{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### NRT Lectures - Statistical Modeling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bayesian Hierarchical Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Rat Tumor Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import random\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "# import graphviz\n",
    "# from pymc3 import model_to_graphviz\n",
    "import pymc3 as pm\n",
    "from pymc3 import Model, sample, Beta, Binomial, Exponential, Uniform, summary, plot_posterior, model_to_graphviz, Deterministic\n",
    "import matplotlib.pyplot as plt\n",
    "# import os\n",
    "# os.environ[\"PATH\"] += os.pathsep + 'C:\\Program Files\\Python37\\Lib\\site-packages\\graphviz\\dot.py'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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>y</th>\n",
       "      <th>N</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>66</th>\n",
       "      <td>16</td>\n",
       "      <td>52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>67</th>\n",
       "      <td>15</td>\n",
       "      <td>46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>68</th>\n",
       "      <td>15</td>\n",
       "      <td>47</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69</th>\n",
       "      <td>9</td>\n",
       "      <td>24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>70</th>\n",
       "      <td>4</td>\n",
       "      <td>14</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>71 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     y   N\n",
       "0    0  20\n",
       "1    0  20\n",
       "2    0  20\n",
       "3    0  20\n",
       "4    0  20\n",
       "..  ..  ..\n",
       "66  16  52\n",
       "67  15  46\n",
       "68  15  47\n",
       "69   9  24\n",
       "70   4  14\n",
       "\n",
       "[71 rows x 2 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d =  pd.read_table(\"rattumor.txt\", sep = \" \")\n",
    "d = d.iloc[:,:2]\n",
    "d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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>y</th>\n",
       "      <th>N</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>71.000000</td>\n",
       "      <td>71.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>3.760563</td>\n",
       "      <td>24.492958</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>3.811504</td>\n",
       "      <td>10.973830</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>10.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>19.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>3.000000</td>\n",
       "      <td>20.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>5.000000</td>\n",
       "      <td>22.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>16.000000</td>\n",
       "      <td>52.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               y          N\n",
       "count  71.000000  71.000000\n",
       "mean    3.760563  24.492958\n",
       "std     3.811504  10.973830\n",
       "min     0.000000  10.000000\n",
       "25%     1.000000  19.000000\n",
       "50%     3.000000  20.000000\n",
       "75%     5.000000  22.500000\n",
       "max    16.000000  52.000000"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A naive estimate of $\\theta_j$ is $\\hat{\\theta_j}=y_j/n_j$.\n",
    "\n",
    "Histogram of  $\\hat{\\theta_j}$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<function matplotlib.pyplot.show(*args, **kw)>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(d.y/d.N, range = (0,1), bins = 18, density=True)\n",
    "plt.title(\"Histogram of naive estimate\")\n",
    "plt.show"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "with Model() as model1:\n",
    "\n",
    "    # Priors\n",
