12_monsters_and_mixtures-2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/ksachdeva/rethinking-tensorflow-probability/blob/master/notebooks/12_monsters_and_mixtures.ipynb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 12. Monsters and Mixtures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import arviz as az\n",
    "import pandas as pd\n",
    "import xarray as xr\n",
    "import matplotlib.pyplot as plt\n",
    "from collections import namedtuple\n",
    "import statsmodels.formula.api as smf\n",
    "\n",
    "import random\n",
    "import jax\n",
    "import jax.numpy as jnp\n",
    "\n",
    "import tensorflow as tf\n",
    "from tensorflow_probability.substrates import jax as tfp\n",
    "tfd = tfp.distributions\n",
    "tfb = tfp.bijectors\n",
    "# to use 'sample_distributions'\n",
    "import tensorflow_probability as xtfp\n",
    "xtfd = xtfp.distributions\n",
    "xtfb = xtfp.bijectors\n",
    "\n",
    "key = tfp.util.SeedStream(1448, salt=\"ch-12\")\n",
    "plt.rcParams['figure.figsize'] = [6, 5]\n",
    "\n",
    "# TFP often requires 64-bit precision (float64) for certain computations \n",
    "# to ensure numerical stability and accuracy, e.g., tfd.Possion.\n",
    "# jax.config.update(\"jax_enable_x64\", True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 12.1 Over-dispersed counts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 12.1.1 Beta-binomial"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 12.1\n",
    "\n",
    "\n",
    "A beta distribution is a probability distribution for probabilities !"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 600x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pbar = 0.5  # mean\n",
    "theta = 5  # total concentration\n",
    "\n",
    "alpha = pbar * theta\n",
    "beta = (1 - pbar) * theta\n",
    "\n",
    "x = np.linspace(0, 1, 101)\n",
    "\n",
    "plt.plot(x, tfd.Beta(alpha, beta).prob(x))\n",
    "plt.xlabel(\"probability\")\n",
    "plt.ylabel(\"Density\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 12.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "d = pd.read_csv(\"./data/UCBadmit.csv\", sep=\";\")\n",
    "d[\"gid\"] = (d[\"applicant.gender\"] != \"male\").astype(int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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>dept</th>\n",
       "      <th>applicant.gender</th>\n",
       "      <th>admit</th>\n",
       "      <th>reject</th>\n",
       "      <th>applications</th>\n",
       "      <th>gid</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>A</td>\n",
       "      <td>male</td>\n",
       "      <td>512</td>\n",
       "      <td>313</td>\n",
       "      <td>825</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>A</td>\n",
       "      <td>female</td>\n",
       "      <td>89</td>\n",
       "      <td>19</td>\n",
       "      <td>108</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>B</td>\n",
       "      <td>male</td>\n",
       "      <td>353</td>\n",
       "      <td>207</td>\n",
       "      <td>560</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>B</td>\n",
       "      <td>female</td>\n",
       "      <td>17</td>\n",
       "      <td>8</td>\n",
       "      <td>25</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>C</td>\n",
       "      <td>male</td>\n",
       "      <td>120</td>\n",
       "      <td>205</td>\n",
       "      <td>325</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>C</td>\n",
       "      <td>female</td>\n",
       "      <td>202</td>\n",
       "      <td>391</td>\n",
       "      <td>593</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>D</td>\n",
       "      <td>male</td>\n",
       "      <td>138</td>\n",
       "      <td>279</td>\n",
       "      <td>417</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>D</td>\n",
       "      <td>female</td>\n",
       "      <td>131</td>\n",
       "      <td>244</td>\n",
       "      <td>375</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>E</td>\n",
       "      <td>male</td>\n",
       "      <td>53</td>\n",
       "      <td>138</td>\n",
       "      <td>191</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>E</td>\n",
       "      <td>female</td>\n",
       "      <td>94</td>\n",
       "      <td>299</td>\n",
       "      <td>393</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>F</td>\n",
       "      <td>male</td>\n",
       "      <td>22</td>\n",
       "      <td>351</td>\n",
       "      <td>373</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>F</td>\n",
       "      <td>female</td>\n",
       "      <td>24</td>\n",
       "      <td>317</td>\n",
       "      <td>341</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   dept applicant.gender  admit  reject  applications  gid\n",
       "1     A             male    512     313           825    0\n",
       "2     A           female     89      19           108    1\n",
       "3     B             male    353     207           560    0\n",
       "4     B           female     17       8            25    1\n",
       "5     C             male    120     205           325    0\n",
       "6     C           female    202     391           593    1\n",
       "7     D             male    138     279           417    0\n",
       "8     D           female    131     244           375    1\n",
       "9     E             male     53     138           191    0\n",
       "10    E           female     94     299           393    1\n",
       "11    F             male     22     351           373    0\n",
       "12    F           female     24     317           341    1"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_12_1(gid, N):\n",
    "\tdef _generator():\n",
    "\t\ta = yield tfd.Sample(tfd.Normal(loc=0.0, scale=1.5), sample_shape=2, name='a')\n",
    "\t\tphi = yield tfd.Exponential(rate=1.0, name='phi')\n",
    "\t\ttheta = phi + 2\n",
    "\t\tpbar = jax.nn.sigmoid(jnp.take(a, gid))\n",
    "\n",
    "\t\tconcentration1 = pbar * theta\n",
    "\t\tconcentration0 = (1 - pbar) * theta\n",
    "\n",
    "\t\tyield tfd.BetaBinomial(\n",
    "\t\t\ttotal_count=N, \n",
    "\t\t\tconcentration1=concentration1, concentration0=concentration0,\n",
    "\t\t\tname='A')\n",
    "\n",
    "\treturn tfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_12_1 = model_12_1(d.gid.values, d.applications.values.astype(np.float32))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_12_1_pin = jd_12_1.experimental_pin(A=d.admit.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jax.jit\n",
    "def run_chain(init_state, seed, step_size=1e-3, num_steps=500, burnin=400):\n",
    "\n",
    "  def target_log_prob(*states):\n",
    "    return jd_12_1_pin.unnormalized_log_prob(states)\n",
    "  \n",
    "  bijectors = [tfb.Identity(), tfb.Exp()]\n",
    "\n",
    "  kernel = tfp.mcmc.NoUTurnSampler(\n",
    "      target_log_prob_fn=target_log_prob,\n",
    "      step_size=step_size)\n",
    "  \n",
    "  kernel = tfp.mcmc.TransformedTransitionKernel(\n",
    "    inner_kernel=kernel,\n",
    "    bijector=bijectors)\n",
    "\n",
    "  kernel = tfp.mcmc.DualAveragingStepSizeAdaptation(\n",
    "    inner_kernel=kernel,\n",
    "    num_adaptation_steps=burnin)\n",
    "\n",
    "  chain_state = tfp.mcmc.sample_chain(\n",
    "      num_results=num_steps,\n",
    "      num_burnin_steps=burnin,\n",
    "      current_state=init_state,\n",
    "      kernel=kernel,\n",
    "      seed=seed,\n",
    "      trace_fn=None)\n",
    "  \n",
    "  return chain_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_chains = 4\n",
    "init_state = jd_12_1_pin.sample_unpinned(num_chains, seed=key())\n",
    "post_1 = run_chain(init_state=init_state, seed=key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_1_dict = {k: jnp.moveaxis(v, 0, 1) for k, v in post_1._asdict().items()}\n",
    "dict_1 = dict(posterior=post_1_dict)\n",
    "idata_1 = az.from_dict(**dict_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\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>hdi_5.5%</th>\n",
