07_ulysses_compass-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/07_ulysses_compass.ipynb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 7. Ulysses' Compass"
   ]
  },
  {
   "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",
    "from tensorflow_probability.substrates import jax as tfp\n",
    "# import tensorflow_probability as tfp\n",
    "tfd = tfp.distributions\n",
    "tfb = tfp.bijectors\n",
    "\n",
    "plt.rcParams['figure.figsize'] = [6, 4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# global key generator for ch-07 notebook\n",
    "key = tfp.util.SeedStream(7, salt=\"ch-07\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7.1 The problem with parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 7.1.1 More parameters(almost) always improve fit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 7.1\n",
    "\n",
    "\n",
    "Below is a dataset for average brain volumes and body masses for 7 hominin species"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "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>species</th>\n",
       "      <th>brain</th>\n",
       "      <th>mass</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>afarensis</td>\n",
       "      <td>438</td>\n",
       "      <td>37.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>africanus</td>\n",
       "      <td>452</td>\n",
       "      <td>35.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>habilis</td>\n",
       "      <td>612</td>\n",
       "      <td>34.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>boisei</td>\n",
       "      <td>521</td>\n",
       "      <td>41.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>rudolfensis</td>\n",
       "      <td>752</td>\n",
       "      <td>55.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>ergaster</td>\n",
       "      <td>871</td>\n",
       "      <td>61.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>sapiens</td>\n",
       "      <td>1350</td>\n",
       "      <td>53.5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       species  brain  mass\n",
       "0    afarensis    438  37.0\n",
       "1    africanus    452  35.5\n",
       "2      habilis    612  34.5\n",
       "3       boisei    521  41.5\n",
       "4  rudolfensis    752  55.5\n",
       "5     ergaster    871  61.0\n",
       "6      sapiens   1350  53.5"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sppnames = [\n",
    "    \"afarensis\",\n",
    "    \"africanus\",\n",
    "    \"habilis\",\n",
    "    \"boisei\",\n",
    "    \"rudolfensis\",\n",
    "    \"ergaster\",\n",
    "    \"sapiens\",\n",
    "]\n",
    "brainvolcc = jnp.array([438, 452, 612, 521, 752, 871, 1350])\n",
    "masskg = jnp.array([37.0, 35.5, 34.5, 41.5, 55.5, 61.0, 53.5])\n",
    "d = pd.DataFrame({\"species\": sppnames, \"brain\": brainvolcc, \"mass\": masskg})\n",
    "d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Reproducing the figure in the book (there is no code fragment for this in R in the book)\n",
    "plt.scatter(d.mass, d.brain, facecolors=\"none\", edgecolors=\"b\")\n",
    "plt.gca().set(\n",
    "    xlim=(30, 70), xlabel=\"body mass (kg)\", ylim=(400, 1400), ylabel=\"brain volume (cc)\"\n",
    ")\n",
    "\n",
    "for i in range(d.shape[0]):\n",
    "    plt.annotate(d.species[i], (d.mass[i], d.brain[i]))\n",
    "\n",
    "plt.tight_layout();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 7.2\n",
    "\n",
    "\n",
    "Author talks about linear vs polynomial regression. He is of the opinion that most of the time polynomial regression is not a good idea (at least when used blindly). But why ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [],
   "source": [
    "d[\"mass_std\"] = (d.mass - d.mass.mean()) / d.mass.std()\n",
    "d[\"brain_std\"] = d.brain / d.brain.max()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note - brain is not standardized as such because you can not have -ive brain"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 7.3\n",
    "\n",
    "Simplest model is the linear one and this is what we will start with"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_71(mass_std):\n",
    "    def _generator():\n",
    "        alpha = yield tfd.Normal(loc=0.5, scale=1.0, name=\"alpha\")\n",
    "        beta = yield tfd.Normal(loc=0.0, scale=10.0, name=\"beta\")\n",
    "        # sigma = yield tfd.LogNormal(loc=0.0, scale=1.0, name=\"sigma\")\n",
    "        log_sigma = yield tfd.Normal(loc=0.0, scale=1.0, name=\"log_sigma\")\n",
    "        mu = alpha + beta * mass_std\n",
    "        sigma = jnp.exp(log_sigma)\n",
    "        yield tfd.Normal(loc=mu, scale=sigma, name=\"brain_std\")\n",
    "\n",
    "    return tfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_71 = model_71(d.mass_std.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_71_pd = jd_71.experimental_pin(brain_std=d.brain_std.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def target_log_prob_71(*states):\n",
    "    return jd_71_pd.unnormalized_log_prob(states)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jax.jit\n",
    "def sample_post_71(init_state, seed):\n",
    "    kernel = tfp.mcmc.NoUTurnSampler(target_log_prob_71, 1e-3)\n",
    "  \n",
    "    return tfp.mcmc.sample_chain(\n",
    "        num_results=1000,\n",
    "        current_state=init_state,\n",
    "        kernel=kernel,\n",
    "        num_burnin_steps=1000,\n",
    "        trace_fn=None, seed=seed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_chains = 4\n",
    "init_state_71 = jd_71_pd.sample_unpinned(num_chains, seed=key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_71 = sample_post_71(init_state_71, key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_71_dict = {k: jnp.moveaxis(v, 0, 1) for k, v in post_71._asdict().items()}\n",
    "dict_71 = dict(posterior=post_71_dict)\n",
    "idata_71 = az.from_dict(**dict_71)"
   ]
  },
  {
   "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>hdi_3%</th>\n",
       "      <th>hdi_97%</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>alpha</th>\n",
       "      <td>0.527</td>\n",
       "      <td>0.114</td>\n",
       "      <td>0.318</td>\n",
       "      <td>0.750</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>2906.0</td>\n",
       "      <td>1802.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta</th>\n",
       "      <td>0.166</td>\n",
       "      <td>0.126</td>\n",
       "      <td>-0.064</td>\n",
       "      <td>0.396</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.002</td>\n",
       "      <td>2711.0</td>\n",
       "      <td>1511.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>log_sigma</th>\n",
       "      <td>-1.370</td>\n",
       "      <td>0.392</td>\n",
       "      <td>-2.102</td>\n",
       "      <td>-0.661</td>\n",
       "      <td>0.017</td>\n",
       "      <td>0.012</td>\n",
       "      <td>525.0</td>\n",
       "      <td>838.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  ess_bulk  \\\n",
       "alpha      0.527  0.114   0.318    0.750      0.002    0.002    2906.0   \n",
       "beta       0.166  0.126  -0.064    0.396      0.003    0.002    2711.0   \n",
       "log_sigma -1.370  0.392  -2.102   -0.661      0.017    0.012     525.0   \n",
       "\n",
       "           ess_tail  r_hat  \n",
       "alpha        1802.0    1.0  \n",
       "beta         1511.0    1.0  \n",
       "log_sigma     838.0    1.0  "
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata_71)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Code 7.4\n",
    "\n",
    "OLS and Bayesian anti-essentialism. \n",
    "\n",
    "Use OLS for the above model. Author has used R's lm package so here we are using statsmodel (..sort of python counterpart to R's lm package) to do oridinary least square.\n",
    "\n",
    "The OLS from the non bayesian statistics is going to provide the point estimates (which would to some extent correspond to the mean (mu) if flat priors are used). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note - In the text book you would see\n",
    "\n",
    "```\n",
    "m7.1_OLS <- lm( brain_std ~ mass_std , data=d ) \n",
    "post <- extract.samples( m7.1_OLS )\n",
    "```\n",
    "\n",
    "extract.samples( m7.1_OLS ) is in the source file https://github.com/rmcelreath/rethinking/blob/master/R/map-quap-class.r\n",
    "\n",
    "Below I have replicated the code for extract.samples for (non-bayesian OLS) using statsmodel & tensorflow probabilty"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Intercept    0.528677\n",
       " mass_std     0.167118\n",
       " dtype: float64,\n",
       "               Intercept      mass_std\n",
       " Intercept  4.980017e-03  2.473601e-11\n",
       " mass_std   2.473601e-11  5.810020e-03)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Use statsmodel OLS\n",
    "m_7_1_OLS = smf.ols(\"brain_std ~ mass_std\", data=d).fit()\n",
    "m_7_1_OLS.params, m_7_1_OLS.cov_params()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "mu = jnp.array(m_7_1_OLS.params)\n",
    "cov = jnp.array(m_7_1_OLS.cov_params())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# we can build a multivariate normal distribution using the mu & cov obtained\n",
    "# from the non bayesian land\n",
    "mvn = tfd.MultivariateNormalFullCovariance(loc=mu, covariance_matrix=cov)\n",
    "posterior = mvn.sample(10000, seed=key())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 7.5\n",
    "\n",
    "\n",
    "Variance explained or $R^2$ is defined as:\n",
    "\n",
    "$R^2$ = 1 - $\\frac{var(residuals)}{var(outcome)}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_pred_71 = jd_71.sample(500, value=post_71, seed=key())._asdict()['brain_std']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(500, 1000, 4, 7)"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# (sample, draw, chain, obs)\n",