    "    alpha = Exponential('alpha', 0.001)\n",
    "    beta = Exponential('beta', 0.001)\n",
    "\n",
    "    theta = Beta('theta', alpha=alpha, beta=beta, shape=71)\n",
    "\n",
    "    # Data likelihood\n",
    "    y_like = Binomial('y_like', n=d.N, p=theta, observed=d.y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Only 100 samples in chain.\n",
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [theta, beta, alpha]\n",
      "Sampling 2 chains, 0 divergences: 100%|██████████| 400/400 [00:02<00:00, 163.90draws/s]\n",
      "The acceptance probability does not match the target. It is 0.9347562092830946, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "The acceptance probability does not match the target. It is 0.966063674632247, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "The rhat statistic is larger than 1.4 for some parameters. The sampler did not converge.\n",
      "The number of effective samples is smaller than 10% for some parameters.\n"
     ]
    }
   ],
   "source": [
    "random.seed(100)\n",
    "with model1:\n",
    "    trace1 = sample(100, tune=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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>hpd_3%</th>\n",
       "      <th>hpd_97%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_mean</th>\n",
       "      <th>ess_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>alpha</th>\n",
       "      <td>45.039</td>\n",
       "      <td>47.525</td>\n",
       "      <td>1.461</td>\n",
       "      <td>121.111</td>\n",
       "      <td>29.701</td>\n",
       "      <td>24.006</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>61.0</td>\n",
       "      <td>1.92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta</th>\n",
       "      <td>256.301</td>\n",
       "      <td>267.787</td>\n",
       "      <td>8.570</td>\n",
       "      <td>710.858</td>\n",
       "      <td>168.620</td>\n",
       "      <td>136.621</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>66.0</td>\n",
       "      <td>1.92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>theta[0]</th>\n",
       "      <td>0.109</td>\n",
       "      <td>0.047</td>\n",
       "      <td>0.015</td>\n",
       "      <td>0.173</td>\n",
       "      <td>0.025</td>\n",
       "      <td>0.020</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>58.0</td>\n",
       "      <td>1.57</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>theta[1]</th>\n",
       "      <td>0.106</td>\n",
       "      <td>0.048</td>\n",
       "      <td>0.022</td>\n",
       "      <td>0.170</td>\n",
       "      <td>0.025</td>\n",
       "      <td>0.019</td>\n",
       "      <td>4.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>113.0</td>\n",
       "      <td>1.37</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>theta[2]</th>\n",
       "      <td>0.108</td>\n",
       "      <td>0.045</td>\n",
       "      <td>0.022</td>\n",
       "      <td>0.171</td>\n",
       "      <td>0.025</td>\n",
       "      <td>0.019</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>60.0</td>\n",
       "      <td>1.54</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>theta[66]</th>\n",
       "      <td>0.211</td>\n",
       "      <td>0.060</td>\n",
       "      <td>0.138</td>\n",
       "      <td>0.337</td>\n",
       "      <td>0.034</td>\n",
       "      <td>0.027</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>79.0</td>\n",
       "      <td>1.66</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>theta[67]</th>\n",
       "      <td>0.216</td>\n",
       "      <td>0.067</td>\n",
       "      <td>0.124</td>\n",
       "      <td>0.332</td>\n",
       "      <td>0.038</td>\n",
       "      <td>0.030</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>87.0</td>\n",