       "      <th>hdi_94.5%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_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>a[0]</th>\n",
       "      <td>-0.449</td>\n",
       "      <td>0.395</td>\n",
       "      <td>-1.074</td>\n",
       "      <td>0.163</td>\n",
       "      <td>0.009</td>\n",
       "      <td>0.008</td>\n",
       "      <td>2108.0</td>\n",
       "      <td>1157.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>a[1]</th>\n",
       "      <td>-0.322</td>\n",
       "      <td>0.402</td>\n",
       "      <td>-0.933</td>\n",
       "      <td>0.310</td>\n",
       "      <td>0.008</td>\n",
       "      <td>0.008</td>\n",
       "      <td>2789.0</td>\n",
       "      <td>1443.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>phi</th>\n",
       "      <td>1.021</td>\n",
       "      <td>0.755</td>\n",
       "      <td>0.001</td>\n",
       "      <td>2.008</td>\n",
       "      <td>0.029</td>\n",
       "      <td>0.021</td>\n",
       "      <td>503.0</td>\n",
       "      <td>373.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       mean     sd  hdi_5.5%  hdi_94.5%  mcse_mean  mcse_sd  ess_bulk  \\\n",
       "a[0] -0.449  0.395    -1.074      0.163      0.009    0.008    2108.0   \n",
       "a[1] -0.322  0.402    -0.933      0.310      0.008    0.008    2789.0   \n",
       "phi   1.021  0.755     0.001      2.008      0.029    0.021     503.0   \n",
       "\n",
       "      ess_tail  r_hat  \n",
       "a[0]    1157.0   1.00  \n",
       "a[1]    1443.0   1.00  \n",
       "phi      373.0   1.01  "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata_1, hdi_prob=0.89)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 12.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# compute the difference between alphas\n",
    "idata_1.posterior[\"da\"] = idata_1.posterior[\"a\"][:, :, 0] - idata_1.posterior[\"a\"][:, :, 1]\n",
    "\n",
    "# compute theta\n",
    "idata_1.posterior[\"theta\"] = idata_1.posterior[\"phi\"] + 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "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>hdi_5.5%</th>\n",
       "      <th>hdi_94.5%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_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>a[0]</th>\n",
       "      <td>-0.449</td>\n",
       "      <td>0.395</td>\n",
       "      <td>-1.074</td>\n",
       "      <td>0.163</td>\n",
       "      <td>0.009</td>\n",
       "      <td>0.008</td>\n",
       "      <td>2108.0</td>\n",
       "      <td>1157.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>a[1]</th>\n",
       "      <td>-0.322</td>\n",
       "      <td>0.402</td>\n",
       "      <td>-0.933</td>\n",
       "      <td>0.310</td>\n",
       "      <td>0.008</td>\n",
       "      <td>0.008</td>\n",
       "      <td>2789.0</td>\n",
       "      <td>1443.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>phi</th>\n",
       "      <td>1.021</td>\n",
       "      <td>0.755</td>\n",
       "      <td>0.001</td>\n",
       "      <td>2.008</td>\n",
       "      <td>0.029</td>\n",
       "      <td>0.021</td>\n",
       "      <td>503.0</td>\n",
       "      <td>373.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>da</th>\n",
       "      <td>-0.127</td>\n",
       "      <td>0.555</td>\n",
       "      <td>-0.922</td>\n",
       "      <td>0.805</td>\n",
       "      <td>0.011</td>\n",
       "      <td>0.013</td>\n",
       "      <td>2681.0</td>\n",
       "      <td>1183.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>theta</th>\n",
       "      <td>3.021</td>\n",
       "      <td>0.755</td>\n",
       "      <td>2.001</td>\n",
       "      <td>4.008</td>\n",
       "      <td>0.029</td>\n",
       "      <td>0.021</td>\n",
       "      <td>503.0</td>\n",
       "      <td>373.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        mean     sd  hdi_5.5%  hdi_94.5%  mcse_mean  mcse_sd  ess_bulk  \\\n",
       "a[0]  -0.449  0.395    -1.074      0.163      0.009    0.008    2108.0   \n",
       "a[1]  -0.322  0.402    -0.933      0.310      0.008    0.008    2789.0   \n",
       "phi    1.021  0.755     0.001      2.008      0.029    0.021     503.0   \n",
       "da    -0.127  0.555    -0.922      0.805      0.011    0.013    2681.0   \n",
       "theta  3.021  0.755     2.001      4.008      0.029    0.021     503.0   \n",
       "\n",
       "       ess_tail  r_hat  \n",
       "a[0]     1157.0   1.00  \n",
       "a[1]     1443.0   1.00  \n",
       "phi       373.0   1.01  \n",
       "da       1183.0   1.00  \n",
       "theta     373.0   1.01  "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata_1, hdi_prob=0.89)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 12.4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array(2.0049706, dtype=float32)"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta = post_1_dict['phi'][0, :] + 2\n",
    "theta[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = post_1_dict['a'][0, :, 1] # female\n",
    "theta = post_1_dict['phi'][0, :] + 2\n",
    "\n",
    "# draw posterior mean beta distribution\n",
    "x = np.linspace(0, 1, 101)\n",
    "pbar = jnp.mean(jax.nn.sigmoid(a))\n",
    "thetabar = jnp.mean(theta)\n",
    "plt.plot(x, tfd.Beta(pbar * thetabar, (1 - pbar) * thetabar).prob(x))\n",
    "plt.gca().set(ylabel=\"Density\", xlabel=\"probability admit\", ylim=(0, 3))\n",
    "\n",
    "# draw 50 beta distributions sampled from posterior\n",
    "for i in np.random.choice(500, 50):\n",
    "\tp = jax.nn.sigmoid(a[i])\n",
    "\tthetai = theta[i]\n",
    "\tplt.plot(x, tfd.Beta(pbar * thetai, (1 - pbar) * thetai).prob(x), \"k\", alpha=0.1)\n",
    "plt.title(\"distribution of female admission rates\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 12.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "# get samples given the posterior distribution\n",
    "N = d.applications.values.astype(np.float32)\n",
    "gid = d.gid.values\n",
    "\n",
    "# prepare the concentration vector\n",
    "concentration1 = pbar * thetabar\n",
    "concentration0 = (1 - pbar) * thetabar\n",
    "\n",
    "dist = tfd.BetaBinomial(\n",
    "  total_count=N, \n",
    "  concentration1=concentration1, concentration0=concentration0)\n",
    "\n",
    "predictive_samples = dist.sample(500, seed=key())\n",
    "admit_rate = predictive_samples / N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(500, 12)"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "admit_rate.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(range(1, 13), d.admit.values / N)\n",
    "plt.errorbar(\n",
    "    range(1, 13),\n",
    "    np.mean(admit_rate, 0),\n",
    "    np.std(admit_rate, 0) / 2,\n",
    "    fmt=\"o\",\n",
    "    c=\"k\",\n",
    "    mfc=\"none\",\n",
    "    ms=7,\n",
    "    elinewidth=1,\n",
    ")\n",
    "plt.plot(range(1, 13), np.percentile(admit_rate, 5.5, 0), \"k+\")\n",
    "plt.plot(range(1, 13), np.percentile(admit_rate, 94.5, 0), \"k+\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the above plot, the vertifical axis shows the predicted proportion admitted, for each case on the horizontal.\n",
    "\n",
    "Blue points show the empirical proportion admitted on each row of data\n",
    "\n",
    "Open circles are the posterior mean pbar and + symbols mark the 89% interval of predicted counts of admission"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 12.1.2 Negative-binomial or gamma-Poisson"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 12.6 \n",
    "\n",
    "Start to use **Gamma-Poisson** (also known as **Negative Binomial**) models.\n",
    "\n",
    "Essentially Gamm-Poisson is about associating a rate to each Posisson count observation. Estimates the shape of gamma distribution to describe the Poisson rates across cases.\n",
    "\n",
    "Gamma-Poisson also expects more variation around the mean rate.\n",
    "\n",
    "The negative binomial distribution arises naturally from a probability experiment of performing a series of independent Bernoulli trials until the occurrence of the rth success where r is a positive integer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "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>culture</th>\n",