    "post_pred_71.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "# mean through [sample, draw, chain]\n",
    "mu = post_pred_71.mean(axis=[0, 1, 2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [],
   "source": [
    "r = mu - d.brain_std.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array(0.5227264, dtype=float32)"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "resid_var = jnp.var(r)\n",
    "outcome_var = jnp.var(d.brain_std.values)\n",
    "1 - (resid_var / outcome_var)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### fit sigma LogNormal directly"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_71(mass_std):\n",
    "    def _generator():\n",
    "        alpha = yield tfd.Normal(loc=0.5, scale=1.0, name=\"alpha\")\n",
    "        beta = yield tfd.Normal(loc=0.0, scale=10.0, name=\"beta\")\n",
    "        sigma = yield tfd.LogNormal(loc=0.0, scale=1.0, name=\"sigma\")\n",
    "        mu = alpha + beta * mass_std\n",
    "        yield tfd.Normal(loc=mu, scale=sigma, name=\"brain_std\")\n",
    "\n",
    "    return tfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_71 = model_71(d.mass_std.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_71_pd = jd_71.experimental_pin(brain_std=d.brain_std.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [],
   "source": [
    "def target_log_prob_71(*states):\n",
    "    return jd_71_pd.unnormalized_log_prob(states)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [],
   "source": [
    "# @jax.jit\n",
    "def sample_post_71(init_state, seed):\n",
    "    kernel = tfp.mcmc.NoUTurnSampler(target_log_prob_71, 1e-3)\n",
    "  \n",
    "    return tfp.mcmc.sample_chain(\n",
    "        num_results=1000,\n",
    "        current_state=init_state,\n",
    "        kernel=kernel,\n",
    "        num_burnin_steps=1000,\n",
    "        trace_fn=None, seed=seed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_chains = 4\n",
    "init_state_71 = jd_71_pd.sample_unpinned(num_chains, seed=key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_71 = sample_post_71(init_state_71, key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_71_dict = {k: jnp.moveaxis(v, 0, 1) for k, v in post_71._asdict().items()}\n",
    "dict_71 = dict(posterior=post_71_dict)\n",
    "idata_71 = az.from_dict(**dict_71)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "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_3%</th>\n",
       "      <th>hdi_97%</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>alpha</th>\n",
       "      <td>0.527</td>\n",
       "      <td>0.107</td>\n",
       "      <td>0.329</td>\n",
       "      <td>0.723</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>1963.0</td>\n",
       "      <td>1595.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta</th>\n",
       "      <td>0.167</td>\n",
       "      <td>0.118</td>\n",
       "      <td>-0.045</td>\n",
       "      <td>0.385</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.002</td>\n",
       "      <td>1540.0</td>\n",
       "      <td>1313.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma</th>\n",
       "      <td>0.268</td>\n",
       "      <td>0.113</td>\n",
       "      <td>0.109</td>\n",
       "      <td>0.468</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.003</td>\n",
       "      <td>968.0</td>\n",
       "      <td>1107.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  ess_bulk  ess_tail  \\\n",
       "alpha  0.527  0.107   0.329    0.723      0.002    0.002    1963.0    1595.0   \n",
       "beta   0.167  0.118  -0.045    0.385      0.003    0.002    1540.0    1313.0   \n",
       "sigma  0.268  0.113   0.109    0.468      0.004    0.003     968.0    1107.0   \n",
       "\n",
       "       r_hat  \n",
       "alpha    1.0  \n",
       "beta     1.0  \n",
       "sigma    1.0  "
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata_71)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 7.7\n",
    "\n",
    "Building some more models to compare to m7.1\n",
    "\n",
    "This one is a poymomial of second degree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_72(mass_std):\n",
    "    def _generator():\n",
    "        alpha = yield tfd.Normal(loc=0.5, scale=1.0, name=\"alpha\")\n",
    "        beta1 = yield tfd.Normal(loc=0.0, scale=10.0, name=\"beta1\")\n",
    "        beta2 = yield tfd.Normal(loc=0.0, scale=10.0, name=\"beta2\")\n",
    "        sigma = yield tfd.LogNormal(loc=0.0, scale=1.0, name=\"sigma\")\n",
    "        mu = alpha + beta1 * mass_std + beta2 * (mass_std**2)\n",
    "        yield tfd.Normal(loc=mu, scale=sigma, name=\"brain_std\")\n",
    "\n",
    "    return tfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_72 = model_72(d.mass_std.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_72_pd = jd_72.experimental_pin(brain_std=d.brain_std.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def target_log_prob_72(*states):\n",
    "    return jd_72_pd.unnormalized_log_prob(states)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jax.jit\n",
    "def sample_post_72(init_state, seed):\n",
    "    kernel = tfp.mcmc.NoUTurnSampler(target_log_prob_72, 1e-3)\n",
    "  \n",
    "    return tfp.mcmc.sample_chain(\n",
    "        num_results=1000,\n",
    "        current_state=init_state,\n",
    "        kernel=kernel,\n",
    "        num_burnin_steps=1000,\n",
    "        trace_fn=None, seed=seed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_chains = 4\n",
    "init_state_72 = jd_72_pd.sample_unpinned(num_chains, seed=key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_72 = sample_post_72(init_state_72, key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_72_dict = {k: jnp.moveaxis(v, 0, 1) for k, v in post_72._asdict().items()}\n",
    "dict_72 = dict(posterior=post_72_dict)\n",
    "idata_72 = az.from_dict(**dict_72)"
   ]
  },
  {
   "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_3%</th>\n",
       "      <th>hdi_97%</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>alpha</th>\n",
       "      <td>0.615</td>\n",
       "      <td>0.243</td>\n",
       "      <td>0.192</td>\n",
       "      <td>1.090</td>\n",
       "      <td>0.009</td>\n",
       "      <td>0.007</td>\n",
       "      <td>710.0</td>\n",
       "      <td>616.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta1</th>\n",
       "      <td>0.197</td>\n",
       "      <td>0.155</td>\n",
       "      <td>-0.098</td>\n",
       "      <td>0.493</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.003</td>\n",
       "      <td>1339.0</td>\n",
       "      <td>1571.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta2</th>\n",
       "      <td>-0.096</td>\n",
       "      <td>0.256</td>\n",
       "      <td>-0.560</td>\n",
       "      <td>0.411</td>\n",
       "      <td>0.010</td>\n",
       "      <td>0.007</td>\n",
       "      <td>683.0</td>\n",
       "      <td>524.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma</th>\n",
       "      <td>0.305</td>\n",
       "      <td>0.154</td>\n",
       "      <td>0.120</td>\n",
       "      <td>0.590</td>\n",
       "      <td>0.008</td>\n",
       "      <td>0.005</td>\n",
       "      <td>533.0</td>\n",
       "      <td>692.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  ess_bulk  ess_tail  \\\n",
       "alpha  0.615  0.243   0.192    1.090      0.009    0.007     710.0     616.0   \n",
       "beta1  0.197  0.155  -0.098    0.493      0.004    0.003    1339.0    1571.0   \n",
       "beta2 -0.096  0.256  -0.560    0.411      0.010    0.007     683.0     524.0   \n",
       "sigma  0.305  0.154   0.120    0.590      0.008    0.005     533.0     692.0   \n",
       "\n",
       "       r_hat  \n",
       "alpha   1.01  \n",
       "beta1   1.00  \n",
       "beta2   1.01  \n",
       "sigma   1.01  "
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata_72)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "d['mass_std_2'] = d['mass_std'].pow(2)\n",
    "d['mass_std_3'] = d['mass_std'].pow(3)\n",
    "d['mass_std_4'] = d['mass_std'].pow(4)\n",
    "d['mass_std_5'] = d['mass_std'].pow(5)\n",
    "d['mass_std_6'] = d['mass_std'].pow(6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gen_model(mass):\n",
    "    ncol = mass.shape[1]\n",
    "    def _generator():\n",
    "        alpha = yield tfd.Normal(loc=0.5, scale=1.0, name=\"alpha\")\n",
    "        beta = yield tfd.Sample(\n",
    "            tfd.Normal(loc=0.0, scale=10.0), sample_shape=ncol, name=\"beta\")\n",
    "        sigma = yield tfd.LogNormal(loc=0.0, scale=1.0, name=\"sigma\")\n",
    "        # match dims with output: (nobs,) not (1, nobs)\n",
    "        mu = alpha + jnp.matmul(beta, mass.T) \n",
    "        yield tfd.Normal(loc=mu, scale=sigma, name=\"brain_std\")\n",
    "\n",
    "    return tfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "mass_2 = d[['mass_std', 'mass_std_2']].to_numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_72 = gen_model(mass_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_72_pd = jd_72.experimental_pin(brain_std=d.brain_std.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [],
   "source": [
    "def target_log_prob_72(*states):\n",
    "    return jd_72_pd.unnormalized_log_prob(states)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jax.jit\n",
    "def sample_post_72(init_state, seed):\n",
    "    kernel = tfp.mcmc.NoUTurnSampler(target_log_prob_72, 1e-3)\n",
    "  \n",
    "    return tfp.mcmc.sample_chain(\n",
    "        num_results=1000,\n",
    "        current_state=init_state,\n",
    "        kernel=kernel,\n",
