log_tau) * theta_prime  # `theta` above\n",
    "    y = ed.Normal(\n",
    "        loc=theta,\n",
    "        scale=np.float32(cfg.sigma),\n",
    "        name=\"y\")  # `y` above\n",
    "    \n",
    "    return y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pymc4.model.base.Model at 0x7fde2cf6a550>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.observe(y = model.cfg.y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'y': array([28.,  8., -3.,  7., -1.,  1., 18., 12.])}"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.observed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "OrderedDict([('mu',\n",
       "              VariableDescription(Dist=<class 'tensorflow.python.ops.distributions.normal.Normal'>, shape=TensorShape([]), rv=<ed.RandomVariable 'mu' shape=() dtype=float32>)),\n",
       "             ('log_tau',\n",
       "              VariableDescription(Dist=<class 'tensorflow.python.ops.distributions.normal.Normal'>, shape=TensorShape([]), rv=<ed.RandomVariable 'log_tau' shape=() dtype=float32>)),\n",
       "             ('theta_prime',\n",
       "              VariableDescription(Dist=<class 'tensorflow.python.ops.distributions.normal.Normal'>, shape=TensorShape([Dimension(8)]), rv=<ed.RandomVariable 'theta_prime' shape=(8,) dtype=float32>))])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.unobserved"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-72.16133  -72.965164  95.40658   15.025141  12.754717 107.28393\n",
      " -24.945261 -30.989164]\n"
     ]
    }
   ],
   "source": [
    "with tf.Session():\n",
    "    print(model._f(model._cfg).eval())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## LogP Mismatch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(-50.24198446)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Centered_eight.logp(mu=1, tau_log__=1, theta=[1,1,1,1,1,1,1,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "pymc4_log_prob = model.target_log_prob_fn()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "OrderedDict([('mu',\n",
       "              VariableDescription(Dist=<class 'tensorflow.python.ops.distributions.normal.Normal'>, shape=TensorShape([]), rv=<ed.RandomVariable 'mu' shape=() dtype=float32>)),\n",
       "             ('log_tau',\n",
       "              VariableDescription(Dist=<class 'tensorflow.python.ops.distributions.normal.Normal'>, shape=TensorShape([]), rv=<ed.RandomVariable 'log_tau' shape=() dtype=float32>)),\n",
       "             ('theta_prime',\n",
       "              VariableDescription(Dist=<class 'tensorflow.python.ops.distributions.normal.Normal'>, shape=TensorShape([Dimension(8)]), rv=<ed.RandomVariable 'theta_prime' shape=(8,) dtype=float32>))])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.unobserved"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-52.967716\n"