       "      <th>population</th>\n",
       "      <th>contact</th>\n",
       "      <th>total_tools</th>\n",
       "      <th>mean_TU</th>\n",
       "      <th>P</th>\n",
       "      <th>contact_id</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Malekula</td>\n",
       "      <td>1100</td>\n",
       "      <td>low</td>\n",
       "      <td>13</td>\n",
       "      <td>3.2</td>\n",
       "      <td>-1.291473</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Tikopia</td>\n",
       "      <td>1500</td>\n",
       "      <td>low</td>\n",
       "      <td>22</td>\n",
       "      <td>4.7</td>\n",
       "      <td>-1.088551</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Santa Cruz</td>\n",
       "      <td>3600</td>\n",
       "      <td>low</td>\n",
       "      <td>24</td>\n",
       "      <td>4.0</td>\n",
       "      <td>-0.515765</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Yap</td>\n",
       "      <td>4791</td>\n",
       "      <td>high</td>\n",
       "      <td>43</td>\n",
       "      <td>5.0</td>\n",
       "      <td>-0.328773</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Lau Fiji</td>\n",
       "      <td>7400</td>\n",
       "      <td>high</td>\n",
       "      <td>33</td>\n",
       "      <td>5.0</td>\n",
       "      <td>-0.044339</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Trobriand</td>\n",
       "      <td>8000</td>\n",
       "      <td>high</td>\n",
       "      <td>19</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.006668</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Chuuk</td>\n",
       "      <td>9200</td>\n",
       "      <td>high</td>\n",
       "      <td>40</td>\n",
       "      <td>3.8</td>\n",
       "      <td>0.098109</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Manus</td>\n",
       "      <td>13000</td>\n",
       "      <td>low</td>\n",
       "      <td>28</td>\n",
       "      <td>6.6</td>\n",
       "      <td>0.324318</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Tonga</td>\n",
       "      <td>17500</td>\n",
       "      <td>high</td>\n",
       "      <td>55</td>\n",
       "      <td>5.4</td>\n",
       "      <td>0.518798</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>Hawaii</td>\n",
       "      <td>275000</td>\n",
       "      <td>low</td>\n",
       "      <td>71</td>\n",
       "      <td>6.6</td>\n",
       "      <td>2.321008</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      culture  population contact  total_tools  mean_TU         P  contact_id\n",
       "0    Malekula        1100     low           13      3.2 -1.291473           0\n",
       "1     Tikopia        1500     low           22      4.7 -1.088551           0\n",
       "2  Santa Cruz        3600     low           24      4.0 -0.515765           0\n",
       "3         Yap        4791    high           43      5.0 -0.328773           1\n",
       "4    Lau Fiji        7400    high           33      5.0 -0.044339           1\n",
       "5   Trobriand        8000    high           19      4.0  0.006668           1\n",
       "6       Chuuk        9200    high           40      3.8  0.098109           1\n",
       "7       Manus       13000     low           28      6.6  0.324318           0\n",
       "8       Tonga       17500    high           55      5.4  0.518798           1\n",
       "9      Hawaii      275000     low           71      6.6  2.321008           0"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d = pd.read_csv(\"./data/Kline.csv\", sep=\";\")\n",
    "d[\"P\"] = d.population.pipe(np.log).pipe(lambda x: (x - x.mean()) / x.std())\n",
    "d[\"contact_id\"] = (d.contact == \"high\").astype(int)\n",
    "d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array([0.20999995, 0.06300002, 0.0189    ], dtype=float32)"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# dgampois( x , mu , scale , log=FALSE )\n",
    "\n",
    "# == dnbinom(x, size=mu/scale, prob=1/(1+scale), mu=mu, log = FALSE)\n",
    "#    - x: number of failures\n",
    "#    - size: number of successes\n",
    "#    - prob: probability of success,  size / (size + mu)\n",
    "#    - mu: size * (1 - prob) / prob\n",
    "\n",
    "# == tfd.NegativeBinomial(total_count=size, probs=1-prob)\n",
    "# NOTE: In the official document says, \n",
    "#        total_count=x, probs=prob.\n",
    "#       But dnbinom outputs match with:\n",
    "#        total_count=size, probs=1-prob\n",
    "\n",
    "tfd.NegativeBinomial(total_count=1., probs=.3).prob([1., 2., 3.])\n",
    "# == dnbinom(c(1, 2, 3), size=1, prob=.7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_12_2(cid, P):\n",
    "\tdef _generator():\n",
    "\t\t# g = yield tfd.Exponential(rate=1.0, name='g')\n",
    "\t\tphi = yield tfd.Exponential(rate=1.0, name='phi')\n",
    "\t\t# a = yield tfd.Normal(loc=1.0, scale=1.0, name='a')\n",
    "\t\t# b = yield tfd.Exponential(rate=1.0, name='b')\n",
    "\t\t# NOTE: the scientific approach does not work\n",
    "\t\t# mu = jnp.exp(jnp.take(a, cid)) * jnp.pow(P, jnp.take(b, cid)) / g\n",
    "\t\tlambda_ = yield tfd.Exponential(rate=1.0, name='lambda_')\n",
    "\t\tyield tfd.Sample(\n",
    "\t\t\ttfd.NegativeBinomial(total_count=lambda_/phi, probs=phi/(1+phi)),\n",
    "\t\t\tsample_shape=10, name='tools')\n",
    "\n",
    "\treturn tfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_12_2 = model_12_2(d.contact_id.values, d.P.values.astype(np.float32))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_12_2_pin = jd_12_2.experimental_pin(tools=d.total_tools.values.astype(np.float32))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jax.jit\n",
    "def run_chain(init_state, seed, step_size=1e-3, num_steps=500, burnin=400):\n",
    "\n",
    "  def target_log_prob(*states):\n",
    "    return jd_12_2_pin.unnormalized_log_prob(states)\n",
    "  \n",
    "  bijectors = [tfb.Exp(), tfb.Exp()]\n",
    "\n",
    "  kernel = tfp.mcmc.NoUTurnSampler(\n",
    "      target_log_prob_fn=target_log_prob,\n",
    "      step_size=step_size)\n",
    "  \n",
    "  kernel = tfp.mcmc.TransformedTransitionKernel(\n",
    "    inner_kernel=kernel,\n",
    "    bijector=bijectors)\n",
    "\n",
    "  kernel = tfp.mcmc.DualAveragingStepSizeAdaptation(\n",
    "    inner_kernel=kernel,\n",
    "    num_adaptation_steps=burnin)\n",
    "\n",
    "  chain_state = tfp.mcmc.sample_chain(\n",
    "      num_results=num_steps,\n",
    "      num_burnin_steps=burnin,\n",
    "      current_state=init_state,\n",
    "      kernel=kernel,\n",
    "      seed=seed,\n",
    "      trace_fn=None)\n",
    "  \n",
    "  return chain_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_chains = 4\n",
    "init_state = jd_12_2_pin.sample_unpinned(num_chains, seed=key())\n",
    "post_2 = run_chain(init_state=init_state, seed=key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_2_dict = {k: jnp.moveaxis(v, 0, 1) for k, v in post_2._asdict().items()}\n",
    "dict_2 = dict(posterior=post_2_dict)\n",
    "idata_2 = az.from_dict(**dict_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "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>hdi_5.5%</th>\n",
       "      <th>hdi_94.5%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_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>lambda_</th>\n",
       "      <td>19.731</td>\n",
       "      <td>3.804</td>\n",
       "      <td>13.814</td>\n",
       "      <td>25.545</td>\n",
       "      <td>0.121</td>\n",
       "      <td>0.086</td>\n",
       "      <td>989.0</td>\n",
       "      <td>1104.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>phi</th>\n",
       "      <td>5.696</td>\n",
       "      <td>1.961</td>\n",
       "      <td>2.708</td>\n",
       "      <td>8.473</td>\n",
       "      <td>0.075</td>\n",
       "      <td>0.053</td>\n",
       "      <td>645.0</td>\n",
       "      <td>580.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           mean     sd  hdi_5.5%  hdi_94.5%  mcse_mean  mcse_sd  ess_bulk  \\\n",