    "        num_burnin_steps=1000,\n",
    "        trace_fn=None, seed=seed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_chains = 4\n",
    "init_state_72 = jd_72_pd.sample_unpinned(num_chains, seed=key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_72 = sample_post_72(init_state_72, key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_72_dict = {k: jnp.moveaxis(v, 0, 1) for k, v in post_72._asdict().items()}\n",
    "dict_72 = dict(posterior=post_72_dict,\n",
    "               dims={\"beta\": [\"coef\"]},\n",
    "               coords={\"coef\": ['1', '2']})\n",
    "idata_72 = az.from_dict(**dict_72)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "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_3%</th>\n",
       "      <th>hdi_97%</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>alpha</th>\n",
       "      <td>0.557</td>\n",
       "      <td>0.243</td>\n",
       "      <td>0.221</td>\n",
       "      <td>1.058</td>\n",
       "      <td>0.052</td>\n",
       "      <td>0.037</td>\n",
       "      <td>19.0</td>\n",
       "      <td>800.0</td>\n",
       "      <td>1.15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta[1]</th>\n",
       "      <td>-2.013</td>\n",
       "      <td>3.830</td>\n",
       "      <td>-8.643</td>\n",
       "      <td>0.388</td>\n",
       "      <td>1.907</td>\n",
       "      <td>1.461</td>\n",
       "      <td>7.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.53</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta[2]</th>\n",
       "      <td>0.013</td>\n",
       "      <td>0.302</td>\n",
       "      <td>-0.512</td>\n",
       "      <td>0.372</td>\n",
       "      <td>0.105</td>\n",
       "      <td>0.077</td>\n",
       "      <td>10.0</td>\n",
       "      <td>703.0</td>\n",
       "      <td>1.34</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma</th>\n",
       "      <td>0.249</td>\n",
       "      <td>0.150</td>\n",
       "      <td>0.098</td>\n",
       "      <td>0.499</td>\n",
       "      <td>0.043</td>\n",
       "      <td>0.031</td>\n",
       "      <td>7.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.52</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  ess_bulk  \\\n",
       "alpha    0.557  0.243   0.221    1.058      0.052    0.037      19.0   \n",
       "beta[1] -2.013  3.830  -8.643    0.388      1.907    1.461       7.0   \n",
       "beta[2]  0.013  0.302  -0.512    0.372      0.105    0.077      10.0   \n",
       "sigma    0.249  0.150   0.098    0.499      0.043    0.031       7.0   \n",
       "\n",
       "         ess_tail  r_hat  \n",
       "alpha       800.0   1.15  \n",
       "beta[1]       4.0   1.53  \n",
       "beta[2]     703.0   1.34  \n",
       "sigma         4.0   1.52  "
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata_72)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "mass_3 = d[['mass_std', 'mass_std_2', 'mass_std_3']].to_numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_73 = gen_model(mass_3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_73_pd = jd_73.experimental_pin(brain_std=d.brain_std.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "def target_log_prob_73(*states):\n",
    "    return jd_73_pd.unnormalized_log_prob(states)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jax.jit\n",
    "def sample_post_73(init_state, seed):\n",
    "    kernel = tfp.mcmc.NoUTurnSampler(target_log_prob_73, 1e-3)\n",
    "  \n",
    "    return tfp.mcmc.sample_chain(\n",
    "        num_results=1000,\n",
    "        current_state=init_state,\n",
    "        kernel=kernel,\n",
    "        num_burnin_steps=1000,\n",
    "        trace_fn=None, seed=seed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_chains = 4\n",
    "init_state_73 = jd_73_pd.sample_unpinned(num_chains, seed=key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_73 = sample_post_73(init_state_73, key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_73_dict = {k: jnp.moveaxis(v, 0, 1) for k, v in post_73._asdict().items()}\n",
    "dict_73 = dict(posterior=post_73_dict,\n",
    "                 dims={\"beta\": [\"coef\"]},\n",
    "                 coords={\"coef\": ['1', '2', '3']})\n",
    "idata_73 = az.from_dict(**dict_73)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "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_3%</th>\n",
       "      <th>hdi_97%</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>alpha</th>\n",
       "      <td>0.528</td>\n",
       "      <td>0.287</td>\n",
       "      <td>0.017</td>\n",
       "      <td>1.096</td>\n",
       "      <td>0.011</td>\n",
       "      <td>0.009</td>\n",
       "      <td>710.0</td>\n",
       "      <td>819.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta[1]</th>\n",
       "      <td>0.440</td>\n",
       "      <td>0.408</td>\n",
       "      <td>-0.267</td>\n",
       "      <td>1.286</td>\n",
       "      <td>0.020</td>\n",
       "      <td>0.017</td>\n",
       "      <td>563.0</td>\n",
       "      <td>461.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta[2]</th>\n",
       "      <td>0.071</td>\n",
       "      <td>0.363</td>\n",
       "      <td>-0.603</td>\n",
       "      <td>0.745</td>\n",
       "      <td>0.016</td>\n",
       "      <td>0.012</td>\n",
       "      <td>597.0</td>\n",
       "      <td>716.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta[3]</th>\n",
       "      <td>-0.246</td>\n",
       "      <td>0.363</td>\n",
       "      <td>-1.036</td>\n",
       "      <td>0.363</td>\n",
       "      <td>0.018</td>\n",
       "      <td>0.014</td>\n",
       "      <td>518.0</td>\n",
       "      <td>425.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma</th>\n",
       "      <td>0.327</td>\n",
       "      <td>0.184</td>\n",
       "      <td>0.107</td>\n",
       "      <td>0.654</td>\n",
       "      <td>0.011</td>\n",
       "      <td>0.008</td>\n",
       "      <td>379.0</td>\n",
       "      <td>304.0</td>\n",
       "      <td>1.02</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  ess_bulk  \\\n",
       "alpha    0.528  0.287   0.017    1.096      0.011    0.009     710.0   \n",
       "beta[1]  0.440  0.408  -0.267    1.286      0.020    0.017     563.0   \n",
       "beta[2]  0.071  0.363  -0.603    0.745      0.016    0.012     597.0   \n",
       "beta[3] -0.246  0.363  -1.036    0.363      0.018    0.014     518.0   \n",
       "sigma    0.327  0.184   0.107    0.654      0.011    0.008     379.0   \n",
       "\n",
       "         ess_tail  r_hat  \n",
       "alpha       819.0   1.01  \n",
       "beta[1]     461.0   1.01  \n",
       "beta[2]     716.0   1.01  \n",
       "beta[3]     425.0   1.01  \n",
       "sigma       304.0   1.02  "
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata_73)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {},
   "outputs": [],
   "source": [
    "mass_new = pd.DataFrame({'mass_seq': np.linspace(d.mass_std.min(), d.mass_std.max(), num=100)})\n",
    "mass_new['mass_seq_2'] = mass_new['mass_seq'].pow(2)\n",
    "mass_new['mass_seq_3'] = mass_new['mass_seq'].pow(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_73_new = gen_model(mass_new.to_numpy())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_pred_73_new = jd_73_new.sample(500, value=post_73, seed=key())[-1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(500, 1000, 4, 100)"
      ]
     },
     "execution_count": 163,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# (sample, draw, chain, obs)\n",
    "post_pred_73_new[0].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4, 1000, 100, 500)"
      ]
     },
     "execution_count": 164,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "post_pred_73_new_dict = {k: jnp.moveaxis(v, (0, 2), (-1, 0)) \\\n",
    "                         for k, v in post_pred_73_new._asdict().items()}\n",
    "# (chain, draw, obs, sample)\n",
    "post_pred_73_new_dict['brain_std'].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {},
   "outputs": [],
   "source": [
    "mass_newx = xr.DataArray(mass_new.to_numpy(), dims=['obs', 'coef'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Coordinates:\n",
       "  * chain    (chain) int64 32B 0 1 2 3\n",
       "  * draw     (draw) int64 8kB 0 1 2 3 4 5 6 7 ... 993 994 995 996 997 998 999\n",
       "  * coef     (coef) <U1 12B '1' '2' '3'"
      ]
     },
     "execution_count": 168,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "idata_73.posterior[\"beta\"].coords"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4, 1000, 100)"
      ]
     },
     "execution_count": 169,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# calculate mu using idata\n",
    "# dot operation through dims both have. here 'coef'\n",
    "mu = idata_73.posterior[\"alpha\"] + idata_73.posterior[\"beta\"].dot(mass_newx)\n",
    "mu.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {},
   "outputs": [],
   "source": [
    "mu_mean = mu.mean(dim=['chain', 'draw'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {},
   "outputs": [],
   "source": [
    "mass_seqx = xr.DataArray(mass_new['mass_seq'].to_numpy())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_lm(y=mu_mean, x=mass_seqx, y_model=mu, kind_pp=\"hdi\", kind_model=\"hdi\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "mass_4 = d[['mass_std', 'mass_std_2', 'mass_std_3', 'mass_std_4']].to_numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_74 = gen_model(mass_4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_74_pd = jd_74.experimental_pin(brain_std=d.brain_std.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "def target_log_prob_74(*states):\n",
    "    return jd_74_pd.unnormalized_log_prob(states)\n",
    "\n",
    "@jax.jit\n",