       "      <td>1.70</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>theta[68]</th>\n",
       "      <td>0.214</td>\n",
       "      <td>0.065</td>\n",
       "      <td>0.138</td>\n",
       "      <td>0.345</td>\n",
       "      <td>0.035</td>\n",
       "      <td>0.028</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>150.0</td>\n",
       "      <td>1.61</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>theta[69]</th>\n",
       "      <td>0.213</td>\n",
       "      <td>0.072</td>\n",
       "      <td>0.125</td>\n",
       "      <td>0.348</td>\n",
       "      <td>0.039</td>\n",
       "      <td>0.030</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>95.0</td>\n",
       "      <td>1.71</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>theta[70]</th>\n",
       "      <td>0.175</td>\n",
       "      <td>0.052</td>\n",
       "      <td>0.111</td>\n",
       "      <td>0.305</td>\n",
       "      <td>0.017</td>\n",
       "      <td>0.012</td>\n",
       "      <td>9.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>106.0</td>\n",
       "      <td>1.26</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>73 rows × 11 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "              mean       sd  hpd_3%  hpd_97%  mcse_mean  mcse_sd  ess_mean  \\\n",
       "alpha       45.039   47.525   1.461  121.111     29.701   24.006       3.0   \n",
       "beta       256.301  267.787   8.570  710.858    168.620  136.621       3.0   \n",
       "theta[0]     0.109    0.047   0.015    0.173      0.025    0.020       3.0   \n",
       "theta[1]     0.106    0.048   0.022    0.170      0.025    0.019       4.0   \n",
       "theta[2]     0.108    0.045   0.022    0.171      0.025    0.019       3.0   \n",
       "...            ...      ...     ...      ...        ...      ...       ...   \n",
       "theta[66]    0.211    0.060   0.138    0.337      0.034    0.027       3.0   \n",
       "theta[67]    0.216    0.067   0.124    0.332      0.038    0.030       3.0   \n",
       "theta[68]    0.214    0.065   0.138    0.345      0.035    0.028       3.0   \n",
       "theta[69]    0.213    0.072   0.125    0.348      0.039    0.030       3.0   \n",
       "theta[70]    0.175    0.052   0.111    0.305      0.017    0.012       9.0   \n",
       "\n",
       "           ess_sd  ess_bulk  ess_tail  r_hat  \n",
       "alpha         3.0       3.0      61.0   1.92  \n",
       "beta          3.0       3.0      66.0   1.92  \n",
       "theta[0]      3.0       4.0      58.0   1.57  \n",
       "theta[1]      4.0       5.0     113.0   1.37  \n",
       "theta[2]      3.0       4.0      60.0   1.54  \n",
       "...           ...       ...       ...    ...  \n",
       "theta[66]     3.0       3.0      79.0   1.66  \n",
       "theta[67]     3.0       3.0      87.0   1.70  \n",
       "theta[68]     3.0       4.0     150.0   1.61  \n",
       "theta[69]     3.0       3.0      95.0   1.71  \n",
       "theta[70]     9.0      15.0     106.0   1.26  \n",
       "\n",
       "[73 rows x 11 columns]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary(trace1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([<matplotlib.axes._subplots.AxesSubplot object at 0x11a112a20>],\n",
       "      dtype=object)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_posterior(trace1['alpha'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([<matplotlib.axes._subplots.AxesSubplot object at 0x11a221eb8>],\n",