       "lambda_  19.731  3.804    13.814     25.545      0.121    0.086     989.0   \n",
       "phi       5.696  1.961     2.708      8.473      0.075    0.053     645.0   \n",
       "\n",
       "         ess_tail  r_hat  \n",
       "lambda_    1104.0    1.0  \n",
       "phi         580.0    1.0  "
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata_2, hdi_prob=0.89)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 12.2 Zero-inflated outcomes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 12.6 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define parameters\n",
    "prob_drink = 0.2 # 20% of days\n",
    "rate_work = 1 # average 1 manuscript per day\n",
    "# sample one year of production\n",
    "N = 365\n",
    "# simulate days monks drink\n",
    "drink = tfd.Bernoulli(probs=prob_drink).sample(N, seed=key())\n",
    "# simulate manuscripts completed\n",
    "y = (1 - drink) * tfd.Poisson(rate=rate_work).sample(N, seed=key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Array(65, dtype=int64), Array(110, dtype=int64), Array(175, dtype=int64))"
      ]
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zeros_drink = jnp.sum(drink)\n",
    "zeros_work = jnp.sum((y==0) & (drink==0))\n",
    "zeros_total = jnp.sum(y==0)\n",
    "\n",
    "zeros_drink, zeros_work, zeros_total"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 12.9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_12_3():\n",
    "\tdef _generator():\n",
    "\t\tal = yield tfd.Normal(loc=1.0, scale=0.5, name='al')\n",
    "\t\tap = yield tfd.Normal(loc=-1.5, scale=1.0, name='ap')\n",
    "\t\tyield tfd.Sample(\n",
    "\t\t\ttfd.Inflated(tfd.Poisson(log_rate=al), inflated_loc_logits=ap), \n",
    "\t\t\tsample_shape=365, name='y')\n",
    "\n",
    "\treturn tfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_12_3 = model_12_3()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_12_3_pin = jd_12_3.experimental_pin(y=y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jax.jit\n",
    "def run_chain(init_state, seed, step_size=1e-3, num_steps=500, burnin=500):\n",
    "\n",
    "  def target_log_prob(*states):\n",
    "    return jd_12_3_pin.unnormalized_log_prob(states)\n",
    "  \n",
    "  bijectors = [tfb.Identity(), tfb.Identity()]\n",
    "\n",
    "  kernel = tfp.mcmc.NoUTurnSampler(\n",
    "      target_log_prob_fn=target_log_prob,\n",
    "      step_size=step_size)\n",
    "  \n",
    "  kernel = tfp.mcmc.TransformedTransitionKernel(\n",
    "    inner_kernel=kernel,\n",
    "    bijector=bijectors)\n",
    "\n",
    "  kernel = tfp.mcmc.DualAveragingStepSizeAdaptation(\n",
    "    inner_kernel=kernel,\n",
    "    num_adaptation_steps=burnin)\n",
    "\n",
    "  chain_state = tfp.mcmc.sample_chain(\n",
    "      num_results=num_steps,\n",
    "      num_burnin_steps=burnin,\n",
    "      current_state=init_state,\n",
    "      kernel=kernel,\n",
    "      seed=seed,\n",
    "      trace_fn=None)\n",
    "  \n",
    "  return chain_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_chains = 4\n",
    "init_state = jd_12_3_pin.sample_unpinned(num_chains, seed=key())\n",
    "post_3 = run_chain(init_state=init_state, seed=key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_3_dict = {k: jnp.moveaxis(v, 0, 1) for k, v in post_3._asdict().items()}\n",
    "dict_3 = dict(posterior=post_3_dict)\n",
    "idata_3 = az.from_dict(**dict_3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "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>hdi_5.5%</th>\n",
       "      <th>hdi_94.5%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_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>al</th>\n",
       "      <td>-0.085</td>\n",
       "      <td>0.093</td>\n",
       "      <td>-0.239</td>\n",
       "      <td>0.048</td>\n",
       "      <td>0.005</td>\n",
       "      <td>0.003</td>\n",
       "      <td>400.0</td>\n",
       "      <td>746.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ap</th>\n",
       "      <td>-1.171</td>\n",
       "      <td>0.541</td>\n",
       "      <td>-1.839</td>\n",
       "      <td>-0.521</td>\n",
       "      <td>0.036</td>\n",
       "      <td>0.026</td>\n",
       "      <td>267.0</td>\n",
       "      <td>308.0</td>\n",
       "      <td>1.02</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     mean     sd  hdi_5.5%  hdi_94.5%  mcse_mean  mcse_sd  ess_bulk  ess_tail  \\\n",
       "al -0.085  0.093    -0.239      0.048      0.005    0.003     400.0     746.0   \n",
       "ap -1.171  0.541    -1.839     -0.521      0.036    0.026     267.0     308.0   \n",
       "\n",
       "    r_hat  \n",
       "al   1.01  \n",
       "ap   1.02  "
      ]
     },
     "execution_count": 179,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata_3, hdi_prob=0.89)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 12.10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Array(0.24943775, dtype=float32), Array(0.9228564, dtype=float32))"
      ]
     },
     "execution_count": 182,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(\n",
    "  jnp.mean(jax.nn.sigmoid(post_3_dict['ap'])), # probability drink\n",
    "  jnp.mean(jnp.exp(post_3_dict['al'])) # rate finish manuscripts, when not drinking\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 12.3 Ordered categorical outcomes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 12.12"
   ]
  },
  {
   "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>case</th>\n",
       "      <th>response</th>\n",
       "      <th>order</th>\n",
       "      <th>id</th>\n",
       "      <th>age</th>\n",
       "      <th>male</th>\n",
       "      <th>edu</th>\n",
       "      <th>action</th>\n",
       "      <th>intention</th>\n",
       "      <th>contact</th>\n",
       "      <th>story</th>\n",
       "      <th>action2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>cfaqu</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>96;434</td>\n",
       "      <td>14</td>\n",
       "      <td>0</td>\n",
       "      <td>Middle School</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>aqu</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>cfbur</td>\n",
       "      <td>2</td>\n",
       "      <td>31</td>\n",
       "      <td>96;434</td>\n",
       "      <td>14</td>\n",
       "      <td>0</td>\n",
       "      <td>Middle School</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>bur</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>cfrub</td>\n",
       "      <td>3</td>\n",
       "      <td>16</td>\n",
       "      <td>96;434</td>\n",
       "      <td>14</td>\n",
       "      <td>0</td>\n",
       "      <td>Middle School</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>rub</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>cibox</td>\n",
       "      <td>2</td>\n",
       "      <td>32</td>\n",
       "      <td>96;434</td>\n",
       "      <td>14</td>\n",
       "      <td>0</td>\n",
       "      <td>Middle School</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>box</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>cibur</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>96;434</td>\n",
       "      <td>14</td>\n",
       "      <td>0</td>\n",
       "      <td>Middle School</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>bur</td>\n",
       "      <td>1</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",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9925</th>\n",
       "      <td>ilpon</td>\n",
       "      <td>2</td>\n",
       "      <td>23</td>\n",
       "      <td>98;299</td>\n",
       "      <td>66</td>\n",
       "      <td>1</td>\n",
       "      <td>Graduate Degree</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>pon</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9926</th>\n",
       "      <td>ilsha</td>\n",
       "      <td>5</td>\n",
       "      <td>15</td>\n",
       "      <td>98;299</td>\n",
       "      <td>66</td>\n",
       "      <td>1</td>\n",
       "      <td>Graduate Degree</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>sha</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9927</th>\n",