    "def sample_post_74(init_state, seed):\n",
    "    kernel = tfp.mcmc.NoUTurnSampler(target_log_prob_74, 1e-3)\n",
    "  \n",
    "    return tfp.mcmc.sample_chain(\n",
    "        num_results=1000,\n",
    "        current_state=init_state,\n",
    "        kernel=kernel,\n",
    "        num_burnin_steps=1000,\n",
    "        trace_fn=None, seed=seed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_chains = 4\n",
    "init_state_74 = jd_74_pd.sample_unpinned(num_chains, seed=key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_74 = sample_post_74(init_state_74, key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_74_dict = {k: jnp.moveaxis(v, 0, 1) for k, v in post_74._asdict().items()}\n",
    "dict_74 = dict(posterior=post_74_dict,\n",
    "                 dims={\"beta\": [\"coef\"]},\n",
    "                 coords={\"coef\": ['1', '2', '3', '4']})\n",
    "idata_74 = az.from_dict(**dict_74)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "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_3%</th>\n",
       "      <th>hdi_97%</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>alpha</th>\n",
       "      <td>0.764</td>\n",
       "      <td>0.543</td>\n",
       "      <td>-0.321</td>\n",
       "      <td>1.828</td>\n",
       "      <td>0.079</td>\n",
       "      <td>0.056</td>\n",
       "      <td>49.0</td>\n",
       "      <td>134.0</td>\n",
       "      <td>1.07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta[1]</th>\n",
       "      <td>0.766</td>\n",
       "      <td>0.804</td>\n",
       "      <td>-1.043</td>\n",
       "      <td>2.196</td>\n",
       "      <td>0.115</td>\n",
       "      <td>0.082</td>\n",
       "      <td>45.0</td>\n",
       "      <td>154.0</td>\n",
       "      <td>1.08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta[2]</th>\n",
       "      <td>-0.795</td>\n",
       "      <td>1.621</td>\n",
       "      <td>-3.967</td>\n",
       "      <td>2.449</td>\n",
       "      <td>0.289</td>\n",
       "      <td>0.206</td>\n",
       "      <td>32.0</td>\n",
       "      <td>73.0</td>\n",
       "      <td>1.10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta[3]</th>\n",
       "      <td>-0.692</td>\n",
       "      <td>0.975</td>\n",
       "      <td>-2.549</td>\n",
       "      <td>1.358</td>\n",
       "      <td>0.155</td>\n",
       "      <td>0.111</td>\n",
       "      <td>38.0</td>\n",
       "      <td>136.0</td>\n",
       "      <td>1.09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta[4]</th>\n",
       "      <td>0.583</td>\n",
       "      <td>1.085</td>\n",
       "      <td>-1.372</td>\n",
       "      <td>2.913</td>\n",
       "      <td>0.196</td>\n",
       "      <td>0.140</td>\n",
       "      <td>31.0</td>\n",
       "      <td>83.0</td>\n",
       "      <td>1.10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma</th>\n",
       "      <td>0.373</td>\n",
       "      <td>0.248</td>\n",
       "      <td>0.094</td>\n",
       "      <td>0.772</td>\n",
       "      <td>0.015</td>\n",
       "      <td>0.010</td>\n",
       "      <td>308.0</td>\n",
       "      <td>500.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  ess_bulk  \\\n",
       "alpha    0.764  0.543  -0.321    1.828      0.079    0.056      49.0   \n",
       "beta[1]  0.766  0.804  -1.043    2.196      0.115    0.082      45.0   \n",
       "beta[2] -0.795  1.621  -3.967    2.449      0.289    0.206      32.0   \n",
       "beta[3] -0.692  0.975  -2.549    1.358      0.155    0.111      38.0   \n",
       "beta[4]  0.583  1.085  -1.372    2.913      0.196    0.140      31.0   \n",
       "sigma    0.373  0.248   0.094    0.772      0.015    0.010     308.0   \n",
       "\n",
       "         ess_tail  r_hat  \n",
       "alpha       134.0   1.07  \n",
       "beta[1]     154.0   1.08  \n",
       "beta[2]      73.0   1.10  \n",
       "beta[3]     136.0   1.09  \n",
       "beta[4]      83.0   1.10  \n",
       "sigma       500.0   1.00  "
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata_74)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "mass_5 = d[['mass_std', 'mass_std_2', 'mass_std_3',\n",
    "            'mass_std_4', 'mass_std_5']].to_numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_75 = gen_model(mass_5)\n",
    "jd_75_pd = jd_75.experimental_pin(brain_std=d.brain_std.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "def target_log_prob_75(*states):\n",
    "    return jd_75_pd.unnormalized_log_prob(states)\n",
    "\n",
    "@jax.jit\n",
    "def sample_post_75(init_state, seed):\n",
    "    kernel = tfp.mcmc.NoUTurnSampler(target_log_prob_75, 1e-3)\n",
    "  \n",
    "    return tfp.mcmc.sample_chain(\n",
    "        num_results=1000,\n",
    "        current_state=init_state,\n",
    "        kernel=kernel,\n",
    "        num_burnin_steps=1000,\n",
    "        trace_fn=None, seed=seed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_chains = 4\n",
    "init_state_75 = jd_75_pd.sample_unpinned(num_chains, seed=key())\n",
    "post_75 = sample_post_75(init_state_75, key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_75_dict = {k: jnp.moveaxis(v, 0, 1) for k, v in post_75._asdict().items()}\n",
    "dict_75 = dict(posterior=post_75_dict,\n",
    "                 dims={\"beta\": [\"coef\"]},\n",
    "                 coords={\"coef\": ['1', '2', '3', '4', '5']})\n",
    "idata_75 = az.from_dict(**dict_75)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "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_3%</th>\n",
       "      <th>hdi_97%</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>alpha</th>\n",
       "      <td>0.741</td>\n",
       "      <td>0.421</td>\n",
       "      <td>-0.100</td>\n",
       "      <td>1.566</td>\n",
       "      <td>0.051</td>\n",
       "      <td>0.053</td>\n",
       "      <td>48.0</td>\n",
       "      <td>197.0</td>\n",
       "      <td>1.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta[1]</th>\n",
       "      <td>2.282</td>\n",
       "      <td>2.565</td>\n",
       "      <td>-1.021</td>\n",
       "      <td>6.285</td>\n",
       "      <td>1.186</td>\n",
       "      <td>0.966</td>\n",
       "      <td>6.0</td>\n",
       "      <td>39.0</td>\n",
       "      <td>1.71</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta[2]</th>\n",
       "      <td>2.012</td>\n",
       "      <td>4.809</td>\n",
       "      <td>-2.506</td>\n",
       "      <td>10.081</td>\n",
       "      <td>2.322</td>\n",
       "      <td>1.828</td>\n",
       "      <td>7.0</td>\n",
       "      <td>157.0</td>\n",
       "      <td>1.54</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta[3]</th>\n",
       "      <td>-0.683</td>\n",
       "      <td>2.427</td>\n",
       "      <td>-4.782</td>\n",
       "      <td>4.350</td>\n",
       "      <td>0.626</td>\n",
       "      <td>0.451</td>\n",
       "      <td>16.0</td>\n",
       "      <td>37.0</td>\n",
       "      <td>1.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta[4]</th>\n",
       "      <td>-0.657</td>\n",
       "      <td>2.149</td>\n",
       "      <td>-3.913</td>\n",
       "      <td>2.093</td>\n",
       "      <td>0.939</td>\n",
       "      <td>0.722</td>\n",
       "      <td>7.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.54</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta[5]</th>\n",
       "      <td>3.220</td>\n",
       "      <td>5.333</td>\n",
       "      <td>-2.012</td>\n",
       "      <td>12.217</td>\n",
       "      <td>2.602</td>\n",
       "      <td>2.032</td>\n",
       "      <td>7.0</td>\n",
       "      <td>43.0</td>\n",
       "      <td>1.68</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma</th>\n",
       "      <td>0.287</td>\n",
       "      <td>0.282</td>\n",
       "      <td>0.039</td>\n",
       "      <td>0.777</td>\n",
       "      <td>0.072</td>\n",
       "      <td>0.052</td>\n",
       "      <td>8.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.49</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  ess_bulk  \\\n",
       "alpha    0.741  0.421  -0.100    1.566      0.051    0.053      48.0   \n",
       "beta[1]  2.282  2.565  -1.021    6.285      1.186    0.966       6.0   \n",
       "beta[2]  2.012  4.809  -2.506   10.081      2.322    1.828       7.0   \n",
       "beta[3] -0.683  2.427  -4.782    4.350      0.626    0.451      16.0   \n",
       "beta[4] -0.657  2.149  -3.913    2.093      0.939    0.722       7.0   \n",
       "beta[5]  3.220  5.333  -2.012   12.217      2.602    2.032       7.0   \n",
       "sigma    0.287  0.282   0.039    0.777      0.072    0.052       8.0   \n",
       "\n",
       "         ess_tail  r_hat  \n",
       "alpha       197.0   1.20  \n",
       "beta[1]      39.0   1.71  \n",
       "beta[2]     157.0   1.54  \n",
       "beta[3]      37.0   1.20  \n",
       "beta[4]       4.0   1.54  \n",
       "beta[5]      43.0   1.68  \n",
       "sigma         4.0   1.49  "
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata_75)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "mass_6 = d[['mass_std', 'mass_std_2', 'mass_std_3',\n",
    "            'mass_std_4', 'mass_std_5', 'mass_std_6']].to_numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_76 = gen_model(mass_6)\n",
    "jd_76_pd = jd_76.experimental_pin(brain_std=d.brain_std.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "def target_log_prob_76(*states):\n",
    "    return jd_76_pd.unnormalized_log_prob(states)\n",
    "\n",
    "# @jax.jit\n",
    "def sample_post_76(init_state, seed):\n",
    "    kernel = tfp.mcmc.NoUTurnSampler(target_log_prob_76, 1e-3)\n",
    "  \n",
    "    return tfp.mcmc.sample_chain(\n",
    "        num_results=1000,\n",
    "        current_state=init_state,\n",