       "      dtype=object)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_posterior(trace1['beta'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYUAAAEGCAYAAACKB4k+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAfBElEQVR4nO3dfZBc1Xnn8e+jVgM9OGaEEURqCUveUsQia5HwFC/WliuGOCK8aVY2RpTZlTds8ceywXgdJaOYMnjXilRRYkhtrZ1icbzaQPFiIINiHMssIrUVOUBGDFgWQkG2sKSRAuO1BrvQrBhJz/7Rt5uennu7b2u6+97u/n2qVNN9+96eh2HmPn3Oec455u6IiIgAzEg6ABERSQ8lBRERKVFSEBGREiUFEREpUVIQEZGSmUkHMB3nnXeeL1iwIOkwRETays6dO3/u7rPDXmvrpLBgwQKGhoaSDkNEpK2Y2c+iXlP3kYiIlCgpiIhIiZKCiIiUKCmIiEiJkoKIiJS0dfWRiEi3GRweYfO2vRweG2dub451KxfTvzzfsPdXUhARaRODwyOsf2oX4xMnARgZG2f9U7sAGpYY1H0kItImNm/bW0oIReMTJ9m8bW/DvoeSgohImzg8Nl7X8dOhpCAi0ibm9ubqOn46lBRERNrEupWLyWUzk47lshnWrVzcsO+hgWYRkRSrrDb69MfyPP/6qKqPRES6TVi10ZM7R9i4emlDE0E5dR+JiKRUK6qNKikpiIikVCuqjSopKYiIpFQrqo0qKSmIiKRUK6qNKmmgWUQkpYqDyc1c66iSkoKISIr1L883NQlUUveRiIiUKCmIiEiJkoKIiJQ0NSmY2RfNbLeZ/djMHjGzs8zsXDN71szeCL7OKjt/vZntM7O9ZraymbGJiJyOweERVmzazsKBZ1ixaTuDwyNJh9RQTUsKZpYH7gT63P2jQAZYAwwAz7n7IuC54DlmdnHw+hLgGuAbZpYJe28RkSQUl50YGRvHeX+Tm05KDM3uPpoJ5MxsJtADHAZWAVuC17cA/cHjVcCj7n7c3fcD+4DLmhyfiEhsSSw70WpNSwruPgL8KXAAOAK84+4/AC5w9yPBOUeA84NL8sDBsrc4FBwTEUmFJJadaLVmdh/NovDpfyEwFzjbzG6tdknIMQ9539vNbMjMhkZHRxsTrIhIDEksO9Fqzew++i1gv7uPuvsE8BTwceAtM5sDEHx9Ozj/EDC/7Pp5FLqbJnH3B9y9z937Zs+e3cTwRUQmS2LZiVZrZlI4AFxhZj1mZsDVwB5gK7A2OGct8HTweCuwxszONLOFwCLgpSbGJyJSl/7leTauXkq+N4cB+d5cU/c2SELTlrlw9xfN7AngZeAEMAw8AHwAeNzMbqOQOG4Kzt9tZo8DrwXn3+HuJ0PfXEQkIa1edqLVzH1Kt33b6Ovr86GhoaTDEBFpK2a20937wl7TjGYRESlRUhARkRItnS0iUsPg8EhL9zRIkpKCiEgVxaUtijOZi0tbAB2ZGNR9JCJSRTcsbVFOSUFEpIpuWNqinJKCiEgVvT3Zuo63OyUFEZEqoqZytfEUr6qUFEREqnhnfKKu4+1OSUFEpIpuWBm1nEpSRaTtNGveQNj7rlu5eFJJKnTeyqjltPaRiLSVuwd38dALByYdy84wNt90SWRiiJNEKucjQOHmv3H1UoCOmrxWbe0jJQURaRuDwyPc9dgroa/15rK8cs9vh15TebM3Cjt4zerJ4l4YH5hhxsmQ+2G+N8eOgasa9Z+QCtWSgrqPRKRtVJswNhYx8Bs2+ax46z967P1rwhICdO58hCgaaBaRtnE6N+jp3tQ7dUA5ipKCiLSNajfoWRGTyaZzU+/kAeUo6j4SkcTFrSZat3Ix6554lYmTk7t6Zhjcc8OS0Pf65EWzeXLnyJQupCgZM065d8SA8ulQUhCRRNWzCmnx+Vf/ZndpPKA3l+XeG5fQvzwf+l5P7hzh0x/L8/zro4yMjZcGmcMUq426LRGUU/eRiCSqkauQRr3X86+PsmPgKt7cdB333byMfG8Oo9Dl1JvLYhSqjLo9IYBaCiKSsHpWIR0cHpnSfTQ2PsG677wa+736l+e7/sZfjVoKIpKoepaR2Lxt75TxBICJU87mbXu7bkmKZlBSEJGWGxweYcWm7SwceIZ3j58gm7FJr0dV/VQrLz08Ns66lYvJZTOx3kvCKSmISEsVB4NHxsZxgklnXujfr9W3X+0T/wwzvvjYK5yVnaFxgmnQmIKItFTYYPDEKafnjJkMf2XqMhXlokpS4f0ZyUePTZDLZrjv5mVKBqdBLQURaanpbG/ZvzzP5s9cMmmimoWc18l7KDebWgoi0lJze3OMhCSAuIPBldVDCweeCT2v29YsahQlBRFpuvJZxr09WbIzjIlT73cBTWcweLpJRiZT95GINFXlwPLRYxNgNGwwWBVHjaWWgog0VejA8klnbHyCfAPWFype20mb4CRJm+yISFMtHHgmcq2holk9We65YYlu5C1SbZMddR+JSFPF6ds/emyC9U/tYnB4pAURSTXqPhKRhqgcTC5ucxk2sBymWEaq1kKylBREZNoql6wu3+by6LEJshmjN5eN3DKzSGWkyVP3kYhMW9hgcrmJk87ZZ87k/puXTakUKqcy0uSppSAikeLuiBbnE/7hsfHStfdu3T2l1aAy0nRQUhCRKQaHRybtbgbVd0SLmkBWeU7x2uIuaSojTR+VpIrIJJXjA5XyvTl2DFw15ZqoheqA0haYjZiXINOXWEmqmfWa2RNm9rqZ7TGzK83sXDN71szeCL7OKjt/vZntM7O9ZraymbGJSLha4wORXUURny/L90QutjZUeppezR5o/nPg++5+EXAJsAcYAJ5z90XAc8FzzOxiYA2wBLgG+IaZRY9IiUhT1BofiNwRLaTk1GxqrtAKpunWtKRgZh8EPgF8C8Dd33P3MWAVsCU4bQvQHzxeBTzq7sfdfT+wD7isWfGJSLhqFUDZGVbXjmhRvdMqPU2vZrYUPgKMAt82s2Eze9DMzgYucPcjAMHX84Pz88DBsusPBccmMbPbzWzIzIZGR0ebGL5Id/rkRbMjX/vAWTPr3hEtjEpP06uZSWEmcCnwTXdfDrxL0FUUIWyvjCmfM9z9AXfvc/e+2bOjf3lFJL7yPZMffuFA5Hljx8Inn9VTSqrS03RrZknqIeCQu78YPH+CQlJ4y8zmuPsRM5sDvF12/vyy6+cBh5sYn0jXKi8HPSeX5d33TkRWDpU7J5eteU4t2jM53ZrWUnD3fwYOmlnxI8HVwGvAVmBtcGwt8HTweCuwxszONLOFwCLgpWbFJ9KtKvc3GBufiJUQAN5970Ro5VDcgeN8by4yIZS3VlZs2q4KpYQ0e/La7wEPm9kZwE+Bf08hET1uZrcBB4CbANx9t5k9TiFxnADucPfoujgROS21Sk6rmTjpoYvWxRk4rtZtVDk3otpEOWmupiYFd38FCJsgcXXE+RuADc2MSaRbRM0Ynm7lT9j1tWY0Z8yqdhuFJSqtmpoMLYgn0oEqu4jKJ41Nt/In7PqwLTGLctkMf/bZS6re3KMSlUpXW09JQaQDVfvkvW7l4tBSv6LeXJZZPYUB5crzorqA+pfn2bh6KfkgYWSscGXc/ZejEpVKV1tPC+KJdKBqn7z7l+cZ+tkvePiFA5NqvnPZzJQbeD2L1hUXuqtUHECu9h7rVi6est6SSleToaQg0oGi+viLn7y/1r+Uvg+fW/OGH3WjjyvuAHLxsVZNTZ5WSRXpQFErnc7qyXLPDUtadrNdsWl7aHIKW2lVWiexVVJFJBnFPv7eislmR49NtHSVUg0gtx8lBZEOEDbxq395nrPPnNpD3MpVSjWA3H6UFETaXLXy06Q/qYeVqmoAOd000CzShsqrgmaYcbJibLDYGqg14NxsGkBuP0oKIm2mchC5MiEUHR4b576blyVe6jndCiZpLSUFkTZQq2UQ5pxcVp/UpW5KCiIpF7dlUKm4oqk+qUs9NNAsknKnu6ppcUVTkXooKYik2ODwSNXVR2vRfACpl7qPRFKq2G1US3HxuqMhW2XGqTKqZ30j6XxKCiIpFbfb6OixCXqyM8hmbNIOanGqjLS5jVRSUhBJqXq6fo5NnCI7w5