     ]
    }
   ],
   "source": [
    "with tf.Session():\n",
    "    print(pymc4_log_prob(1, 1., (1., 1., 1., 1., 1., 1., 1., 1.)).eval())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n",
      "/home/sharan/anaconda3/envs/pymc3/lib/python3.6/site-packages/tensorflow/python/util/tf_inspect.py:45: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() or inspect.getfullargspec()\n",
      "  if d.decorator_argspec is not None), _inspect.getargspec(target))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Acceptance rate: 0.6192\n"
     ]
    }
   ],
   "source": [
    "trace = sample(model, num_burnin_steps=1000, num_results=5000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'mu': array([-1.4385958, -1.4385958, -1.4385958, ...,  9.872691 ,  8.878326 ,\n",
       "         8.165668 ], dtype=float32),\n",
       " 'log_tau': array([2.6707418, 2.6707418, 2.6707418, ..., 3.1494684, 1.3626628,\n",
       "        2.6146834], dtype=float32),\n",
       " 'theta_prime': array([[ 0.9217021 ,  0.7332041 , -0.69482315, ...,  0.31827638,\n",
       "          0.87768406,  0.93878686],\n",
       "        [ 0.9217021 ,  0.7332041 , -0.69482315, ...,  0.31827638,\n",
       "          0.87768406,  0.93878686],\n",
       "        [ 0.9217021 ,  0.7332041 , -0.69482315, ...,  0.31827638,\n",
       "          0.87768406,  0.93878686],\n",
       "        ...,\n",
       "        [ 0.12429702, -0.19490498, -1.5399917 , ..., -0.30469486,\n",
       "          0.22185168, -0.52403253],\n",
       "        [ 0.9992132 ,  0.9186932 ,  0.71775293, ..., -0.19752336,\n",
       "         -0.77504003, -0.24895237],\n",
       "        [-0.62771237,  1.1626923 , -1.2299166 , ..., -1.2041072 ,\n",
       "          0.42344823, -0.89037424]], dtype=float32)}"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trace"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta = (\n",
    "    trace['mu'][:, np.newaxis] +\n",
    "    np.exp(trace['log_tau'])[:, np.newaxis] * trace['theta_prime'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5000, 8)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([  9.,  55.,  91., 160., 261., 292., 285., 353., 355., 334., 372.,\n",
       "        332., 276., 229., 212., 208., 220., 158., 117., 108., 102., 100.,\n",
       "         45.,  64.,  27.,  35.,  18.,  50.,  21.,   9.,  42.,  25.,   5.,\n",
       "          4.,   1.,   4.,   0.,   1.,  15.,   5.]),\n",
       " array([ 1.0316025,  2.0316025,  3.0316025,  4.0316025,  5.0316025,\n",
       "         6.0316025,  7.0316025,  8.0316025,  9.0316025, 10.0316025,\n",
       "        11.0316025, 12.0316025, 13.0316025, 14.0316025, 15.0316025,\n",
       "        16.0316025, 17.0316025, 18.0316025, 19.0316025, 20.0316025,\n",