    "        kernel=kernel,\n",
    "        num_burnin_steps=1000,\n",
    "        trace_fn=None, seed=seed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_chains = 4\n",
    "init_state_76 = jd_76_pd.sample_unpinned(num_chains, seed=key())\n",
    "post_76 = sample_post_76(init_state_76, key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_76_dict = {k: jnp.moveaxis(v, 0, 1) for k, v in post_76._asdict().items()}\n",
    "dict_76 = dict(posterior=post_76_dict,\n",
    "                 dims={\"beta\": [\"coef\"]},\n",
    "                 coords={\"coef\": ['1', '2', '3', '4', '5', '6']})\n",
    "idata_76 = az.from_dict(**dict_76)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "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_3%</th>\n",
       "      <th>hdi_97%</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>alpha</th>\n",
       "      <td>0.481</td>\n",
       "      <td>0.598</td>\n",
       "      <td>-0.478</td>\n",
       "      <td>1.788</td>\n",
       "      <td>0.199</td>\n",
       "      <td>0.145</td>\n",
       "      <td>11.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>1.83</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta[1]</th>\n",
       "      <td>2.668</td>\n",
       "      <td>3.530</td>\n",
       "      <td>-1.394</td>\n",
       "      <td>8.283</td>\n",
       "      <td>1.680</td>\n",
       "      <td>1.329</td>\n",
       "      <td>6.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>1.95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta[2]</th>\n",
       "      <td>-0.648</td>\n",
       "      <td>4.411</td>\n",
       "      <td>-6.606</td>\n",
       "      <td>5.650</td>\n",
       "      <td>2.026</td>\n",
       "      <td>1.532</td>\n",
       "      <td>6.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta[3]</th>\n",
       "      <td>0.256</td>\n",
       "      <td>3.403</td>\n",
       "      <td>-6.832</td>\n",
       "      <td>6.527</td>\n",
       "      <td>1.253</td>\n",
       "      <td>0.923</td>\n",
       "      <td>8.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>1.47</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta[4]</th>\n",
       "      <td>-1.281</td>\n",
       "      <td>5.309</td>\n",
       "      <td>-9.985</td>\n",
       "      <td>7.741</td>\n",
       "      <td>2.357</td>\n",
       "      <td>1.773</td>\n",
       "      <td>6.0</td>\n",
       "      <td>18.0</td>\n",
       "      <td>1.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta[5]</th>\n",
       "      <td>2.341</td>\n",
       "      <td>5.399</td>\n",
       "      <td>-3.569</td>\n",
       "      <td>11.044</td>\n",
       "      <td>2.603</td>\n",
       "      <td>2.042</td>\n",
       "      <td>5.0</td>\n",
       "      <td>39.0</td>\n",
       "      <td>2.09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta[6]</th>\n",
       "      <td>1.112</td>\n",
       "      <td>2.141</td>\n",
       "      <td>-2.639</td>\n",
       "      <td>5.091</td>\n",
       "      <td>0.895</td>\n",
       "      <td>0.669</td>\n",
       "      <td>6.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>1.83</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma</th>\n",
       "      <td>0.351</td>\n",
       "      <td>0.344</td>\n",
       "      <td>0.023</td>\n",
       "      <td>0.883</td>\n",
       "      <td>0.051</td>\n",
       "      <td>0.036</td>\n",
       "      <td>81.0</td>\n",
       "      <td>102.0</td>\n",
       "      <td>1.38</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  ess_bulk  \\\n",
       "alpha    0.481  0.598  -0.478    1.788      0.199    0.145      11.0   \n",
       "beta[1]  2.668  3.530  -1.394    8.283      1.680    1.329       6.0   \n",
       "beta[2] -0.648  4.411  -6.606    5.650      2.026    1.532       6.0   \n",
       "beta[3]  0.256  3.403  -6.832    6.527      1.253    0.923       8.0   \n",
       "beta[4] -1.281  5.309  -9.985    7.741      2.357    1.773       6.0   \n",
       "beta[5]  2.341  5.399  -3.569   11.044      2.603    2.042       5.0   \n",
       "beta[6]  1.112  2.141  -2.639    5.091      0.895    0.669       6.0   \n",
       "sigma    0.351  0.344   0.023    0.883      0.051    0.036      81.0   \n",
       "\n",
       "         ess_tail  r_hat  \n",
       "alpha        16.0   1.83  \n",
       "beta[1]      30.0   1.95  \n",
       "beta[2]       4.0   1.90  \n",
       "beta[3]      14.0   1.47  \n",
       "beta[4]      18.0   1.98  \n",
       "beta[5]      39.0   2.09  \n",
       "beta[6]      16.0   1.83  \n",
       "sigma       102.0   1.38  "
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata_76)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 7.2.3 From entropy to accuracy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 7.2.4 Estimating divergence"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 7.13"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# BUG: jd.sample_distributions(value) works only with zero dim values  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(StructTuple(\n",
       "   alpha=<tfp.distributions.Normal 'alpha' batch_shape=[] event_shape=[] dtype=float32>,\n",
       "   beta=<tfp.distributions.Normal 'beta' batch_shape=[] event_shape=[] dtype=float32>,\n",
       "   log_sigma=<tfp.distributions.Normal 'log_sigma' batch_shape=[] event_shape=[] dtype=float32>,\n",
       "   brain_std=<tfp.distributions.Normal 'brain_std' batch_shape=[7] event_shape=[] dtype=float32>\n",
       " ),\n",
       " StructTuple(\n",
       "   alpha=Array(0., dtype=float32),\n",
       "   beta=Array(-0.2, dtype=float32),\n",
       "   log_sigma=Array(6.1, dtype=float32),\n",
       "   brain_std=Array([ 726.3438 , -742.3146 , -258.90024,   83.36224,  274.41556,\n",
       "            -126.8707 ,  676.07635], dtype=float32)\n",
       " ))"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "jd_71.sample_distributions(value=[0.0, -0.2, 6.1], seed=key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(StructTuple(\n",
       "   alpha=<tfp.distributions.Normal 'alpha' batch_shape=[] event_shape=[] dtype=float32>,\n",
       "   beta=<tfp.distributions.Normal 'beta' batch_shape=[] event_shape=[] dtype=float32>,\n",
       "   log_sigma=<tfp.distributions.Normal 'log_sigma' batch_shape=[] event_shape=[] dtype=float32>,\n",
       "   brain_std=<tfp.distributions.Normal 'brain_std' batch_shape=[7] event_shape=[] dtype=float32>\n",
       " ),\n",
       " StructTuple(\n",
       "   alpha=Array(0., dtype=float32),\n",
       "   beta=Array(-0.2, dtype=float32),\n",
       "   log_sigma=Array(6.1, dtype=float32),\n",
       "   brain_std=Array([-711.87915 ,  186.92088 ,  319.87506 ,  437.5431  ,  144.0621  ,\n",
       "            -202.03775 ,    6.832624], dtype=float32)\n",
       " ))"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "StateTuple = namedtuple('StateTuple', ['alpha', 'beta', 'sigma'])\n",
    "jd_71.sample_distributions(value=StateTuple(0.0, -0.2, 6.1), seed=key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "Attempt to convert a value (<object object at 0x321ac2350>) with an unsupported type (<class 'object'>) to a Tensor.",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[64], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mjd_71\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43msample_distributions\u001b[49m\u001b[43m(\u001b[49m\u001b[43mvalue\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mStateTuple\u001b[49m\u001b[43m(\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;241;43m0.0\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m0.0\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;241;43m-\u001b[39;49m\u001b[38;5;241;43m0.2\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m0.0\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;241;43m6.1\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m5.4\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mseed\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mkey\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/miniforge3/envs/dl/lib/python3.12/site-packages/tensorflow_probability/substrates/jax/distributions/joint_distribution.py:524\u001b[0m, in \u001b[0;36mJointDistribution.sample_distributions\u001b[0;34m(self, sample_shape, seed, value, name, **kwargs)\u001b[0m\n\u001b[1;32m    520\u001b[0m value \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_resolve_value(value\u001b[38;5;241m=\u001b[39mvalue,\n\u001b[1;32m    521\u001b[0m                             allow_partially_specified\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mTrue\u001b[39;00m,\n\u001b[1;32m    522\u001b[0m                             \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n\u001b[1;32m    523\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[0;32m--> 524\u001b[0m   ds, xs \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_call_flat_sample_distributions\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m    525\u001b[0m \u001b[43m      \u001b[49m\u001b[43msample_shape\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mseed\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mseed\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mvalue\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mvalue\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    526\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mTypeError\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m e:\n\u001b[1;32m    527\u001b[0m   \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mFailed to convert elements\u001b[39m\u001b[38;5;124m'\u001b[39m \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mstr\u001b[39m(e):\n",