       "      <td>ilshi</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>98;299</td>\n",
       "      <td>66</td>\n",
       "      <td>1</td>\n",
       "      <td>Graduate Degree</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>shi</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9928</th>\n",
       "      <td>ilswi</td>\n",
       "      <td>1</td>\n",
       "      <td>18</td>\n",
       "      <td>98;299</td>\n",
       "      <td>66</td>\n",
       "      <td>1</td>\n",
       "      <td>Graduate Degree</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>swi</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9929</th>\n",
       "      <td>nfrub</td>\n",
       "      <td>1</td>\n",
       "      <td>17</td>\n",
       "      <td>98;299</td>\n",
       "      <td>66</td>\n",
       "      <td>1</td>\n",
       "      <td>Graduate Degree</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>rub</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>9930 rows × 12 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       case  response  order      id  age  male              edu  action  \\\n",
       "0     cfaqu         3      2  96;434   14     0    Middle School       0   \n",
       "1     cfbur         2     31  96;434   14     0    Middle School       0   \n",
       "2     cfrub         3     16  96;434   14     0    Middle School       0   \n",
       "3     cibox         2     32  96;434   14     0    Middle School       0   \n",
       "4     cibur         2      4  96;434   14     0    Middle School       0   \n",
       "...     ...       ...    ...     ...  ...   ...              ...     ...   \n",
       "9925  ilpon         2     23  98;299   66     1  Graduate Degree       0   \n",
       "9926  ilsha         5     15  98;299   66     1  Graduate Degree       0   \n",
       "9927  ilshi         6      7  98;299   66     1  Graduate Degree       0   \n",
       "9928  ilswi         1     18  98;299   66     1  Graduate Degree       0   \n",
       "9929  nfrub         1     17  98;299   66     1  Graduate Degree       1   \n",
       "\n",
       "      intention  contact story  action2  \n",
       "0             0        1   aqu        1  \n",
       "1             0        1   bur        1  \n",
       "2             0        1   rub        1  \n",
       "3             1        1   box        1  \n",
       "4             1        1   bur        1  \n",
       "...         ...      ...   ...      ...  \n",
       "9925          1        0   pon        0  \n",
       "9926          1        0   sha        0  \n",
       "9927          1        0   shi        0  \n",
       "9928          1        0   swi        0  \n",
       "9929          0        0   rub        1  \n",
       "\n",
       "[9930 rows x 12 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d = pd.read_csv(\"./data/Trolley.csv\", sep=\";\")\n",
    "d['response'] = d['response'] - 1\n",
    "d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_12_4():\n",
    "\tdef _generator():\n",
    "\t\tcutpoints = yield tfd.TransformedDistribution(\n",
    "\t\t\tdistribution=tfd.Sample(tfd.Normal(loc=0., scale=1.5), sample_shape=6), \n",
    "\t\t\tbijector=tfb.Ascending(), name='cutpoints')\n",
    "\t\tyield tfd.Sample(\n",
    "\t\t\ttfd.OrderedLogistic(cutpoints=cutpoints, loc=0.), \n",
    "\t\t\tsample_shape=9930, name='response')\n",
    "\n",
    "\treturn tfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_12_4 = model_12_4()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_12_4_pin = jd_12_4.experimental_pin(response=d.response.values.astype(np.float32))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jax.jit\n",
    "def run_chain(init_state, seed, step_size=1e-3, num_steps=500, burnin=500):\n",
    "\n",
    "  def target_log_prob(*states):\n",
    "    return jd_12_4_pin.unnormalized_log_prob(states)\n",
    "  \n",
    "  bijectors = [tfb.Identity()]\n",
    "\n",
    "  kernel = tfp.mcmc.NoUTurnSampler(\n",
    "      target_log_prob_fn=target_log_prob,\n",
    "      step_size=step_size)\n",
    "  \n",
    "  kernel = tfp.mcmc.TransformedTransitionKernel(\n",
    "    inner_kernel=kernel,\n",
    "    bijector=bijectors)\n",
    "\n",
    "  kernel = tfp.mcmc.DualAveragingStepSizeAdaptation(\n",
    "    inner_kernel=kernel,\n",
    "    num_adaptation_steps=burnin)\n",
    "\n",
    "  chain_state = tfp.mcmc.sample_chain(\n",
    "      num_results=num_steps,\n",
    "      num_burnin_steps=burnin,\n",
    "      current_state=init_state,\n",
    "      kernel=kernel,\n",
    "      seed=seed,\n",
    "      trace_fn=None)\n",
    "  \n",
    "  return chain_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_chains = 4\n",
    "init_state = jd_12_4_pin.sample_unpinned(num_chains, seed=key())\n",
    "post_4 = run_chain(init_state=init_state, seed=key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_4_dict = {k: jnp.moveaxis(v, 0, 1) for k, v in post_4._asdict().items()}\n",
    "dict_4 = dict(posterior=post_4_dict)\n",
    "idata_4 = az.from_dict(**dict_4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "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>hdi_5.5%</th>\n",
       "      <th>hdi_94.5%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_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>cutpoints[0]</th>\n",
       "      <td>-1.915</td>\n",
       "      <td>0.029</td>\n",
       "      <td>-1.961</td>\n",
       "      <td>-1.869</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>1165.0</td>\n",
       "      <td>1285.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cutpoints[1]</th>\n",
       "      <td>-1.267</td>\n",
       "      <td>0.024</td>\n",
       "      <td>-1.306</td>\n",
       "      <td>-1.230</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>1074.0</td>\n",
       "      <td>1305.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cutpoints[2]</th>\n",
       "      <td>-0.719</td>\n",
       "      <td>0.021</td>\n",
       "      <td>-0.753</td>\n",
       "      <td>-0.685</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.000</td>\n",
       "      <td>1055.0</td>\n",
       "      <td>1208.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cutpoints[3]</th>\n",
       "      <td>0.248</td>\n",
       "      <td>0.021</td>\n",
       "      <td>0.216</td>\n",
       "      <td>0.282</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.000</td>\n",
       "      <td>1089.0</td>\n",
       "      <td>900.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cutpoints[4]</th>\n",
       "      <td>0.889</td>\n",
       "      <td>0.023</td>\n",
       "      <td>0.855</td>\n",
       "      <td>0.928</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.000</td>\n",
       "      <td>1074.0</td>\n",
       "      <td>1034.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cutpoints[5]</th>\n",
       "      <td>1.769</td>\n",
       "      <td>0.029</td>\n",
       "      <td>1.723</td>\n",
       "      <td>1.816</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>1131.0</td>\n",
       "      <td>1122.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               mean     sd  hdi_5.5%  hdi_94.5%  mcse_mean  mcse_sd  ess_bulk  \\\n",
       "cutpoints[0] -1.915  0.029    -1.961     -1.869      0.001    0.001    1165.0   \n",
       "cutpoints[1] -1.267  0.024    -1.306     -1.230      0.001    0.001    1074.0   \n",
       "cutpoints[2] -0.719  0.021    -0.753     -0.685      0.001    0.000    1055.0   \n",
       "cutpoints[3]  0.248  0.021     0.216      0.282      0.001    0.000    1089.0   \n",
       "cutpoints[4]  0.889  0.023     0.855      0.928      0.001    0.000    1074.0   \n",
       "cutpoints[5]  1.769  0.029     1.723      1.816      0.001    0.001    1131.0   \n",
       "\n",
       "              ess_tail  r_hat  \n",
       "cutpoints[0]    1285.0    1.0  \n",
       "cutpoints[1]    1305.0    1.0  \n",
       "cutpoints[2]    1208.0    1.0  \n",
       "cutpoints[3]     900.0    1.0  \n",