jVk2Xs2ETNT/zF1kFY15Q2t+luSgoiKVVrN7NKE6ecnjNmMvyV3656XtRieeU0FtG9NNAsklLVdjOLEudmHqdbSmsTdS+1FERSqnzi2cjYOAbUmqEQ52ZeK3FobaLupqQgkqCwyh+YOgM5qv+/XNybebVuqbyqj7qeNtkRScjg8AjrvvMqE6eq/w3mspmq3T0GdZWSho0phG3FKZ2r2iY7sVsKZnYdsAQ4q3jM3f/L9MMT6U73bt1dMyFAoRooE7HekQH33bysrpu51kOSamIlBTP7C6AH+CTwIPAZ4KUmxiXStuJOBhsbnzrZLMpJ99AxBYfTKh/VekgSJW710cfd/d8BR939q8CVwPzmhSXSnqpteDMd+d5c5CDzdJbBEKkUNykUf+uOmdlcYAJY2JyQRNpXWLln1PaXxeUpasllM3zyotmRr2fM6gtSpIq4YwrfNbNeYDPwMoVW64NNi0qkTdXa/rK8a+mcXLyksHH10qqrncZdSlskjrgthT9x9zF3fxL4MHAR8LXmhSXSnqptVF/ZtRR3TKF/eb7q3IK8JppJA8VtKfwDcCmAux8HjpvZy8VjIt2qclB5wYdyHA5u+kXF+QOnsy9Cb9CaiJpbYKCJZtJQVZOCmf06kAdyZracwu8gwAcpVCOJdK2wFUYrb9wGXHrhObEmn1XKzjDuvXEJULjxV84tMOBzV1yoKiJpqFothZXA54F5wNfLjv8S+KMmxSSSatVWGK3kwA9/8ouay1NUmtWT5Z4blpRu+JpbIK0Sa0azmX06GE9IFc1ollaLs8LodPTmstx74xLd7KWpqs1ojjvQvMPMvmVmfxu84cVmdlvDIhRpE6e7X3JcZ585UwlBEhU3KXwb2AbMDZ7/E3BXUyISSbF69xmodwaB9jGQpMVNCue5++PAKQB3PwE07+OSSErVs89AvjfH5664cMqeCLlsJnLimvYxkKTFTQrvmtmHCJZeMbMrgHeaFpVISsXd+KY3l2XHwFV8rX8pG1cvJd+bwygkio2rl3LPDUtCk4XKSyVpcecp/GdgK/ARM9sBzKawKJ5IV6msAooq0yifmFZt8TlVE0naxE0KrwF/DRwDfgUMUhhXqMnMMsAQMOLu15vZucBjwALgTeCz7n40OHc9cBuFrqk73X1b7P8SkRYpv8kvGHimIe8jkhZxu4/+F4WlLf4Y+G/AIuCvYl77BWBP2fMB4Dl3XwQ8FzzHzC4G1lDYs+Ea4BtBQhFJraixgVk9WQaHR1ixaTsLB55hxabt014pVaQV4iaFxe7+H9z9+eDf7cBv1LrIzOYB1zF58bxVwJbg8Ragv+z4o+5+3N33A/uAy2LGJ9Jyg8MjHI8oT714zq81ZQltkWaLmxSGg8FlAMzscmBHjOvuB/6AoGopcIG7HwEIvp4fHM8DB8vOOxQcm8TMbjezITMbGh0djRm+SGMVJ7EdmzgV+voLPz0aewltkTSpmhTMbJeZ/Qi4HPihmb1pZvspLJD3iRrXXg+87e47Y8YSVtI9ZRzP3R9w9z5375s9O3qNeZFmqjWJLWo5a81DkLSrNdB8/TTeewVwo5ldS2Ff5w+a2UPAW2Y2x92PmNkc4O3g/ENM3s1tHnB4Gt9fJFLcLTOj1Lq5R+2prHkIknZVWwru/rNq/2pcu97d57n7AgoDyNvd/VYKpa1rg9PWAk8Hj7cCa8zsTDNbSGEwW/tAS8M1YsvMajf3XDbDLZfP1zwEaUtxxxQaaRPwKTN7A/hU8Bx33w08TqH89fvAHe6uWdPScPVsmRklahJbby7LxtVLIyetqQRV0i7uPIVpcfe/A/4uePx/gasjztsAbGhFTNIdwrqJam2ZGUecpaw1D0HaUUuSgkgSwjbBWf/ULs7JZUO3wqy3v183felESXQfibREVDeRGVO6frIZ493jJzTRTLqekoJ0rKjuoLFjE5P6+2f1ZMEL6xVpopl0OyUF6VhR3UFze3P0L8+zY+Aq9m+6jp4zZjJxanL5qCaaSbdSUpCOFVYhFFYW2oiBZ5FOoaQgHat/eT5WWWi1FoVIt1H1kSRmurOK44hTIbRu5eJJVUqgiWbSvZQUJBFR5aJFrdx8Js6cA5FuYR6xcFc76Ovr86GhoaTDkNOwYtN2RkL67HtzWY6fODXlU7tmA4s0jpntdPe+sNc0piCJiCwXHZ/QktMiCVL3kSRibm8utKUQ5fDYeEvGIES6nVoKkoioctGo7S17e7LayUykBZQUJBFR5aL33LAkNFm4o24lkRZQ95Ekplq5aGU30RcfeyX0PE0wE2ksJQVJnbBksXnb3tAxCE0wE2ksdR9JW4i7ZIWITI9aCtJQ5RVCvT1Z3OGd8YlpVwtpgplIaygpSMNUzlI+euz9jWzKZyxPJzEoCYg0l7qPpGHCNrUpp2ohkfRTUpCGiVMJpGohkXRTUpCGiVMJpGohkXRTUpCGCasQKqdqIZH000Cz1KXa+kOVFUKNrD4SkdZQUpDYqu2BUJ4YdOMXaV/qPpLYwqqLVFEk0lmUFCS2qMqhepbAFpF0U1KQ2KIqhwy0hLVIh1BSkNjWrVyMhRx3UBeSSIfQQLPUVF5xFLWjtyaliXQGJQWpqrLiKIompYl0BiWFLlRtrkHla+8eP1EzIWhSmkjnMPeoDoH06+vr86GhoaTDaCthn/yzGePsM2YyNj6BQWQXUSUDTUoTaUNmttPd+8JeU0uhy4TNNZg46YyNF5a5jpsQ8r05dgxc1eDoRCRpqj7qMo2YU6DuIpHOpZZCFxkcHqmre6hoVk+WnjNmasczkS6gpNBFNm/bW3dCyGUz3HPDEiUBkS7RtO4jM5tvZs+b2R4z221mXwiOn2tmz5rZG8HXWWXXrDezfWa218xWNiu2bhV3LkFxglq+N8fG1UuVEES6SDNbCieAL7n7y2b2a8BOM3sW+DzwnLtvMrMBYAD4QzO7GFgDLAHmAv/bzH7D3avXQ0psc3tzNccUDLjv5mVKBCJdqmktBXc/4u4vB49/BewB8sAqYEtw2hagP3i8CnjU3Y+7+35gH3BZs+LrRrU2wcnOMCUEkS7XkuojM1sALAdeBC5w9yNQSBzA+cFpeeBg2WWHgmOV73W7mQ2Z2dDo6Ggzw+44/cvzbFy9lHxvDqMwgNyby2IUuoo233SJEoJIl2v6QLOZfQB4ErjL3X9pFrakWuHUkGNTxkXd/QHgAShMXmtUnN1Cm+CISDVNbSmYWZZCQnjY3Z8KDr9lZnOC1+cAbwfHDwHzyy6fBxxuZnwiIjJZM6uPDPgWsMfdv1720lZgbfB4LfB02fE1ZnammS0EFgEvNSs+ERGZqpndRyuAfwvsMrNXgmN/BGwCHjez24ADwE0A7r7bzB4HXqNQuXSHKo9ERFqraUnB3f+e8HECgKsjrtkAbGhWTJ3m7sFdPPLiQU66kzHjlsvn87X+pUmHJSJtTDOa29Tdg7t46IUDpecn3UvPlRhE5HRpQbw29ciLB+s6LiISh5JCmzoZsQ9G1HERkTiUFNpUJmK+R9RxEZE4lBTa1C2Xz6/ruIhIHBpoTqniXskjY+NkzDjpTr5sL4PiYLKqj0SkkbRHcwqF7aNclMtmtJy1iExLtT2a1X2UQmH7KBeNT5xk87a9LY5IRLqFkkIK1doMJ+5mOSIi9dKYQkoUxxAOj40zIxhDiDK3N9fCyESkmygppEDlGEK1hJDLZli3cnGrQhORLqOkkLDB4RG+9PiroYmgWHUUVn0kItIMSgoJKrYQoloGp9x5c9N1LY5KRLqZBpoTVK3KCDR2ICKtp6SQoGpVRBo7EJEkKCkkKKolkDHTBDURSYSSQoLWrVxMLpuZdCyXzfBnn71ECUFEEqGB5gQVb/zF+QlzVV0kIglTUkhY//K8koCIpIa6j0REpERJQURESpQURESkRElBRERKlBRERKRESUFEREpUklqHweERvvo3uzl6bAKA3lyWe29copJSEekYSgoxDQ6PsO6JV5k4+f6KpmPjE6z7zqsASgwi0hGUFGoYHB7h3q27GRufCH194pSzedteJQUR6QhKClXcPbiLh144UPM87ZksIp1CA80RBodHeDhGQgDteyAinUMthQp3D+7i4RcOEL1L8mTZGaZ9D0SkYygpBBYMPFP3Nao+EpFO09VJYXB4hLsee6Xu67IZY/NntOeBiHSerk0Kn/sf/8COn/yi7uvOPiPDhn+jXdFEpDN1ZVK46Mvf4/+djDtqUJAx045oItLxuq766PINz9adEAAlBBHpCl2XFN761Xt1X3PrFRcqIYhIV0hdUjCza8xsr5ntM7OBJGPJzoD7b17G1/qXJhmGiEjLpGpMwcwywH8HPgUcAv7RzLa6+2utjuX+m5epdSAiXSdtLYXLgH3u/lN3fw94FFjV6iCUEESkW6WqpQDkgYNlzw8Bl5efYGa3A7cDXHjhhXV/g7MyFjnQbMD+TdfV/Z4iIp0ibS0FCzk26Q7u7g+4e5+7982ePbvub/D6hms5KzP129x/8zIlBBHpemlrKRwC5pc9nwccbvQ3eX3DtY1+SxGRjpC2lsI/AovMbKGZnQGsAbYmHJOISNdIVUvB3U+Y2X8CtgEZ4C/dfXfCYYmIdI1UJQUAd/8e8L2k4xAR6UZp6z4SEZEEKSmIiEiJude/OFxamNko8LM6LzsP+HkTwmkUxTd9aY8x7fFB+mNMe3yQ7hg/7O6hNf1tnRROh5kNuXtf0nFEUXzTl/YY0x4fpD/GtMcH7RFjGHUfiYhIiZKCiIiUdGNSeCDpAGpQfNOX9hjTHh+kP8a0xwftEeMUXTemICIi0bqxpSAiIhGUFEREpKRrkkKatvkM4plvZs+b2R4z221mXwiOn2tmz5rZG8HXWSmINWNmw2b23bTFaGa9ZvaEmb0e/CyvTFN8QYxfDP4f/9jMHjGzs5KM0cz+0szeNrMflx2LjMfM1gd/N3vNbGWCMW4O/j//yMz+2sx6k4oxLL6y137fzNzMzksqvunoiqRQts3n7wAXA7eY2cXJRsUJ4Evu/i+BK4A7gpgGgOfcfRHwXPA8aV8A9pQ9T1OMfw58390vAi6hEGdq4jOzPHAn0OfuH6Ww0OOahGP8n8A1FcdC4wl+J9cAS4JrvhH8PSUR47PAR939XwH/BKxPMMaw+DCz+RS2Ez5Qdiypn+Fp6YqkQEq2+Szn7kfc/eXg8a8o3MzyQVxbgtO2AP3JRFhgZvOA64AHyw6nIkYz+yDwCeBbAO7+nruPpSW+MjOBnJnNBHoo7BGSWIzu/n+AX1QcjopnFfCoux939/3APgp/Ty2P0d1/4O4ngqcvUNhvJZEYI36GAPcBf8DkzcES+Rmerm5JCmHbfKZmE2YzWwAsB14ELnD3I1BIHMD5yUUGwP0UfslPlR1LS4wfAUaBbwfdWw+a2dkpig93HwH+lMInxyPAO+7+gzTFGIiKJ61/O78L/G3wOBUxmtmNwIi7v1rxUirii6tbkkLNbT6TYmYfAJ4E7nL3XyYdTzkzux542913Jh1LhJnApcA33X058C7p6G4rCfrmVwELgbnA2WZ2a7JR1SV1fztm9mUK3a8PFw+FnNbSGM2sB/gy8JWwl0OOpeL+E6ZbkkJLtvmsl5llKSSEh939qeDwW2Y2J3h9DvB2UvEBK4AbzexNCl1uV5nZQ6QnxkPAIXd/MXj+BIUkkZb4AH4L2O/uo+4+ATwFfDxlMVIlnlT97ZjZWuB64HP+/iSrNMT4Lygk/leDv5d5wMtm9uspiS+2bkkKqdvm08yMQl/4Hnf/etlLW4G1weO1wNOtjq3I3de7+zx3X0DhZ7bd3W8lJTG6+z8DB81scXDoauA1UhJf4ABwhZn1BP/Pr6YwfpSmGCE6nq3AGjM708wWAouAlxKIDzO7BvhD4EZ3P1b2UuIxuvsudz/f3RcEfy+HgEuD39HE46uLu3fFP+BaChULPwG+nIJ4/jWFJuSPgFeCf9cCH6JQ/fFG8PXcpGMN4v1N4LvB49TECCwDhoKf4yAwK03xBTF+FXgd+DHwV8CZScYIPEJhfGOCws3rtmrxUOgW+QmwF/idBGPcR6Fvvvj38hdJxRgWX8XrbwLnJfkzPN1/WuZCRERKuqX7SEREYlBSEBGREiUFEREpUVIQEZESJQURESlRUhA5TWb2ZvlKmKd7jkiaKCmIiEiJkoJIDGY2aGY7g30Rbq94bUGwzv+WYK3/J4K1cIp+z8xeNrNdZnZRcM1lZvbDYCG/H5bNyhZJlJKCSDy/6+4fA/qAO83sQxWvLwYe8MJa/78E/mPZaz9390uBbwK/Hxx7HfiEFxby+wrwx02NXiQmJQWReO40s1cprOM/n8L6NeUOuvuO4PFDFJYxKSoudrgTWBA8Pgf4TrBz130UNmARSZySgkgNZvabFFY7vdLdLwGGgbMqTqtcL6b8+fHg60kKy30D/FfgeS/sxnZDyPuJJEJJQaS2c4Cj7n4sGBO4IuScC83syuDxLcDfx3jPkeDx5xsSpUgDKCmI1PZ9YKaZ/YjCJ/wXQs7ZA6wNzjmXwvhBNX8CbDSzHRT2bRZJBa2SKjJNwXaq3w26gkTamloKIiJSopaCiIiUqKUgIiIlSgoiIlKipCAiIiVKCiIiUqKkICIiJf8frycQ0JB0qtEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "alpha = trace1.get_values(varname='alpha')\n",
    "beta = trace1.get_values(varname='beta')\n",
    "plt.scatter(alpha, beta)\n",
    "plt.xlabel('alpha')\n",
    "plt.ylabel('beta')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(np.log(alpha/beta), np.log(alpha+beta))\n",
    "plt.xlabel('log(alpha/beta)')\n",
    "plt.ylabel('log(alpha+beta)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Try another prior"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "with Model() as model2:\n",
    "\n",
    "    phi1 = Uniform('phi1', lower=0, upper=1)\n",
    "    phi2 = Uniform('phi2', lower=0, upper=1000)\n",
    "\n",
    "    alpha = Deterministic('alpha', phi1 / (phi2**2))\n",
    "    beta = Deterministic('beta', (1-phi1) / phi2**2)\n",
    "\n",
    "    theta = Beta('theta', alpha=alpha, beta=beta, shape=71)\n",
    "\n",
    "    # Data likelihood\n",
    "    y_like = Binomial('y_like', n=d.N, p=theta, observed=d.y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Only 100 samples in chain.\n",