       "        21.0316025, 22.0316025, 23.0316025, 24.0316025, 25.0316025,\n",
       "        26.0316025, 27.0316025, 28.0316025, 29.0316025, 30.0316025,\n",
       "        31.0316025, 32.0316025, 33.0316025, 34.0316025, 35.0316025,\n",
       "        36.0316025, 37.0316025, 38.0316025, 39.0316025, 40.0316025,\n",
       "        41.0316025]),\n",
       " <a list of 40 Patch objects>)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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vSdICVuSIvqoeT/Im4N+B04Cbq2rfSuxLkrSwFRujr6rbgduX6eNGGuKZAusaj3WNx7rGY10nkaqadg2SpBXks24kqXMzHfSz+hiFJAeSfCnJ7iS7pljHzUmOJNk71HZWkjuSfLW9P2dG6np7kkOtz3YnuWwKdW1IcleSB5LsS/Lm1j7VPlugrqn2WZKnJ7knyf2trne09nOT3N1+Lz/aLriYhbpuSfKNof7auJp1DdV3WpIvJvlUm59qfwFQVTP5YnAS92vAc4GnAfcD50+7rlbbAeDsGajjN4ALgb1DbX8NbGvT24B3zkhdbwf+eMr9tRa4sE0/G/gv4Pxp99kCdU21z4AAz2rTpwN3AxcDtwJXtfZ/AP5wRuq6BXjtNP+NtZr+CPhn4FNtfqr9VVUzfUT/48coVNX/Asceo6Cmqj4LfOe45s3Ajja9A7hiVYvipHVNXVUdrqr72vQPgAcZ3MU91T5boK6pqoFH2+zp7VXAJcDHWvs0+utkdU1dkvXA5cA/tvkw5f6C2R66OdFjFKb+j78p4D+S3Nvu8J0la6rqcJv+FrBmmsUc501J9rShnVUfUhqWZB64gMHR4Mz02XF1wZT7rA1D7AaOAHcw+F/2I1X1eFtlKr+Xx9dVVcf667rWXzckOWO16wL+FvhT4Edt/ueZgf6a5aCfZS+tqguBVwPXJPmNaRd0IjX4v+JMHOkANwLPAzYCh4F3TauQJM8CPg68paq+P7xsmn12grqm3mdV9URVbWRwd/tFwPNXu4YTOb6uJC8ErmVQ34uBs4C3rWZNSX4LOFJV967mfkcxy0G/6GMUpqWqDrX3I8AnGfwCzIqHk6wFaO9HplwPAFX1cPvl/BHwPqbUZ0lOZxCmH6qqT7TmqffZieqalT5rtTwC3AX8OnBmkmP34Ez193KorkvbEFhV1WPA+1n9/noJ8NtJDjAYar4EeA8z0F+zHPQz+RiFJM9M8uxj08Argb0Lb7WqdgJb2vQW4LYp1vJjx4K0eQ1T6LM2XnoT8GBVvXto0VT77GR1TbvPkswlObNNP4PB90s8yCBYX9tWm0Z/naiuLw/9sQ6DcfBV7a+quraq1lfVPIO8+kxV/S5T7q9jxc3sC7iMwRUIXwP+fNr1tJqey+AKoPuBfdOsC/gwg//S/x+Dsb+rGYwJ3gl8FfhP4KwZqeuDwJeAPQyCde0U6nopg2GZPcDu9rps2n22QF1T7TPgV4Evtv3vBf6itT8XuAfYD/wLcMaM1PWZ1l97gX+iXZkzjRfwMn5y1c1U+6uqvDNWkno3y0M3kqRlYNBLUucMeknqnEEvSZ0z6CWpcwa9JHXOoJekzhn0ktS5/wezapkfXtL2dAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# trace plot tau\n",
    "import seaborn as sns\n",
    "plt.hist(np.exp(trace['log_tau']), bins=np.arange(np.exp(trace['log_tau']).min(), np.exp(trace['log_tau']).max()+1))\n",
    "# sns.distplot(np.exp(trace['log_tau']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fddfb1886a0>]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.exp(trace['log_tau']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fddf9155320>]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(mlogtau, lw=0.9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5000,)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta[:,0].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(5000, 8)\n",
      "0 Mean: 13.1466675 sd: 10.361167\n",
      "1 Mean: 6.248073 sd: 7.912224\n",
      "2 Mean: 1.172592 sd: 10.112816\n",
      "3 Mean: 5.117202 sd: 8.129532\n",