       "cutpoints[4]    1034.0    1.0  \n",
       "cutpoints[5]    1122.0    1.0  "
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary_4 = az.summary(idata_4, hdi_prob=0.89)\n",
    "summary_4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 12.19"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "cutpoints[0]    0.128420\n",
       "cutpoints[1]    0.219771\n",
       "cutpoints[2]    0.327613\n",
       "cutpoints[3]    0.561684\n",
       "cutpoints[4]    0.708684\n",
       "cutpoints[5]    0.854333\n",
       "Name: mean, dtype: float64"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary_4['mean'].pipe(lambda x: 1 / (1 + np.exp(-x)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 12.20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array([0.12842017, 0.09135107, 0.10784199, 0.23407094, 0.14699959,\n",
       "       0.1456495 , 0.14566673], dtype=float64)"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coef_4 = summary_4['mean'].values\n",
    "pk = tfd.OrderedLogistic(cutpoints=coef_4, loc=0.).prob(jnp.arange(7))\n",
    "pk"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 12.21"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array(4.19949416, dtype=float64)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "jnp.sum(pk * (jnp.arange(7) + 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 12.22"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array([0.082036  , 0.06387981, 0.08219667, 0.20921881, 0.15871065,\n",
       "       0.18452957, 0.21942848], dtype=float64)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pk = tfd.OrderedLogistic(cutpoints=coef_4 - 0.5, loc=0.).prob(jnp.arange(7))\n",
    "pk"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 12.23"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array(4.72999096, dtype=float64)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "jnp.sum(pk * (jnp.arange(7) + 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 12.24\n",
    "\n",
    "NOTE: 'AutoBatched' does not interpret/transform batch of 'tfd.OrderedLogistic' to event. Use tfd.Independent.\n",
    "\n",
    "Time: tfp (4min~) vs Numpyro (15s)\n",
    "\n",
    "All of the previous models run within 10s. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_12_5(I, A, C):\n",
    "\tdef _generator():\n",
    "\t\tbA = yield tfd.Normal(loc=0., scale=0.5, name='bA')\n",
    "\t\tbI = yield tfd.Normal(loc=0., scale=0.5, name='bI')\n",
    "\t\tbC = yield tfd.Normal(loc=0., scale=0.5, name='bC')\n",
    "\t\tbIA = yield tfd.Normal(loc=0., scale=0.5, name='bIA')\n",
    "\t\tbIC = yield tfd.Normal(loc=0., scale=0.5, name='bIC')\n",
    "\t\tBI = bI + bIA*A + bIC*C\n",
    "\t\tphi = bA*A + bC*C + BI*I\n",
    "\t\tcutpoints = yield tfd.TransformedDistribution(\n",
    "\t\t\tdistribution=tfd.Sample(tfd.Normal(loc=0., scale=1.5), sample_shape=6), \n",
    "\t\t\tbijector=tfb.Ascending(), name='cutpoints')\t\n",
    "\t\tyield tfd.Independent(\n",
    "\t\t\ttfd.OrderedLogistic(cutpoints=cutpoints, loc=phi), \n",
    "\t\t\treinterpreted_batch_ndims=1, name='response')\n",
    "\n",
    "\treturn tfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_12_5 = model_12_5(A=d.action.values.astype(np.float32), \n",
    "                     I=d.intention.values.astype(np.float32), \n",
    "                     C=d.contact.values.astype(np.float32))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_12_5_pin = jd_12_5.experimental_pin(response=d.response.values.astype(np.float32))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jax.jit\n",
    "def run_chain(init_state, seed, step_size=1e-3, num_steps=500, burnin=400):\n",
    "\n",
    "  def target_log_prob(*states):\n",
    "    return jd_12_5_pin.unnormalized_log_prob(states)\n",
    "  \n",
    "  bijectors = [tfb.Identity(), tfb.Identity(), tfb.Identity(),\n",
    "               tfb.Identity(), tfb.Identity(), tfb.Identity()]\n",
    "\n",
    "  kernel = tfp.mcmc.NoUTurnSampler(\n",
    "      target_log_prob_fn=target_log_prob,\n",
    "      step_size=step_size)\n",
    "  \n",
    "  kernel = tfp.mcmc.TransformedTransitionKernel(\n",
    "    inner_kernel=kernel,\n",
    "    bijector=bijectors)\n",
    "\n",
    "  kernel = tfp.mcmc.DualAveragingStepSizeAdaptation(\n",
    "    inner_kernel=kernel,\n",
    "    num_adaptation_steps=burnin)\n",
    "\n",
    "  chain_state = tfp.mcmc.sample_chain(\n",
    "      num_results=num_steps,\n",
    "      num_burnin_steps=burnin,\n",
    "      current_state=init_state,\n",
    "      kernel=kernel,\n",
    "      seed=seed,\n",
    "      trace_fn=None)\n",
    "  \n",
    "  return chain_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_chains = 3\n",
    "init_state = jd_12_5_pin.sample_unpinned(num_chains, seed=key())\n",
    "post_5 = run_chain(init_state=init_state, seed=key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_5_dict = {k: jnp.moveaxis(v, 0, 1) for k, v in post_5._asdict().items()}\n",
    "dict_5 = dict(posterior=post_5_dict)\n",
    "idata_5 = az.from_dict(**dict_5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "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>hdi_5.5%</th>\n",
       "      <th>hdi_94.5%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_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>bA</th>\n",
       "      <td>-0.476</td>\n",
       "      <td>0.053</td>\n",
       "      <td>-0.562</td>\n",
       "      <td>-0.391</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>579.0</td>\n",
       "      <td>752.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bC</th>\n",
       "      <td>-0.346</td>\n",
       "      <td>0.067</td>\n",
       "      <td>-0.452</td>\n",
       "      <td>-0.242</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.002</td>\n",
       "      <td>572.0</td>\n",
       "      <td>936.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bI</th>\n",
       "      <td>-0.294</td>\n",
       "      <td>0.056</td>\n",
       "      <td>-0.382</td>\n",
       "      <td>-0.203</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>542.0</td>\n",
       "      <td>645.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bIA</th>\n",
       "      <td>-0.431</td>\n",
       "      <td>0.077</td>\n",
       "      <td>-0.560</td>\n",
       "      <td>-0.320</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.002</td>\n",
       "      <td>658.0</td>\n",
       "      <td>705.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bIC</th>\n",
       "      <td>-1.234</td>\n",
       "      <td>0.095</td>\n",
       "      <td>-1.382</td>\n",
       "      <td>-1.082</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.003</td>\n",
       "      <td>570.0</td>\n",
       "      <td>677.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cutpoints[0]</th>\n",
       "      <td>-2.636</td>\n",
       "      <td>0.051</td>\n",
       "      <td>-2.718</td>\n",
       "      <td>-2.558</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>556.0</td>\n",
       "      <td>741.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cutpoints[1]</th>\n",
       "      <td>-1.941</td>\n",
       "      <td>0.047</td>\n",
       "      <td>-2.013</td>\n",
       "      <td>-1.864</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.001</td>\n",
       "      <td>504.0</td>\n",
       "      <td>552.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cutpoints[2]</th>\n",
       "      <td>-1.346</td>\n",
       "      <td>0.044</td>\n",
       "      <td>-1.414</td>\n",
       "      <td>-1.275</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.001</td>\n",
       "      <td>478.0</td>\n",
       "      <td>614.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cutpoints[3]</th>\n",
       "      <td>-0.311</td>\n",
       "      <td>0.043</td>\n",
       "      <td>-0.382</td>\n",
       "      <td>-0.247</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.001</td>\n",
       "      <td>449.0</td>\n",
       "      <td>498.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cutpoints[4]</th>\n",
       "      <td>0.360</td>\n",
       "      <td>0.043</td>\n",