      "File \u001b[0;32m~/miniforge3/envs/dl/lib/python3.12/site-packages/tensorflow_probability/substrates/jax/distributions/joint_distribution.py:548\u001b[0m, in \u001b[0;36mJointDistribution._call_flat_sample_distributions\u001b[0;34m(self, sample_shape, seed, value)\u001b[0m\n\u001b[1;32m    544\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21m_call_flat_sample_distributions\u001b[39m(\u001b[38;5;28mself\u001b[39m,\n\u001b[1;32m    545\u001b[0m                                     sample_shape\u001b[38;5;241m=\u001b[39m(),\n\u001b[1;32m    546\u001b[0m                                     seed\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m,\n\u001b[1;32m    547\u001b[0m                                     value\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m):\n\u001b[0;32m--> 548\u001b[0m   \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mzip\u001b[39m(\u001b[38;5;241m*\u001b[39m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_call_execute_model\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m    549\u001b[0m \u001b[43m      \u001b[49m\u001b[43msample_shape\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    550\u001b[0m \u001b[43m      \u001b[49m\u001b[43mseed\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mseed\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    551\u001b[0m \u001b[43m      \u001b[49m\u001b[43mvalue\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mvalue\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    552\u001b[0m \u001b[43m      \u001b[49m\u001b[43msample_and_trace_fn\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mtrace_distributions_and_values\u001b[49m\u001b[43m)\u001b[49m)\n",
      "File \u001b[0;32m~/miniforge3/envs/dl/lib/python3.12/site-packages/tensorflow_probability/substrates/jax/distributions/joint_distribution.py:882\u001b[0m, in \u001b[0;36mJointDistribution._call_execute_model\u001b[0;34m(self, sample_shape, seed, value, sample_and_trace_fn)\u001b[0m\n\u001b[1;32m    878\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m sample_shape_may_be_nontrivial:\n\u001b[1;32m    879\u001b[0m   vectorized_execute_model \u001b[38;5;241m=\u001b[39m vectorization_util\u001b[38;5;241m.\u001b[39miid_sample(\n\u001b[1;32m    880\u001b[0m       vectorized_execute_model, sample_shape)\n\u001b[0;32m--> 882\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mvectorized_execute_model\u001b[49m\u001b[43m(\u001b[49m\u001b[43mflat_value\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mseed\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mseed\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/miniforge3/envs/dl/lib/python3.12/site-packages/tensorflow_probability/substrates/jax/distributions/joint_distribution.py:876\u001b[0m, in \u001b[0;36mJointDistribution._call_execute_model.<locals>.<lambda>\u001b[0;34m(fv, seed)\u001b[0m\n\u001b[1;32m    864\u001b[0m vectorized_execute_model_helper \u001b[38;5;241m=\u001b[39m vectorization_util\u001b[38;5;241m.\u001b[39mmake_rank_polymorphic(\n\u001b[1;32m    865\u001b[0m     \u001b[38;5;28;01mlambda\u001b[39;00m fv, seed: (  \u001b[38;5;66;03m# pylint: disable=g-long-lambda\u001b[39;00m\n\u001b[1;32m    866\u001b[0m         \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_execute_model(\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m    870\u001b[0m             sample_and_trace_fn\u001b[38;5;241m=\u001b[39msample_and_trace_fn)),\n\u001b[1;32m    871\u001b[0m     core_ndims\u001b[38;5;241m=\u001b[39m[flat_value_core_ndims, \u001b[38;5;28;01mNone\u001b[39;00m])\n\u001b[1;32m    872\u001b[0m \u001b[38;5;66;03m# Redefine the polymorphic fn to hack around `make_rank_polymorphic`\u001b[39;00m\n\u001b[1;32m    873\u001b[0m \u001b[38;5;66;03m# not currently supporting keyword args. This is needed because the\u001b[39;00m\n\u001b[1;32m    874\u001b[0m \u001b[38;5;66;03m# `iid_sample` wrapper below expects to pass through a `seed` kwarg.\u001b[39;00m\n\u001b[1;32m    875\u001b[0m vectorized_execute_model \u001b[38;5;241m=\u001b[39m (\n\u001b[0;32m--> 876\u001b[0m     \u001b[38;5;28;01mlambda\u001b[39;00m fv, seed: \u001b[43mvectorized_execute_model_helper\u001b[49m\u001b[43m(\u001b[49m\u001b[43mfv\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mseed\u001b[49m\u001b[43m)\u001b[49m)  \u001b[38;5;66;03m# pylint: disable=unnecessary-lambda\u001b[39;00m\n\u001b[1;32m    878\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m sample_shape_may_be_nontrivial:\n\u001b[1;32m    879\u001b[0m   vectorized_execute_model \u001b[38;5;241m=\u001b[39m vectorization_util\u001b[38;5;241m.\u001b[39miid_sample(\n\u001b[1;32m    880\u001b[0m       vectorized_execute_model, sample_shape)\n",
      "File \u001b[0;32m~/miniforge3/envs/dl/lib/python3.12/site-packages/tensorflow_probability/substrates/jax/internal/vectorization_util.py:327\u001b[0m, in \u001b[0;36mmake_rank_polymorphic.<locals>.vectorized_fn\u001b[0;34m(*args)\u001b[0m\n\u001b[1;32m    322\u001b[0m   vectorized_args_with_flattened_batch_dim \u001b[38;5;241m=\u001b[39m [\n\u001b[1;32m    323\u001b[0m       tf\u001b[38;5;241m.\u001b[39mreshape(part, ps\u001b[38;5;241m.\u001b[39mconcat([[n], core_shape], axis\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m0\u001b[39m))\n\u001b[1;32m    324\u001b[0m       \u001b[38;5;28;01mfor\u001b[39;00m (part, core_shape) \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mzip\u001b[39m(\n\u001b[1;32m    325\u001b[0m           broadcast_vectorized_args, core_shapes)]\n\u001b[1;32m    326\u001b[0m   result_batch_dims \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m1\u001b[39m\n\u001b[0;32m--> 327\u001b[0m   batched_result \u001b[38;5;241m=\u001b[39m \u001b[43mtf\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mvectorized_map\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m    328\u001b[0m \u001b[43m      \u001b[49m\u001b[43mfn_of_vectorized_args\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mvectorized_args_with_flattened_batch_dim\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    330\u001b[0m \u001b[38;5;66;03m# Unflatten any `Tensor`s in the result.\u001b[39;00m\n\u001b[1;32m    331\u001b[0m unflatten \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mlambda\u001b[39;00m x: tf\u001b[38;5;241m.\u001b[39mreshape(x, ps\u001b[38;5;241m.\u001b[39mconcat([  \u001b[38;5;66;03m# pylint: disable=g-long-lambda\u001b[39;00m\n\u001b[1;32m    332\u001b[0m     broadcast_batch_shape, ps\u001b[38;5;241m.\u001b[39mshape(x)[result_batch_dims:]], axis\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m0\u001b[39m))\n",
      "File \u001b[0;32m~/miniforge3/envs/dl/lib/python3.12/site-packages/tensorflow_probability/python/internal/backend/jax/_utils.py:62\u001b[0m, in \u001b[0;36mcopy_docstring.<locals>.wrap\u001b[0;34m(***failed resolving arguments***)\u001b[0m\n\u001b[1;32m     59\u001b[0m \u001b[38;5;129m@wrapt\u001b[39m\u001b[38;5;241m.\u001b[39mdecorator\n\u001b[1;32m     60\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mwrap\u001b[39m(wrapped, instance, args, kwargs):\n\u001b[1;32m     61\u001b[0m   \u001b[38;5;28;01mdel\u001b[39;00m instance, wrapped\n\u001b[0;32m---> 62\u001b[0m   \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mnew_fn\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/miniforge3/envs/dl/lib/python3.12/site-packages/tensorflow_probability/python/internal/backend/jax/functional_ops.py:103\u001b[0m, in \u001b[0;36m_vectorized_map\u001b[0;34m(fn, elems)\u001b[0m\n\u001b[1;32m    101\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m JAX_MODE:\n\u001b[1;32m    102\u001b[0m   \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mjax\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m vmap  \u001b[38;5;66;03m# pylint: disable=g-import-not-at-top\u001b[39;00m\n\u001b[0;32m--> 103\u001b[0m   \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mvmap\u001b[49m\u001b[43m(\u001b[49m\u001b[43mfn\u001b[49m\u001b[43m)\u001b[49m\u001b[43m(\u001b[49m\u001b[43melems\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    105\u001b[0m \u001b[38;5;66;03m# In the NumPy backend, we don't actually vectorize.\u001b[39;00m\n\u001b[1;32m    106\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m _map_fn(fn, elems)\n",
      "    \u001b[0;31m[... skipping hidden 7 frame]\u001b[0m\n",
      "File \u001b[0;32m~/miniforge3/envs/dl/lib/python3.12/site-packages/tensorflow_probability/substrates/jax/internal/auto_composite_tensor.py:813\u001b[0m, in \u001b[0;36mpytree_unflatten\u001b[0;34m(cls, aux_data, children)\u001b[0m\n\u001b[1;32m    809\u001b[0m keys, metadata \u001b[38;5;241m=\u001b[39m aux_data\n\u001b[1;32m    810\u001b[0m parameters \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mdict\u001b[39m(\u001b[38;5;28mlist\u001b[39m(\u001b[38;5;28mzip\u001b[39m(keys, children)),\n\u001b[1;32m    811\u001b[0m                   \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mmetadata[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mnon_tensor_params\u001b[39m\u001b[38;5;124m'\u001b[39m],\n\u001b[1;32m    812\u001b[0m                   \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mmetadata[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mcallable_params\u001b[39m\u001b[38;5;124m'\u001b[39m])\n\u001b[0;32m--> 813\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mcls\u001b[39;49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mparameters\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/miniforge3/envs/dl/lib/python3.12/site-packages/decorator.py:232\u001b[0m, in \u001b[0;36mdecorate.