      "4 Mean: 0.76633567 sd: 7.127367\n",
      "5 Mean: 2.0183334 sd: 8.09595\n",
      "6 Mean: 11.76272 sd: 8.364141\n",
      "7 Mean: 6.1588736 sd: 10.1365595\n"
     ]
    }
   ],
   "source": [
    "print(theta.shape)\n",
    "\n",
    "for school in range(theta.shape[1]):\n",
    "    print(str(school) + \" Mean:\", np.mean(theta[:, school]), \"sd:\", np.std(theta[:, school]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mu Mean: 3.3309453\n",
      "tau Mean: 13.029848\n",
      "theta_prime Mean: 0.17966528\n"
     ]
    }
   ],
   "source": [
    "for i in trace.keys():\n",
    "    if i != \"log_tau\":\n",
    "        print(i, \"Mean:\", np.mean(trace[i]))\n",
    "    else:\n",
    "        print(\"tau Mean:\", np.mean(np.exp(trace[i])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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6nwfbdiiiX2pxtjyxNAe4A3gE6GwN/hIwAyAiLpJ0FnAmSY+qRuBfI+Lu9PgTgQuAPHBJRHyrt2vW1dXF/Pnz+7somRz9vdt4Ln2o7zdzD+H98+7pdr+b/+Vwdp44ivf89G46An75sYM58Yd3sKy+qdv9377XJH76oTdRyOfY0NzGHU+v4E0zxzNpTDUNLW1878anWVbfyNzDd+X5lRv400NL+cuTr03+lM+JGRNG8pmjd+PIPScxoQ89wPpi9cYWrrjvJVZtaGHn2lHsWjuKO55ZyW/vf5n2CNo7grb2oD2Cjo6grSM25W/ciMKADsMyfmSBXWprGDuiQE7w5LL1LF7TyPiRBcaNrKS6kEfAS6sbKOTF3juNoSIdBr92dBUtbR1U5MWIQp4pY6rZf8Y4Jo+pZkx1gRGFPIUKUZnPsa6xlZrqCqoq8lvkobmtnQUvrOGRJet46tX1PLF0PR0dwQ41ybNAk0ZXMX5UJZUVOQq5HBI0tLTz5LJ6XljZQFUhx5qNLbywKunWvcvEUdQ3tVKZz7Gsvon07SUnNi0D7Fo7ijm7TWT/GeOoyOVobG1nxfpmxo4o0NTaTkVOTBlbTVUhT1VFjtqaKsaOKFDI5xg3sjCgAXXlhmbaO4KJ6Y+KrF5a1cBVCxfz5LJ6mlo7aOvoYPLoaiaMqqQin2N0dQVTxlQzbfwImtIfI5UVOUZXVbDjuBFMHl1FRZl/aLW1d1Df1MbIyjzVhS0/HwNJ0oKIqMu0b7kCxmAYzIBx/o1PcuGtz26RXlWRo/l1TsR0zN6T+cYp+/Lei+5m8ZrG13WuqeNGMKIyzwn7TuHe51fzxNJ6poyp5m17JW0vG5pbaWzpYF1jK8+t2MBn3rYbJ++3E42t7Wxsbqd2dBWPvbKOp1/dQERw2G4TqS7ked9Fd/Psitf/FHxOMG5kJeNGFqjM59hp3Agq8zlyOXhuxUbaOoKaqgqaWttpaEn+o69rbGX1xhbaO4beZ1mCmRNG0tDSztrGVnarraEjgudWbtzmJugaO6LA3juOYY/JNUwbP5La0VWsb2ollxMjK/MU8jnqG9tYtaGZVRtbqG9sZURlnrWNrUQEjS3trEvTRlYmd84CNra00dLWQUdAIS9yEq+sbdwUDDt/9EyfMJIJIwubBeHW9o5NPz4igqeWrWfhS2tfVzlzgkmjq5kytpqJmx7MDSKS6RAKeTFpdDWjqytobuugubWdmuoK2tqDQj5HU2tSzvaOoLUjNq23tHVQ39TK8vpmNjS3bbremOoKxo+qZNyIwqb3Jdj8s5zPifrGNnKCdY2t5HNK75pzVFbkqKrI8ZFDZ3FMURtqVg4Yg6ChpY29v3LjZmlH7VnLzz5cxw//8nS3waSrI/es5S27JtVIv773JZ5ZvmGr8lLIi9b25N/1gBnjeHTJuk3rA238yAKHpmXqiOSX1ejqCnabVMPahlYWr2mkkM+xS+0oTt5vJ6ZPGLHVv2IjgmdXbCAn0RGwaPl6Vm9spT2CyrxoaGmnrT146tX1LF7TQH1jGy3tHew+qYbpE0ayckMzaza2kM+Jto5g6rgR1De18eKqjQhobutgTUMLhXyOCGhsbe+XEY3Hjiiw79TkLmZDcxtrG1p4tcuXSqeJNVXsteNoXq1vYkx1gTm7T+TV+maeXbGB2poqmtuSqrvqQp6OCFraO9hxTDWQTAh23/OreWjxum0uWG2NnSeOYkx1BbmceHl1Axub22mP2G7L/s137cuHDpnZ5+P6EjA8NEg/GVlZwcwdRvLiqtee/H5f3XQqK3J87rg38L43TefI79222TFTx41gdHUFIyvznHfKvpu1mZxx2M6sb2rllP++a1NVV3dOnr0T65taWd/UxhmHzeKtu9cyprqCiOTXrSTWbGzh/hdWc+tTy7nivpc3O76mqoKKvFjb0EpFToyurmBDc9tWBZh/OGAq579vNi+tbuDxV+oZM6KCw3aduMUkVeUiid0mvdYpYbdJNWW/5or1zTyyZG1yB9HQSlNrOxua22hsbWfKmGperW/mmVfXU5P+Oz+7YiM1VRXMmDCSulnjOXSXHbptU4H013N70NrRQXTAiMp8v7RBNLe188yrGyjkc4wo5BldXUFLewcjKvM0NCdBsKmtnaaWdl5a3UBbR3J38PSr63nslXpeXLWRjS3tJa9RU1XB2BEF1jS0MLGmikI++UXcWfXV0NKOJNo7OtLPYA7Bpm2Tx1Tz5p0nMG5kgcVrG3lxZQNL1jayrrGV9U2tm770K/JJ21VLWzsRsMukGg6aOZ731U3frINKsY3NbTy0eC0Nze2MG1mgqiJPS3sH9Y2tvLKukaVrm1i6roml6xpZvbEFSYjk/1N7RxKEl6xppKW9g6qK3Kbq4kI+R2t7B9UVSTkLFaIil/z6H1NdoLoyT2U+x/QJIxg7osCY6gLrm9pYvbGZNQ2trGlooam1neRq0PknIqnCHVNdIIDR1RV0dCSBr6W9Y9PfSaPLP0yR7zD60XdveJKfFjV2P/mN4zern4wIGlqSL5TO/zy9uXvRSj7w8+TxlR3HVnPDOYdT39TKtPFb90u8pa2DDc1trGloYfKYamqqKogI6hvbqKmuIJ9Tcivd3sGld7/A/c+vRoLZ08bR1hH88aFXmD5hJIfvUUshLx5/pZ5X65s4ft8pvPdN092FeJh4ZW0jja3tjK6ugID6plbaO5IvswmjKge9Xn4gFPfma+8I8jnR0RED9gOpv7hKapC0dwS7fuk6AP7fsXtw1tF9eqSkR40t7dz42DKO3msSY6p7DzJmZlm5SmqQ5HPi+f84kdUbW/q1N9KIyjzvOiDrqCpmZuXhgNHPJHnIczPbLvkpHjMzy8QBw8zMMnHAMDOzTBwwzMwsEwcMMzPLxAHDzMwyccAwM7NMHDDMzCwTBwwzM8vEAcPMzDIpOTSIpGkk06O+FdiJZFa8R4E/A9dHxPY5sLyZmW2hxzsMSb8ALgFagO8CpwH/DNwCHA/cKenwEsdPl3SrpMclPSbpnG72+aCkhyU9IuluSbOLtr2Qpj8oafCGoDUzM6D0Hcb3I+LRbtIfBa6WVEk6P3cP2oDPRsRCSaOBBZJujojHi/Z5HjgiItZIOgGYB7y5aPtREbEyW1HMzKycegwYPQSL4u0twKIS25cCS9Pl9ZKeAKYCjxftc3fRIfcA07Jl28zMBlqvw5tLeh7YYpaliNgl60UkzQIOAO4tsdvHgeuLLwHcJCmAn0XEvB7OPReYCzBjRqkbHjMzez2yzIdRPBNTNfA+YELWC0iqAa4Czo2I+h72OYokYMwpSp4TEUskTQJulvRkRNze9dg0kMyDZMa9rPkyM7O+6bVbbUSsKnotiYgLgHdkObmkAkmwuDwiru5hn/2AnwOnRMSqousuSf8uB64BDs5yTTMzK48sVVIHFq3mSO44shwn4GLgiYj4QQ/7zACuBj4cEU8XpY8CcmnbxyjgWOC83q5pZmblk6VK6vtFy23AC8A/ZjjuMODDwCOSHkzTvkTasyoiLgK+AuwA/CSJL7Slk5FPBq5J0yqAX0fEDRmuaWZmZdJrwIiIo7bmxBFxJ6Be9vkE8Ilu0p8DZm95hJmZDZYsdxhIegewD0mjNwAR4SoiM7NhpNdGb0kXAe8HPkNyx/A+YGaZ82VmZkNMlsEH3xIRHwHWRMTXgUOBPcqbLTMzG2qyBIzG9G+DpJ2AVmDH8mXJzMyGoixtGH+SNA44H1hI8gT2z8uaKzMzG3KyBIz/jIhm4CpJfyJp+G4qb7bMzGyoyVIl9ffOhYhojoh1xWlmZjY89HiHIWkKyeiyIyQdwGvPVIwBRg5A3szMbAgpVSV1HPBRkiHHv89rAaOe5IltMzMbRkrNh/FL4JeS3hMRVw1gnszMbAgqNUXrhySpp2AhaVdJc7rbZmZm259SVVI7AA9KWgAsAFaQ9JDaDTgCWAl8oew5NDOzIaFUldQPJf03cDTJyLP7kTzE9wTJcOQvDUwWzcxsKCj5HEZEtAM3py8zMxvGskyE9KNuktcB8yPi//o/S2ZmNhRleXCvGtgfeCZ97UfS1fbjki4oY97MzGwIyRIw9gOOiogfR8SPgbcDbwDeTTJ1arckTZd0q6THJT0m6Zxu9pGkH0laJOnh4ulgJZ0u6Zn0dXrfi2ZmZv0py1hS44EakmoogFHAhIhol9Rc4rg24LMRsVDSaGCBpJsj4vGifU4Adk9fbwZ+CrxZ0gTgqyTzh0d67LURsaYvhTMzs/6TafBBku61t5E87X048G1Jo4BbejooIpYCS9Pl9ZKeIBlqpDhgnAJcFhEB3CNpnKQdgSOBmyNiNYCkm4HjgSv6VjwzM+svWeb0vljSdcDBadKXIuKVdPlzWS4iaRZwAHBvl01TgZeL1henaT2ld3fuucBcgBkzZmTJjpmZbYUsbRgABwFvTV9v6ssFJNUAVwHnRkR937LXu4iYFxF1EVFXW1vb36c3M7NUljm9vwOcQ1KV9DhwtqRvZzm5pAJJsLg8Iq7uZpclwPSi9WlpWk/pZmY2SLLcYZwIHBMRl0TEJSRtCSf1dpAkARcDT0TED3rY7VrgI2lvqUOAdWnbx43AsZLGSxpP0hvrxgx5NTOzMsnS6A0wDlidLo/NeMxhwIeBRyQ9mKZ9CZgBEBEXAdeRBKRFQANwRrpttaRvAPenx53X2QBuZmaDI0vA+A/gAUm38lovqV4HHYyIO