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [theta, phi2, phi1]\n",
      "Sampling 2 chains, 0 divergences: 100%|██████████| 400/400 [00:05<00:00, 72.73draws/s]\n",
      "The acceptance probability does not match the target. It is 0.9425353776422641, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "The acceptance probability does not match the target. It is 0.9515178810489138, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "The rhat statistic is larger than 1.05 for some parameters. This indicates slight problems during sampling.\n"
     ]
    }
   ],
   "source": [
    "random.seed(100)\n",
    "with model2:\n",
    "    trace2 = sample(100, tune=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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>hpd_3%</th>\n",
       "      <th>hpd_97%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_mean</th>\n",
       "      <th>ess_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>phi1</th>\n",
       "      <td>0.144</td>\n",
       "      <td>0.014</td>\n",
       "      <td>0.121</td>\n",
       "      <td>0.172</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>209.0</td>\n",
       "      <td>209.0</td>\n",
       "      <td>208.0</td>\n",
       "      <td>180.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>phi2</th>\n",
       "      <td>0.260</td>\n",
       "      <td>0.042</td>\n",
       "      <td>0.179</td>\n",
       "      <td>0.329</td>\n",
       "      <td>0.006</td>\n",
       "      <td>0.004</td>\n",
       "      <td>53.0</td>\n",
       "      <td>53.0</td>\n",
       "      <td>53.0</td>\n",
       "      <td>150.0</td>\n",
       "      <td>1.05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha</th>\n",
       "      <td>2.301</td>\n",
       "      <td>0.791</td>\n",
       "      <td>1.120</td>\n",
       "      <td>3.768</td>\n",
       "      <td>0.112</td>\n",
       "      <td>0.080</td>\n",
       "      <td>50.0</td>\n",
       "      <td>50.0</td>\n",
       "      <td>46.0</td>\n",
       "      <td>134.0</td>\n",
       "      <td>1.07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta</th>\n",
       "      <td>13.699</td>\n",
       "      <td>4.728</td>\n",
       "      <td>6.619</td>\n",
       "      <td>23.070</td>\n",
       "      <td>0.628</td>\n",
       "      <td>0.446</td>\n",
       "      <td>57.0</td>\n",
       "      <td>57.0</td>\n",
       "      <td>55.0</td>\n",
       "      <td>150.0</td>\n",
       "      <td>1.05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>theta[0]</th>\n",
       "      <td>0.058</td>\n",
       "      <td>0.044</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.143</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.002</td>\n",
       "      <td>193.0</td>\n",
       "      <td>193.0</td>\n",
       "      <td>147.0</td>\n",
       "      <td>127.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>theta[66]</th>\n",
       "      <td>0.272</td>\n",
       "      <td>0.055</td>\n",
       "      <td>0.177</td>\n",
       "      <td>0.378</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.003</td>\n",
       "      <td>170.0</td>\n",
       "      <td>123.0</td>\n",
       "      <td>187.0</td>\n",
       "      <td>55.0</td>\n",
       "      <td>1.04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>theta[67]</th>\n",
       "      <td>0.274</td>\n",
       "      <td>0.052</td>\n",
       "      <td>0.182</td>\n",
       "      <td>0.364</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>460.0</td>\n",
       "      <td>460.0</td>\n",
       "      <td>460.0</td>\n",
       "      <td>186.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>theta[68]</th>\n",
       "      <td>0.283</td>\n",
       "      <td>0.059</td>\n",