<locals>.fun\u001b[0;34m(*args, **kw)\u001b[0m\n\u001b[1;32m    230\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m kwsyntax:\n\u001b[1;32m    231\u001b[0m     args, kw \u001b[38;5;241m=\u001b[39m fix(args, kw, sig)\n\u001b[0;32m--> 232\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mcaller\u001b[49m\u001b[43m(\u001b[49m\u001b[43mfunc\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mextras\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m+\u001b[39;49m\u001b[43m \u001b[49m\u001b[43margs\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkw\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/miniforge3/envs/dl/lib/python3.12/site-packages/tensorflow_probability/substrates/jax/distributions/distribution.py:342\u001b[0m, in \u001b[0;36m_DistributionMeta.__new__.<locals>.wrapped_init\u001b[0;34m(***failed resolving arguments***)\u001b[0m\n\u001b[1;32m    339\u001b[0m \u001b[38;5;66;03m# Note: if we ever want to have things set in `self` before `__init__` is\u001b[39;00m\n\u001b[1;32m    340\u001b[0m \u001b[38;5;66;03m# called, here is the place to do it.\u001b[39;00m\n\u001b[1;32m    341\u001b[0m self_\u001b[38;5;241m.\u001b[39m_parameters \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mNone\u001b[39;00m\n\u001b[0;32m--> 342\u001b[0m \u001b[43mdefault_init\u001b[49m\u001b[43m(\u001b[49m\u001b[43mself_\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    343\u001b[0m \u001b[38;5;66;03m# Note: if we ever want to override things set in `self` by subclass\u001b[39;00m\n\u001b[1;32m    344\u001b[0m \u001b[38;5;66;03m# `__init__`, here is the place to do it.\u001b[39;00m\n\u001b[1;32m    345\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m self_\u001b[38;5;241m.\u001b[39m_parameters \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m    346\u001b[0m   \u001b[38;5;66;03m# We prefer subclasses will set `parameters = dict(locals())` because\u001b[39;00m\n\u001b[1;32m    347\u001b[0m   \u001b[38;5;66;03m# this has nearly zero overhead. However, failing to do this, we will\u001b[39;00m\n\u001b[1;32m    348\u001b[0m   \u001b[38;5;66;03m# resolve the input arguments dynamically and only when needed.\u001b[39;00m\n",
      "File \u001b[0;32m~/miniforge3/envs/dl/lib/python3.12/site-packages/tensorflow_probability/substrates/jax/distributions/normal.py:136\u001b[0m, in \u001b[0;36mNormal.__init__\u001b[0;34m(self, loc, scale, validate_args, allow_nan_stats, name)\u001b[0m\n\u001b[1;32m    134\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m tf\u001b[38;5;241m.\u001b[39mname_scope(name) \u001b[38;5;28;01mas\u001b[39;00m name:\n\u001b[1;32m    135\u001b[0m   dtype \u001b[38;5;241m=\u001b[39m dtype_util\u001b[38;5;241m.\u001b[39mcommon_dtype([loc, scale], dtype_hint\u001b[38;5;241m=\u001b[39mtf\u001b[38;5;241m.\u001b[39mfloat32)\n\u001b[0;32m--> 136\u001b[0m   \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_loc \u001b[38;5;241m=\u001b[39m \u001b[43mtensor_util\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mconvert_nonref_to_tensor\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m    137\u001b[0m \u001b[43m      \u001b[49m\u001b[43mloc\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdtype\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mdtype\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mname\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mloc\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m    138\u001b[0m   \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_scale \u001b[38;5;241m=\u001b[39m tensor_util\u001b[38;5;241m.\u001b[39mconvert_nonref_to_tensor(\n\u001b[1;32m    139\u001b[0m       scale, dtype\u001b[38;5;241m=\u001b[39mdtype, name\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mscale\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[1;32m    140\u001b[0m   \u001b[38;5;28msuper\u001b[39m(Normal, \u001b[38;5;28mself\u001b[39m)\u001b[38;5;241m.\u001b[39m\u001b[38;5;21m__init__\u001b[39m(\n\u001b[1;32m    141\u001b[0m       dtype\u001b[38;5;241m=\u001b[39mdtype,\n\u001b[1;32m    142\u001b[0m       reparameterization_type\u001b[38;5;241m=\u001b[39mreparameterization\u001b[38;5;241m.\u001b[39mFULLY_REPARAMETERIZED,\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m    145\u001b[0m       parameters\u001b[38;5;241m=\u001b[39mparameters,\n\u001b[1;32m    146\u001b[0m       name\u001b[38;5;241m=\u001b[39mname)\n",
      "File \u001b[0;32m~/miniforge3/envs/dl/lib/python3.12/site-packages/tensorflow_probability/substrates/jax/internal/tensor_util.py:119\u001b[0m, in \u001b[0;36mconvert_nonref_to_tensor\u001b[0;34m(value, dtype, dtype_hint, as_shape_tensor, name)\u001b[0m\n\u001b[1;32m    116\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m as_shape_tensor:\n\u001b[1;32m    117\u001b[0m   \u001b[38;5;28;01mreturn\u001b[39;00m prefer_static\u001b[38;5;241m.\u001b[39mconvert_to_shape_tensor(\n\u001b[1;32m    118\u001b[0m       value, dtype\u001b[38;5;241m=\u001b[39mdtype, dtype_hint\u001b[38;5;241m=\u001b[39mdtype_hint, name\u001b[38;5;241m=\u001b[39mname)\n\u001b[0;32m--> 119\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mtf\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mconvert_to_tensor\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m    120\u001b[0m \u001b[43m    \u001b[49m\u001b[43mvalue\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdtype\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mdtype\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdtype_hint\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mdtype_hint\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mname\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mname\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/miniforge3/envs/dl/lib/python3.12/site-packages/tensorflow_probability/python/internal/backend/jax/_utils.py:62\u001b[0m, in \u001b[0;36mcopy_docstring.<locals>.wrap\u001b[0;34m(***failed resolving arguments***)\u001b[0m\n\u001b[1;32m     59\u001b[0m \u001b[38;5;129m@wrapt\u001b[39m\u001b[38;5;241m.\u001b[39mdecorator\n\u001b[1;32m     60\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mwrap\u001b[39m(wrapped, instance, args, kwargs):\n\u001b[1;32m     61\u001b[0m   \u001b[38;5;28;01mdel\u001b[39;00m instance, wrapped\n\u001b[0;32m---> 62\u001b[0m   \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mnew_fn\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/miniforge3/envs/dl/lib/python3.12/site-packages/tensorflow_probability/python/internal/backend/jax/ops.py:167\u001b[0m, in \u001b[0;36m_convert_to_tensor\u001b[0;34m(value, dtype, dtype_hint, name)\u001b[0m\n\u001b[1;32m    164\u001b[0m     \u001b[38;5;28;01mpass\u001b[39;00m\n\u001b[1;32m    166\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m ret \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[0;32m--> 167\u001b[0m   ret \u001b[38;5;241m=\u001b[39m \u001b[43mconversion_func\u001b[49m\u001b[43m(\u001b[49m\u001b[43mvalue\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdtype\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mdtype\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    168\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m ret\n",
      "File \u001b[0;32m~/miniforge3/envs/dl/lib/python3.12/site-packages/tensorflow_probability/python/internal/backend/jax/ops.py:231\u001b[0m, in \u001b[0;36m_default_convert_to_tensor\u001b[0;34m(value, dtype)\u001b[0m\n\u001b[1;32m    226\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mhasattr\u001b[39m(value[\u001b[38;5;241m0\u001b[39m], \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mdtype\u001b[39m\u001b[38;5;124m'\u001b[39m) \u001b[38;5;129;01mand\u001b[39;00m jax\u001b[38;5;241m.\u001b[39mdtypes\u001b[38;5;241m.\u001b[39missubdtype(\n\u001b[1;32m    227\u001b[0m         value[\u001b[38;5;241m0\u001b[39m]\u001b[38;5;241m.\u001b[39mdtype, jax\u001b[38;5;241m.\u001b[39mdtypes\u001b[38;5;241m.\u001b[39mprng_key\n\u001b[1;32m    228\u001b[0m     ):\n\u001b[1;32m    229\u001b[0m       \u001b[38;5;28;01mreturn\u001b[39;00m np\u001b[38;5;241m.\u001b[39mstack(value, axis\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m0\u001b[39m)\n\u001b[0;32m--> 231\u001b[0m inferred_dtype \u001b[38;5;241m=\u001b[39m \u001b[43m_infer_dtype\u001b[49m\u001b[43m(\u001b[49m\u001b[43mvalue\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mnp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mfloat32\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    232\u001b[0m \u001b[38;5;66;03m# When a dtype is provided, we can go ahead and try converting to the dtype\u001b[39;00m\n\u001b[1;32m    233\u001b[0m \u001b[38;5;66;03m# and force overflow/underflow if an int64 is converted to an int32.\u001b[39;00m\n\u001b[1;32m    234\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m dtype \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n",
      "File \u001b[0;32m~/miniforge3/envs/dl/lib/python3.12/site-packages/tensorflow_probability/python/internal/backend/jax/ops.py:195\u001b[0m, in \u001b[0;36m_infer_dtype\u001b[0;34m(value, default_dtype)\u001b[0m\n\u001b[1;32m    193\u001b[0m   \u001b[38;5;28;01mexcept\u001b[39;00m (\u001b[38;5;167;01mIndexError\u001b[39;00m, \u001b[38;5;167;01mTypeError\u001b[39;00m):\n\u001b[1;32m    194\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m default_dtype\n\u001b[0;32m--> 195\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m((\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mAttempt to convert a value (\u001b[39m\u001b[38;5;132;01m{}\u001b[39;00m\u001b[38;5;124m)\u001b[39m\u001b[38;5;124m'\u001b[39m\n\u001b[1;32m    196\u001b[0m                   \u001b[38;5;124m'\u001b[39m\u001b[38;5;124m with an unsupported type (\u001b[39m\u001b[38;5;132;01m{}\u001b[39;00m\u001b[38;5;124m) to a Tensor.\u001b[39m\u001b[38;5;124m'\u001b[39m)\u001b[38;5;241m.\u001b[39mformat(\n\u001b[1;32m    197\u001b[0m                       value, \u001b[38;5;28mtype\u001b[39m(value)))\n",
      "\u001b[0;31mValueError\u001b[0m: Attempt to convert a value (<object object at 0x321ac2350>) with an unsupported type (<class 'object'>) to a Tensor."