3ltDo2e9gng0z1suwS4JEP+zMxsAGTpJXVF2qX2oDTp3yJiWVlzZWZmQ06pKVoP7JK0OP27k6SdImJh+bJlZmZDTak7jO+X2BYkw56bmdkwUWo+jKMGMiNmZja0ZX1wz8zMhjkHDDMzy6THgCHpsPRv1cBlx8zMhqpSdxidM+39fSAyYmZmQ1upXlKtkuYBU7ubpjUizi5ftszMbKgpFTBOIpld7zhgwcBkx8zMhqpS3WpXAldKeiIiHhrAPJmZ2RCUpZfUKknXSFqevq6SNK3sOTMzsyElS8D4Bckw5Dulrz+maWZmNoxkCRiTIuIXEdGWvi4FPLWdmdkwkyVgrJT0IUn59PUhYFW5M2ZmZkNLloDxMeAfgWXAUuC9pBMdmZnZ8JFlPowXgXcOQF7MzGwIyzpFa59JuoTkWY7lEbFvN9s/B3ywKB97AbXp9KwvAOuBdqAtIurKlU8zM8umnIMPXgoc39PGiDg/IvaPiP2BLwJ/6zJv91HpdgcLM7MhoGwBIyJuB1b3umPiNOCKcuXFzMxev16rpNLRat8DzCrePyLO648MSBpJcidyVlFyADdJCuBnETGvxPFzgbkAM2bM6I8smZlZN7K0YfwfsI5kPKnmMuThZOCuLtVRcyJiiaRJwM2SnkzvWLaQBpN5AHV1dVGG/JmZGdkCxrSI6LEtoh+cSpfqqIhYkv5dLuka4GCg24BhZmYDI0sbxt2S3liOi0saCxxBchfTmTZK0ujOZeBY4NFyXN/MzLLLcocxB/iopOdJqqQERETsV+ogSVcARwITJS0GvgoUSA6+KN3t3cBNEbGx6NDJwDWSOvP364i4IXOJzMysLLIEjBO25sQRcVqGfS4l6X5bnPYcMHtrrmlmZuWT9Ulv0gbo6rLnyMzMhqRe2zAkvVPSM8DzwN+AF4Dry5wvMzMbYrI0en8DOAR4OiJ2Bt4G3FPWXJmZ2ZCTJWC0RsQqICcpFxG3Ah6uw8xsmMnS6L1WUg1wB3C5pOXAxl6OMTOz7UyWO4xTgAbgXOAG4FmSp7PNzGwYydJLaqOkmcDuEfHLdOynfPmzZmZmQ0mWXlL/BPwe+FmaNBX4QzkzZWZmQ0+WKqlPA4cB9QAR8QwwqZyZMjOzoSdLwGiOiJbOFUkVJMOPm5nZMJIlYPxN0peAEZKOAX4H/LG82TIzs6EmS8D4ArACeAT4JHAd8O/lzJSZmQ09WXpJdQD/k77MzGyYytJL6iRJD0haLale0npJ9QOROTMzGzqyPOl9AfAPwCMR4cZuM7NhKksbxsvAow4WZmbDW5Y7jM8D10n6G8mMewBExA9KHSTpEuAkYHlE7NvN9iNJpmZ9Pk26OiLOS7cdD/yQ5Inyn0fEdzLk08zMyihLwPgWsIFk8qTKPpz7UuC/gctK7HPFA6MmAAAOM0lEQVRHRJxUnCApD1wIHAMsBu6XdG1EPN6Ha5uZWT/LEjB26u4OoTcRcbukWX3OERwMLEqnakXSlSQDIDpgmJkNoixtGNdJOrZM1z9U0kOSrpe0T5o2laTdpNPiNK1bkuZKmi9p/ooVK8qUTTMzyxIwzgRukNTYz91qFwIzI2I28GO2ckDDiJgXEXURUVdbW9sP2TIzs+70GjAiYnRE5CJiRESMSdfHvN4LR0R9RGxIl68DCpImAkuA6UW7TkvTzMxsEGW5wygLSVMkKV0+OM3LKuB+YHdJO0uqBE4Frh2sfJqZWSJLo/dWkXQFcCQwUdJi4KtAASAiLgLeC5wpqQ1oBE5Nn/Vok3QWcCNJt9pLIuKxcuXTzMyy0fb0PF5dXV3Mnz9/sLNhZrbNkLQgIuqy7NtjlZSkgySd0E36iZLe9HoyaGZm255SbRjfpftnHx4Dzi9PdszMbKgqFTBGR8SLXRPTtInly5KZmQ1FpQLG+BLbRvZ3RszMbGgrFTBukfStzq6vAEqcB/y1/FkzM7OhpFS32s8CPwcWSXowTZsNzAc+Ue6MmZnZ0NJjwIiIjcBpknYBOsd5eqxzUEAzMxteegwYkg4sWu0cmmNcZ3pELCxnxszMbGgpVSU1H3gUWJmuq2hbAEeXK1NmZjb0lAoY/0oyfEcjcCVwTedggWZmNvz02EsqIi6IiDnAZ0hGj/2LpN9K2n/AcmdmZkNGluHNnyOZe/smktnw9ih3pszMbOgp1ei9C8nQ4qeQzIB3JfDtiGgcoLyZmdkQUqoNYxHwMMndRT0wg2Q4cgAi4gdlz52ZmQ0ZpQLGeSS9oQBqBiAvZmY2hJV6cO9rA5gPMzMb4krNh3G+pE92k/5JSd/p7cSSLpG0XNKjPWz/oKSHJT0i6W5Js4u2vZCmPyjJMyKZmQ0BpXpJHQ3M6yb9f4CTMpz7UuD4EtufB46IiDcC3+jmWkdFxP5ZZ4IyM7PyKhUwqqKb+VsjooPNn/ruVkTcDqwusf3uiFiTrt4DTOvtnGZmNnhKBYxGSbt3TUzT+rtr7ceB64vWA7hJ0gJJc/v5WmZmthVK9ZL6CnC9pG8CC9K0OuCLwLn9lQFJR5EEjDlFyXMiYomkScDNkp5M71i6O34uMBdgxowZ/ZUtMzProtTQINcD7wKOImmPuDRdfk9EXNcfF5e0H8mcG6dExKqiay9J/y4HriF5wrynfM6LiLqIqKutre2PbJmZWTdK3WEQEY8Cp5fjwpJmAFcDH46Ip4vSRwG5iFifLh9L8kyImZkNolJDg1xb6sCIeGep7ZKuAI4EJkpaDHwVKKTHXkRS5bUD8JP06fG2tEfUZOCaNK0C+HVE3JCxPGZmVial7jAOJRlD6grgXjL0jCoWEaf1sv0TdDPVazrY4ewtjzAzs8FUKmBMAY4BTgM+APwZuCIiHhuIjJmZ2dBSqtG7PSJuiIjTgUNIBiO8TdJZA5Y7MzMbMko2ekuqAt5BcpcxC/gRSa8lMzMbZko1el8G7AtcB3w97TFlZmbDVKk7jA8BG4FzgLM758EgafyOiBhT5ryZmdkQUmp4816nbzUzs+HDQcHMzDJxwDAzs0wcMMzMLBMHDDMzy8QBw8zMMnHAMDOzTBwwzMwsEwcMMzPLxAHDzMwyccAwM7NMHDDMzCyTsgYMSZdIWi6p25FulfiRpEWSHpZ0YNG20yU9k77KMq+4mZllV+47jEuB40tsPwHYPX3NBX4KIGkCyRzgbwYOBr4qaXxZc2pmZiWVNWBExO3A6hK7nAJcFol7gHGSdgSOA26OiNURsQa4mdKBx8zMymyw2zCmAi8XrS9O03pK34KkuZLmS5q/YsWKsmXUzGy4G+yA8bpFxLyIqIuIutra2sHOjpnZdmuwA8YSYHrR+rQ0rad0MzMbJIMdMK4FPpL2ljoEWBcRS4EbgWMljU8bu49N08zMbJCUmtP7dZN0BXAkMFHSYpKeTwWAiLgIuA44EVgENABnpNtWS/oGcH96qvMiolTjuZmZlVlZA0ZEnNbL9gA+3cO2S4BLypEvMzPru8GukjIzs22EA4aZmWXigGFmZpk4YJiZWSYOGGZmlokDhpmZZeKAYWZmmThgmJlZJg4YZmaWiQOGmZll4oBhZmaZOGCYmVkmDhhmZpaJA4aZmWXigGFmZpk4YJiZWSZlDRiSjpf0lKRFkr7Qzfb/kvRg+npa0tqibe1F264tZz7NzKx3ZZtxT1IeuBA4BlgM3C/p2oh4vHOfiPiXov0/AxxQdIrGiNi/L9dctWoVl1566evKt5mZda+cU7QeDCyKiOcAJF0JnAI83sP+p5HM+b3VmpubefHFF1/PKczMrAflDBhTgZeL1hcDb+5uR0kzgZ2BvxYlV0uaD7QB34mIP/R2waqqKmbOnLn1OTYzsx6VM2D0xanA7yOivShtZkQskbQL8FdJj0TEs10PlDQXmAswY8YMPvrRjw5Ihs3MtgdnnHFG5n3L2ei9BJhetD4tTevOqcAVxQkRsST9+xxwG5u3bxTvNy8i6iKirra29vXm2czMelDOgHE/sLuknSVVkgSFLXo7SXoDMB74e1HaeElV6fJE4DB6bvswM7MBULYqqYhok3QWcCOQBy6JiMcknQfMj4jO4HEqcGVERNHhewE/k9RBEtS+U9y7yszMBp42/57ettXV1cX8+fMHOxtmZtsMSQsioi7Lvn7S28zMMnHAMDOzTBwwzMwsk+2qDUPSCmBrH/WeCKzsx+xsC1zm7d9wKy+4zH01MyIyPZOwXQWM10PS/KwNP9sLl3n7N9zKCy5zOblKyszMMnHAMDOzTBwwXjNvsDMwCFzm7d9wKy+4zGXjNgwzM8vEdxhmZpaJA4aZmWUy7ANGb/OOb0skXSJpuaRHi9ImSLpZ0jPp3/FpuiT9KC33w5IOLDrm9HT/ZySdPhhlyUrSdEm3Snpc0mOSzknTt9tyS6qWdJ+kh9Iyfz1N31nSvWnZfpOOEo2kqnR9Ubp9VtG5vpimPyXpuMEpUTaS8pIekPSndH27Li+ApBckPSLpwXRCucH9bEfEsH2RjKL7LLALUAk8BOw92Pl6HeU5HDgQeLQo7T+BL6TLXwC+my6fCFwPCDgEuDdNnwA8l/4dny6PH+yylSjzjsCB6fJo4Glg7+253Gnea9LlAnBvWpbfAqem6RcBZ6bL/wxclC6fCvwmXd47/cxXkcx4+SyQH+zylSj3vwK/Bv6Urm/X5U3z/AIwsUvaoH22h/sdxqZ5xyOiBeicd3ybFBG3A6u7JJ8C/DJd/iXwrqL0yyJxDzBO0o7AccDNEbE6ItYANwPHlz/3WycilkbEwnR5PfAEyfTA222507xvSFcL6SuAo4Hfp+ldy9z5XvweeJskpelXRkRzRDwPLCL5PzHkSJoGvAP4eboutuPy9mLQPtvDPWB0N+/41EHKS7lMjoil6fIyYHK63FPZt9n3JK16OIDkF/d2Xe60euZBYDnJF8CzwNqIaEt3Kc7/prKl29cBO7BtlfkC4PNAR7q+A9t3eTsFcJOkBUqmo4ZB/GwPlTm9bQBEREjaLvtRS6oBrgLOjYj65AdlYnssd0S0A/tLGgdcA7xhkLNUNpJOApZHxAJJRw52fgbYnIhYImkScLOkJ4s3DvRne7jfYfRl3vFt1avpbSnp3+Vpek9l3+beE0kFkmBxeURcnSZv9+UGiIi1wK3AoSRVEJ0/Aovzv6ls6faxwCq2nTIfBrxT0gsk1cZHAz9k+y3vJhGxJP27nOSHwcEM4md7uAeMTPOOb+OuBTp7RZwO/F9R+kfSnhWHAOvS29wbgWOVzKs+Hjg2TRuS0rrpi4EnIuIHRZu223JLqk3vLJA0AjiGpO3mVuC96W5dy9z5XrwX+GskraHXAqemvYp2BnYH7huYUmQXEV+MiGkRMYvk/+hfI+KDbKfl7SRplKTRncskn8lHGczP9mD3AhjsF0nPgqdJ6oC/PNj5eZ1luQJYCrSS1FN+nKTu9i/AM8AtwIR0XwEXpuV+BKgrOs/HSBoEFwFnDHa5einzHJJ63oeBB9PXidtzuYH9gAfSMj8KfCVN34XkC3AR8DugKk2vTtcXpdt3KTrXl9P34inghMEuW4ayH8lrvaS26/Km5XsofT3W+f00mJ9tDw1iZmaZDPcqKTMzy8gBw8zMMnHAMDOzTBwwzMwsEwcMMzPLxAHDrBuSNqR/Z0n6QD+f+0td1u/uz/OblYsDhllps4A+BYyip497slnAiIi39DFPZoPCAcOstO8Ab03nI/iXdNC/8yXdn8458EkASUdKukPStcDjadof0kHjHuscOE7Sd4AR6fkuT9M672aUnvvRdA6E9xed+zZJv5f0pKTLVTxYltkA8eCDZqV9Afh/EXESQPrFvy4iDpJUBdwl6aZ03wOBfSMZOhvgYxGxOh2+435JV0XEFySdFRH7d3OtfwD2B2YDE9Njbk+3HQDsA7wC3EUyvtKd/V9cs575DsOsb44lGa/nQZJh1HcgGZMI4L6iYAFwtqSHgHtIBn/bndLmAFdERHtEvAr8DTio6NyLI6KDZPiTWf1SGrM+8B2GWd8I+ExEbDZ4Wzrs9sYu628HDo2IBkm3kYxxtLWai5bb8f9dGwS+wzArbT3J1K+dbgTOTIdUR9Ie6UiiXY0F1qTB4g0kU2Z2au08vos7gPen7SS1JFPuDtnRVG348a8Us9IeBtrTqqVLSeZhmAUsTBueV/DaFJnFbgA+JekJkpFR7ynaNg94WNLCSIbp7nQNybwWD5GMwPv5iFiWBhyzQefRas3MLBNXSZmZWSYOGGZmlokDhpmZZeKAYWZmmThgmJlZJg4YZmaWiQOGmZll8v8BKhbFe/CXytkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mlogtau = [np.mean(trace[\"log_tau\"][:i]) for i in np.arange(1, len(trace[\"log_tau\"]))]\n",
    "# plt.figure(figsize=(15, 4))\n",
    "plt.axhline(0.7657852, lw=2.5, color='gray')\n",
    "plt.plot(mlogtau, lw=2.5)\n",
    "# plt.ylim(0, 2)\n",
    "plt.xlabel('Iteration')\n",
    "plt.ylabel('MCMC mean of log(tau)')\n",
    "plt.title('MCMC estimation of log(tau)');\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x720 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "fig, axes = plt.subplots(8, 2, sharex='col', sharey='col')\n",
    "fig.set_size_inches(12, 10)\n",
    "for i in range(J):\n",
    "    axes[i][0].plot(trace['theta_prime'][:,i])\n",
    "    axes[i][0].title.set_text(\"School {} treatment effect chain\".format(i))\n",
    "    sns.kdeplot(trace['theta_prime'][:,i], ax=axes[i][1], shade=True)\n",
    "    axes[i][1].title.set_text(\"School {} treatment effect distribution\".format(i))\n",
    "axes[J - 1][0].set_xlabel(\"Iteration\")\n",
    "axes[J - 1][1].set_xlabel(\"School effect\")\n",
    "fig.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "school_effects_low = np.array([\n",
    "    np.percentile(trace[\"theta_prime\"][:, i], 2.5) for i in range(J)\n",
    "])\n",
    "school_effects_med = np.array([\n",
    "    np.percentile(trace[\"theta_prime\"][:, i], 50) for i in range(J)\n",
    "])\n",
    "school_effects_hi = np.array([\n",
    "    np.percentile(trace[\"theta_prime\"][:, i], 97.5)\n",
    "    for i in range(J)\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Inferred posterior mean: 0.18\n",
      "Inferred posterior mean se: 0.81\n"
     ]
    }
   ],
   "source": [
    "print(\"Inferred posterior mean: {0:.2f}\".format(\n",
    "    np.mean(trace[\"theta_prime\"][:,])))\n",
    "print(\"Inferred posterior mean se: {0:.2f}\".format(\n",
    "    np.std(trace[\"theta_prime\"][:,])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python (pymc3)",
   "language": "python",
   "name": "pymc3"
  },
  "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": 2
}