       "      <td>0.296</td>\n",
       "      <td>0.430</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.001</td>\n",
       "      <td>539.0</td>\n",
       "      <td>721.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cutpoints[5]</th>\n",
       "      <td>1.265</td>\n",
       "      <td>0.047</td>\n",
       "      <td>1.195</td>\n",
       "      <td>1.345</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.001</td>\n",
       "      <td>568.0</td>\n",
       "      <td>759.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               mean     sd  hdi_5.5%  hdi_94.5%  mcse_mean  mcse_sd  ess_bulk  \\\n",
       "bA           -0.476  0.053    -0.562     -0.391      0.002    0.002     579.0   \n",
       "bC           -0.346  0.067    -0.452     -0.242      0.003    0.002     572.0   \n",
       "bI           -0.294  0.056    -0.382     -0.203      0.002    0.002     542.0   \n",
       "bIA          -0.431  0.077    -0.560     -0.320      0.003    0.002     658.0   \n",
       "bIC          -1.234  0.095    -1.382     -1.082      0.004    0.003     570.0   \n",
       "cutpoints[0] -2.636  0.051    -2.718     -2.558      0.002    0.002     556.0   \n",
       "cutpoints[1] -1.941  0.047    -2.013     -1.864      0.002    0.001     504.0   \n",
       "cutpoints[2] -1.346  0.044    -1.414     -1.275      0.002    0.001     478.0   \n",
       "cutpoints[3] -0.311  0.043    -0.382     -0.247      0.002    0.001     449.0   \n",
       "cutpoints[4]  0.360  0.043     0.296      0.430      0.002    0.001     539.0   \n",
       "cutpoints[5]  1.265  0.047     1.195      1.345      0.002    0.001     568.0   \n",
       "\n",
       "              ess_tail  r_hat  \n",
       "bA               752.0   1.00  \n",
       "bC               936.0   1.00  \n",
       "bI               645.0   1.00  \n",
       "bIA              705.0   1.00  \n",
       "bIC              677.0   1.00  \n",
       "cutpoints[0]     741.0   1.00  \n",
       "cutpoints[1]     552.0   1.00  \n",
       "cutpoints[2]     614.0   1.01  \n",
       "cutpoints[3]     498.0   1.00  \n",
       "cutpoints[4]     721.0   1.00  \n",
       "cutpoints[5]     759.0   1.00  "
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary_5 = az.summary(idata_5, hdi_prob=0.89)\n",
    "summary_5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 12.4 Ordered categorical predictors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 12.30"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "categories=['Elementary School', 'Middle School', 'Some High School', \n",
    "            'High School Graduate', 'Some College', \"Bachelor's Degree\", \n",
    "            \"Master's Degree\", 'Graduate Degree']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "d['edu_new'] = pd.Categorical(d.edu.values, categories=categories).codes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha = [2., 2, 2, 2]\n",
    "dist = tfd.Dirichlet(alpha)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [],
   "source": [
    "ss = dist.sample(1, seed=key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array([0.3283747 , 0.22594854, 0.274829  , 0.17084776], dtype=float32)"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ss = ss.squeeze()\n",
    "ss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array([0.        , 0.32837471, 0.55432326, 0.82915223, 1.        ],      dtype=float64)"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ss = jnp.concat([jnp.zeros(1), jnp.cumsum(ss)])\n",
    "ss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array([0.        , 0.32837471, 0.55432326], dtype=float64)"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "jnp.take(ss, jnp.array([0, 1, 2]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array([2., 2., 2., 2., 2., 2., 2.], dtype=float64)"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "jnp.ones(7) * 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_12_6(I, A, C, E):\n",
    "\tdef _generator():\n",
    "\t\tbA = yield tfd.Normal(loc=0., scale=1.0, name='bA')\n",
    "\t\tbI = yield tfd.Normal(loc=0., scale=1.0, name='bI')\n",
    "\t\tbC = yield tfd.Normal(loc=0., scale=1.0, name='bC')\n",
    "\t\tbE = yield tfd.Normal(loc=0., scale=1.0, name='bE')\n",
    "\t\tdelta_ = yield tfd.Dirichlet(jnp.ones(7) * 2, name='delta_')\n",
    "\t\t# delta_: (1, 7)-array\n",
    "\t\tdelta_cumsum = jnp.concat([jnp.zeros(1), jnp.cumsum(delta_.squeeze())])\n",
    "\t\tphi = bE*jnp.take(delta_cumsum, E) + bA*A + bC*C + bI*I\n",
    "\n",
    "\t\tcutpoints = yield tfd.TransformedDistribution(\n",
    "\t\t\tdistribution=tfd.Sample(tfd.Normal(loc=0., scale=1.5), sample_shape=6), \n",
    "\t\t\tbijector=tfb.Ascending(), name='cutpoints')\n",
    "\t\t\n",
    "\t\tyield tfd.Independent(\n",
    "\t\t\ttfd.OrderedLogistic(cutpoints=cutpoints, loc=phi), \n",
    "\t\t\treinterpreted_batch_ndims=1, name='response')\n",
    "\n",
    "\treturn tfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('float64')"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d.action.values.astype(np.float64).dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_12_6 = model_12_6(A=d.action.values.astype(jnp.float32), \n",
    "                     I=d.intention.values.astype(jnp.float32), \n",
    "                     C=d.contact.values.astype(jnp.float32),\n",
    "                     E=d.edu_new.values.astype(jnp.int32))\n",
    "# jd_12_6 = model_12_6(A=d.action.values, \n",
    "#                      I=d.intention.values, \n",
    "#                      C=d.contact.values,\n",
    "#                      E=d.edu_new.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_12_6_pin = jd_12_6.experimental_pin(response=d.response.values.astype(jnp.float32))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jax.jit\n",
    "def run_chain(init_state, seed, step_size=1e-3, num_steps=400, burnin=300):\n",
    "\n",
    "  def target_log_prob(*states):\n",
    "    return jd_12_6_pin.unnormalized_log_prob(states)\n",
    "  \n",
    "  bijectors = [tfb.Identity(), tfb.Identity(), tfb.Identity(),\n",
    "               tfb.Identity(), tfb.SoftmaxCentered(), tfb.Identity()]\n",
    "\n",
    "  kernel = tfp.mcmc.NoUTurnSampler(\n",
    "      target_log_prob_fn=target_log_prob,\n",
    "      step_size=step_size)\n",
    "  \n",
    "  kernel = tfp.mcmc.TransformedTransitionKernel(\n",
    "    inner_kernel=kernel,\n",
    "    bijector=bijectors)\n",
    "\n",
    "  kernel = tfp.mcmc.DualAveragingStepSizeAdaptation(\n",
    "    inner_kernel=kernel,\n",
    "    num_adaptation_steps=burnin)\n",
    "\n",
    "  chain_state = tfp.mcmc.sample_chain(\n",
    "      num_results=num_steps,\n",
    "      num_burnin_steps=burnin,\n",
    "      current_state=init_state,\n",
    "      kernel=kernel,\n",
    "      seed=seed,\n",
    "      trace_fn=None)\n",
    "  \n",
    "  return chain_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jun/miniforge3/envs/dl/lib/python3.12/site-packages/jax/_src/numpy/array_methods.py:69: UserWarning: Explicitly requested dtype int64 requested in astype is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return lax_numpy.astype(arr, dtype, copy=copy, device=device)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.12/site-packages/jax/_src/numpy/array_methods.py:69: UserWarning: Explicitly requested dtype int64 requested in astype is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return lax_numpy.astype(arr, dtype, copy=copy, device=device)\n"
     ]
    }
   ],
   "source": [
    "num_chains = 3\n",
    "init_state = jd_12_6_pin.sample_unpinned(num_chains, seed=key())\n",
    "post_6 = run_chain(init_state=init_state, seed=key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_6_dict = {k: jnp.moveaxis(v, 0, 1) for k, v in post_6._asdict().items()}\n",
    "dict_6 = dict(posterior=post_6_dict)\n",
    "idata_6 = az.from_dict(**dict_6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "        text-align: right;\n",
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       "<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>hdi_5.5%</th>\n",