       "      <td>0.170</td>\n",
       "      <td>0.387</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.002</td>\n",
       "      <td>460.0</td>\n",
       "      <td>449.0</td>\n",
       "      <td>460.0</td>\n",
       "      <td>173.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>theta[69]</th>\n",
       "      <td>0.285</td>\n",
       "      <td>0.066</td>\n",
       "      <td>0.163</td>\n",
       "      <td>0.408</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.003</td>\n",
       "      <td>258.0</td>\n",
       "      <td>227.0</td>\n",
       "      <td>258.0</td>\n",
       "      <td>98.0</td>\n",
       "      <td>1.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>theta[70]</th>\n",
       "      <td>0.211</td>\n",
       "      <td>0.075</td>\n",
       "      <td>0.063</td>\n",
       "      <td>0.356</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.003</td>\n",
       "      <td>354.0</td>\n",
       "      <td>336.0</td>\n",
       "      <td>384.0</td>\n",
       "      <td>160.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>75 rows × 11 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             mean     sd  hpd_3%  hpd_97%  mcse_mean  mcse_sd  ess_mean  \\\n",
       "phi1        0.144  0.014   0.121    0.172      0.001    0.001     209.0   \n",
       "phi2        0.260  0.042   0.179    0.329      0.006    0.004      53.0   \n",
       "alpha       2.301  0.791   1.120    3.768      0.112    0.080      50.0   \n",
       "beta       13.699  4.728   6.619   23.070      0.628    0.446      57.0   \n",
       "theta[0]    0.058  0.044   0.004    0.143      0.003    0.002     193.0   \n",
       "...           ...    ...     ...      ...        ...      ...       ...   \n",
       "theta[66]   0.272  0.055   0.177    0.378      0.004    0.003     170.0   \n",
       "theta[67]   0.274  0.052   0.182    0.364      0.002    0.002     460.0   \n",
       "theta[68]   0.283  0.059   0.170    0.387      0.003    0.002     460.0   \n",
       "theta[69]   0.285  0.066   0.163    0.408      0.004    0.003     258.0   \n",
       "theta[70]   0.211  0.075   0.063    0.356      0.004    0.003     354.0   \n",
       "\n",
       "           ess_sd  ess_bulk  ess_tail  r_hat  \n",
       "phi1        209.0     208.0     180.0   1.01  \n",
       "phi2         53.0      53.0     150.0   1.05  \n",
       "alpha        50.0      46.0     134.0   1.07  \n",
       "beta         57.0      55.0     150.0   1.05  \n",
       "theta[0]    193.0     147.0     127.0   1.00  \n",
       "...           ...       ...       ...    ...  \n",
       "theta[66]   123.0     187.0      55.0   1.04  \n",
       "theta[67]   460.0     460.0     186.0   1.00  \n",
       "theta[68]   449.0     460.0     173.0   1.00  \n",
       "theta[69]   227.0     258.0      98.0   1.03  \n",
       "theta[70]   336.0     384.0     160.0   1.00  \n",
       "\n",
       "[75 rows x 11 columns]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary(trace2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([<matplotlib.axes._subplots.AxesSubplot object at 0x1277a2f28>],\n",
       "      dtype=object)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_posterior(trace2['alpha'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([<matplotlib.axes._subplots.AxesSubplot object at 0x1277c6f60>],\n",
       "      dtype=object)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_posterior(trace2['beta'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "alpha2 = trace2.get_values(varname='alpha')\n",
    "beta2 = trace2.get_values(varname='beta')\n",
    "plt.scatter(np.log(alpha2/beta2), np.log(alpha2+beta2))\n",
    "plt.xlabel('log(alpha/beta)')\n",
    "plt.ylabel('log(alpha+beta)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}