       "      <th>hdi_94.5%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_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>bA</th>\n",
       "      <td>-0.707</td>\n",
       "      <td>0.041</td>\n",
       "      <td>-0.766</td>\n",
       "      <td>-0.638</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>1156.0</td>\n",
       "      <td>876.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bC</th>\n",
       "      <td>-0.957</td>\n",
       "      <td>0.051</td>\n",
       "      <td>-1.034</td>\n",
       "      <td>-0.873</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.001</td>\n",
       "      <td>1101.0</td>\n",
       "      <td>853.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bE</th>\n",
       "      <td>-0.371</td>\n",
       "      <td>0.195</td>\n",
       "      <td>-0.653</td>\n",
       "      <td>-0.049</td>\n",
       "      <td>0.006</td>\n",
       "      <td>0.004</td>\n",
       "      <td>974.0</td>\n",
       "      <td>935.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bI</th>\n",
       "      <td>-0.717</td>\n",
       "      <td>0.036</td>\n",
       "      <td>-0.777</td>\n",
       "      <td>-0.664</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>1137.0</td>\n",
       "      <td>971.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cutpoints[0]</th>\n",
       "      <td>-3.128</td>\n",
       "      <td>0.181</td>\n",
       "      <td>-3.400</td>\n",
       "      <td>-2.844</td>\n",
       "      <td>0.006</td>\n",
       "      <td>0.004</td>\n",
       "      <td>978.0</td>\n",
       "      <td>999.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cutpoints[1]</th>\n",
       "      <td>-2.445</td>\n",
       "      <td>0.180</td>\n",
       "      <td>-2.722</td>\n",
       "      <td>-2.177</td>\n",
       "      <td>0.006</td>\n",
       "      <td>0.004</td>\n",
       "      <td>969.0</td>\n",
       "      <td>934.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cutpoints[2]</th>\n",
       "      <td>-1.863</td>\n",
       "      <td>0.179</td>\n",
       "      <td>-2.126</td>\n",
       "      <td>-1.584</td>\n",
       "      <td>0.006</td>\n",
       "      <td>0.004</td>\n",
       "      <td>961.0</td>\n",
       "      <td>989.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cutpoints[3]</th>\n",
       "      <td>-0.842</td>\n",
       "      <td>0.177</td>\n",
       "      <td>-1.094</td>\n",
       "      <td>-0.554</td>\n",
       "      <td>0.006</td>\n",
       "      <td>0.004</td>\n",
       "      <td>951.0</td>\n",
       "      <td>961.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cutpoints[4]</th>\n",
       "      <td>-0.172</td>\n",
       "      <td>0.177</td>\n",
       "      <td>-0.439</td>\n",
       "      <td>0.100</td>\n",
       "      <td>0.006</td>\n",
       "      <td>0.004</td>\n",
       "      <td>948.0</td>\n",
       "      <td>998.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cutpoints[5]</th>\n",
       "      <td>0.735</td>\n",
       "      <td>0.178</td>\n",
       "      <td>0.480</td>\n",
       "      <td>1.018</td>\n",
       "      <td>0.006</td>\n",
       "      <td>0.004</td>\n",
       "      <td>944.0</td>\n",
       "      <td>971.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>delta_[0]</th>\n",
       "      <td>0.261</td>\n",
       "      <td>0.155</td>\n",
       "      <td>0.007</td>\n",
       "      <td>0.473</td>\n",
       "      <td>0.005</td>\n",
       "      <td>0.004</td>\n",
       "      <td>827.0</td>\n",
       "      <td>683.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>delta_[1]</th>\n",
       "      <td>0.142</td>\n",
       "      <td>0.088</td>\n",
       "      <td>0.018</td>\n",
       "      <td>0.259</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.002</td>\n",
       "      <td>931.0</td>\n",
       "      <td>745.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>delta_[2]</th>\n",
       "      <td>0.189</td>\n",
       "      <td>0.109</td>\n",
       "      <td>0.025</td>\n",
       "      <td>0.351</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.002</td>\n",
       "      <td>1236.0</td>\n",
       "      <td>756.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>delta_[3]</th>\n",
       "      <td>0.162</td>\n",
       "      <td>0.100</td>\n",
       "      <td>0.019</td>\n",
       "      <td>0.301</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.002</td>\n",
       "      <td>893.0</td>\n",
       "      <td>519.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>delta_[4]</th>\n",
       "      <td>0.037</td>\n",
       "      <td>0.039</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.076</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>764.0</td>\n",
       "      <td>521.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>delta_[5]</th>\n",
       "      <td>0.089</td>\n",
       "      <td>0.060</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.165</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.001</td>\n",
       "      <td>869.0</td>\n",
       "      <td>788.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>delta_[6]</th>\n",
       "      <td>0.121</td>\n",
       "      <td>0.074</td>\n",
       "      <td>0.015</td>\n",
       "      <td>0.227</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.003</td>\n",
       "      <td>263.0</td>\n",
       "      <td>475.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               mean     sd  hdi_5.5%  hdi_94.5%  mcse_mean  mcse_sd  ess_bulk  \\\n",
       "bA           -0.707  0.041    -0.766     -0.638      0.001    0.001    1156.0   \n",
       "bC           -0.957  0.051    -1.034     -0.873      0.002    0.001    1101.0   \n",
       "bE           -0.371  0.195    -0.653     -0.049      0.006    0.004     974.0   \n",
       "bI           -0.717  0.036    -0.777     -0.664      0.001    0.001    1137.0   \n",
       "cutpoints[0] -3.128  0.181    -3.400     -2.844      0.006    0.004     978.0   \n",
       "cutpoints[1] -2.445  0.180    -2.722     -2.177      0.006    0.004     969.0   \n",
       "cutpoints[2] -1.863  0.179    -2.126     -1.584      0.006    0.004     961.0   \n",
       "cutpoints[3] -0.842  0.177    -1.094     -0.554      0.006    0.004     951.0   \n",
       "cutpoints[4] -0.172  0.177    -0.439      0.100      0.006    0.004     948.0   \n",
       "cutpoints[5]  0.735  0.178     0.480      1.018      0.006    0.004     944.0   \n",
       "delta_[0]     0.261  0.155     0.007      0.473      0.005    0.004     827.0   \n",
       "delta_[1]     0.142  0.088     0.018      0.259      0.003    0.002     931.0   \n",
       "delta_[2]     0.189  0.109     0.025      0.351      0.003    0.002    1236.0   \n",
       "delta_[3]     0.162  0.100     0.019      0.301      0.003    0.002     893.0   \n",
       "delta_[4]     0.037  0.039     0.000      0.076      0.001    0.001     764.0   \n",
       "delta_[5]     0.089  0.060     0.003      0.165      0.002    0.001     869.0   \n",
       "delta_[6]     0.121  0.074     0.015      0.227      0.004    0.003     263.0   \n",
       "\n",
       "              ess_tail  r_hat  \n",
       "bA               876.0   1.00  \n",
       "bC               853.0   1.00  \n",
       "bE               935.0   1.00  \n",
       "bI               971.0   1.00  \n",
       "cutpoints[0]     999.0   1.01  \n",
       "cutpoints[1]     934.0   1.01  \n",
       "cutpoints[2]     989.0   1.01  \n",
       "cutpoints[3]     961.0   1.01  \n",
       "cutpoints[4]     998.0   1.01  \n",
       "cutpoints[5]     971.0   1.01  \n",
       "delta_[0]        683.0   1.00  \n",
       "delta_[1]        745.0   1.00  \n",
       "delta_[2]        756.0   1.00  \n",
       "delta_[3]        519.0   1.00  \n",
       "delta_[4]        521.0   1.00  \n",
       "delta_[5]        788.0   1.01  \n",
       "delta_[6]        475.0   1.00  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary_6 = az.summary(idata_6, hdi_prob=0.89)\n",
    "summary_6"
   ]
  }
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