     ]
    }
   ],
   "source": [
    "# jd_71.sample_distributions(value=[[0.0, 0.0], [-0.2, 0.0], [6.1, 5.4]], seed=key())\n",
    "jd_71.sample_distributions(value=StateTuple([0.0, 0.0], [-0.2, 0.0], [6.1, 5.4]), seed=key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# # In a better world. intuitive and elegant\n",
    "# ds, samples = jd_71.sample_distributions(value=post_71, seed=key())\n",
    "# ll = ds[-1].log_prob(d.brain_std.values) # (draw, chain, 7)\n",
    "# # lppd\n",
    "# jax.scipy.special.logsumexp(ll[:,0,:], b=1/draw, axis=0) # first chain or\n",
    "# jax.scipy.special.logsumexp(ll, b=1/(draw*chain), axis=[0, 1]) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7.3 Golem Taming: Regularization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7.4 Predicting predictive accuracy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Overthinking: WAIC calculations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 7.19"
   ]
  },
  {
   "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>rownames</th>\n",
       "      <th>speed</th>\n",
       "      <th>dist</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>7</td>\n",
       "      <td>22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>8</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   rownames  speed  dist\n",
       "0         1      4     2\n",
       "1         2      4    10\n",
       "2         3      7     4\n",
       "3         4      7    22\n",
       "4         5      8    16"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d = pd.read_csv(\"./data/cars.csv\")\n",
    "d.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "rownames    float32\n",
       "speed       float32\n",
       "dist        float32\n",
       "dtype: object"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d = d.astype('float32')\n",
    "d.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_cars(speed):\n",
    "    def _generator():\n",
    "        a = yield tfd.Normal(loc=0.0, scale=100.0, name=\"a\")\n",
    "        b = yield tfd.Normal(loc=0.0, scale=10.0, name=\"b\")\n",
    "        sigma = yield tfd.Exponential(rate=1.0, name=\"sigma\")\n",
    "        mu = a + b * speed\n",
    "        # BUG: DO NOT USE 'dist' as a name!!!! \n",
    "        yield tfd.Normal(loc=mu, scale=sigma, name=\"distance\")\n",
    "\n",
    "    return tfd.JointDistributionCoroutineAutoBatched(_generator, validate_args=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_cars = model_cars(speed=d.speed.values)\n",
    "jd_cars_pd = jd_cars.experimental_pin(distance=d.dist.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "def target_log_prob_cars(*states):\n",
    "    return jd_cars_pd.unnormalized_log_prob(states)\n",
    "\n",
    "@jax.jit\n",
    "def sample_post_cars(init_state, seed):\n",
    "    kernel = tfp.mcmc.NoUTurnSampler(target_log_prob_cars, 1e-3)\n",
    "  \n",
    "    return tfp.mcmc.sample_chain(\n",
    "        num_results=1000,\n",
    "        current_state=init_state,\n",
    "        kernel=kernel,\n",
    "        num_burnin_steps=2000,\n",
    "        trace_fn=None, seed=seed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "# # too braod prior for 'a'\n",
    "# num_chains = 4\n",
    "# init_state_cars = jd_cars_pd.sample_unpinned(num_chains, seed=key())\n",
    "# post_cars = sample_post_cars(init_state_cars, key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "state_name_cars = jd_cars_pd.sample_unpinned(seed=key())._fields\n",
    "StateTuple = namedtuple(\"StateTuple\", state_name_cars)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_chains = 4\n",
    "init_state_cars = [jnp.ones(num_chains), \n",
    "                   jnp.ones(num_chains), jnp.ones(num_chains)]\n",
    "init_state_cars = StateTuple(**dict(zip(state_name_cars, init_state_cars)))\n",
    "post_cars = sample_post_cars(init_state_cars, key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_cars_dict = {k: jnp.moveaxis(v, 0, 1) for k, v in post_cars._asdict().items()}\n",
    "dict_cars = dict(posterior=post_cars_dict)\n",
    "idata_cars = az.from_dict(**dict_cars)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "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_3%</th>\n",
       "      <th>hdi_97%</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</th>\n",
       "      <td>-17.777</td>\n",
       "      <td>5.456</td>\n",
       "      <td>-28.257</td>\n",
       "      <td>-8.578</td>\n",
       "      <td>1.890</td>\n",
       "      <td>1.439</td>\n",
       "      <td>8.0</td>\n",
       "      <td>25.0</td>\n",
       "      <td>1.45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b</th>\n",
       "      <td>3.944</td>\n",
       "      <td>0.337</td>\n",
       "      <td>3.301</td>\n",
       "      <td>4.542</td>\n",
       "      <td>0.110</td>\n",
       "      <td>0.081</td>\n",
       "      <td>9.0</td>\n",
       "      <td>29.0</td>\n",
       "      <td>1.37</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma</th>\n",
       "      <td>13.867</td>\n",
       "      <td>1.191</td>\n",
       "      <td>11.714</td>\n",
       "      <td>16.105</td>\n",
       "      <td>0.082</td>\n",
       "      <td>0.058</td>\n",
       "      <td>208.0</td>\n",
       "      <td>393.0</td>\n",
       "      <td>1.03</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  ess_bulk  ess_tail  \\\n",
       "a     -17.777  5.456 -28.257   -8.578      1.890    1.439       8.0      25.0   \n",
       "b       3.944  0.337   3.301    4.542      0.110    0.081       9.0      29.0   \n",
       "sigma  13.867  1.191  11.714   16.105      0.082    0.058     208.0     393.0   \n",
       "\n",
       "       r_hat  \n",
       "a       1.45  \n",
       "b       1.37  \n",
       "sigma   1.03  "
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata_cars)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: black;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-1 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-1 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-1 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-1 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-1 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 1ex;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-1 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LinearRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;LinearRegression<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.linear_model.LinearRegression.html\">?<span>Documentation for LinearRegression</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>LinearRegression()</pre></div> </div></div></div></div>"
      ],
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = LinearRegression()\n",
    "m.fit(d.speed.values.reshape(-1, 1), d.dist.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "intercept: -17.579082489013672\n",
      "slope: [3.932408]\n"
     ]
    }
   ],
   "source": [
    "print(f\"intercept: {m.intercept_}\")\n",
    "print(f\"slope: {m.coef_}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 7.20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {},
   "outputs": [],
   "source": [
    "# idata_cars.posterior['a']: (chain, draw)\n",
    "# mu: (chain, draw, obs)\n",
    "mu = idata_cars.posterior['a'] + idata_cars.posterior['b'] * xr.DataArray(d.speed.values)\n",
    "mu = mu.to_numpy()\n",
    "# add newaxis to braodcast through obs\n",
    "sigma = idata_cars.posterior['sigma'].to_numpy()[..., np.newaxis]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [],
   "source": [
    "normal = tfd.Normal(loc=mu, scale=sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 265,
   "metadata": {},
   "outputs": [],
   "source": [
    "# (chain, draw, obs)\n",
    "ll_i = normal.log_prob(d.dist.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# from source: /arviz/stats/stats.py: def waic() ...\n",
    "# \n",
    "# waic_i = scale_value * (lppd_i - vars_lpd)\n",
    "# waic_se = (n_data_points * np.var(waic_i.values)) ** 0.5\n",
    "# waic_sum = np.sum(waic_i.values)\n",
    "# p_waic = np.sum(vars_lpd.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 272,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "elpd_waic: 420.5662841796875, se:15.613472938537598\n",
      "p_wais: 3.6938436031341553\n"
     ]
    }
   ],
   "source": [
    "lppd_i = jax.scipy.special.logsumexp(ll_i, b=1/4000, axis=(0, 1))\n",
    "vars_lpd = jnp.var(ll_i, axis=(0, 1))\n",
    "waic_i = -2*(lppd_i - vars_lpd)\n",
    "print(f\"elpd_waic: {jnp.sum(waic_i)}, se:{jnp.sqrt(len(obs) * jnp.var(waic_i))}\")\n",
    "print(f\"p_wais: {jnp.sum(vars_lpd)}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 273,
   "metadata": {},
   "outputs": [],
   "source": [
    "dict_cars.update(log_likelihood={'ll': ll_i},\n",
    "                 dims={\"ll\": [\"obs\"]},\n",
    "                 coords={\"obs\": jnp.arange(len(d.dist.values))})\n",
    "idata_cars = az.from_dict(**dict_cars)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 274,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jun/miniforge3/envs/dl/lib/python3.12/site-packages/arviz/stats/stats.py:1632: UserWarning: For one or more samples the posterior variance of the log predictive densities exceeds 0.4. This could be indication of WAIC starting to fail. \n",
      "See http://arxiv.org/abs/1507.04544 for details\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Computed from 4000 posterior samples and 50 observations log-likelihood matrix.\n",
       "\n",
       "              Estimate       SE\n",
       "deviance_waic   420.57    15.94\n",
       "p_waic            3.69        -\n",
       "\n",
       "There has been a warning during the calculation. Please check the results."
      ]
     },
     "execution_count": 274,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.waic(idata_cars, scale='deviance')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array([0.7092146, 1.2408626], dtype=float32)"
      ]
     },
     "execution_count": 207,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# UserWarning: For one or more samples the posterior variance of the log predictive densities exceeds 0.4. This could be indication of WAIC starting to fail. \n",
    "# See http://arxiv.org/abs/1507.04544 for details\n",
    "ll_vars = jnp.var(ll_i, axis=(0, 1))\n",
    "ll_vars[jnp.where(ll_vars > 0.4)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 275,
   "metadata": {},
   "outputs": [],
   "source": [
    "# az.waic() without waning cases \n",
    "obs = jnp.where(ll_vars <= 0.4)[0]\n",
    "ll_i = ll_i[..., obs]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 276,
   "metadata": {},
   "outputs": [],
   "source": [
    "dict_cars.update(log_likelihood={'ll': ll_i},\n",
    "                 dims={\"ll\": [\"obs\"]},\n",
    "                 coords={\"obs\": jnp.arange(len(obs))})\n",
    "idata_cars = az.from_dict(**dict_cars)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 277,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Computed from 4000 posterior samples and 48 observations log-likelihood matrix.\n",
       "\n",
       "              Estimate       SE\n",
       "deviance_waic   384.62     7.95\n",
       "p_waic            1.74        -"
      ]
     },
     "execution_count": 277,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.waic(idata_cars, scale='deviance')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 278,
   "metadata": {},
   "outputs": [],
   "source": [
    "# by hand with the selected obs\n",
    "lppd_i = jax.scipy.special.logsumexp(ll_i, b=1/4000, axis=(0, 1))\n",
    "vars_lpd = jnp.var(ll_i, axis=(0, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 279,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "elpd_waic: 384.6249694824219, se:7.945420742034912\n",
      "p_wais: 1.7437663078308105\n"
     ]
    }
   ],
   "source": [
    "waic_i = -2*(lppd_i - vars_lpd)\n",
    "# elpd_waic\n",
    "print(f\"elpd_waic: {jnp.sum(waic_i)}, se:{jnp.sqrt(len(obs) * jnp.var(waic_i))}\")\n",
    "print(f\"p_wais: {jnp.sum(vars_lpd)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 7.4.3 Comparing CV, PSIS, and WAIC"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7.5 Model comparison"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 7.25\n",
    "\n",
    "\n",
    "Here we need to first redefine models from the previous chapters i.e. m6_6,m6_7,m6_8 and compute the log likelihoods as well and only then we will compute the WAIC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 282,
   "metadata": {},
   "outputs": [],
   "source": [
    "def simulate():\n",
    "    seed = tfp.util.SeedStream(613, salt=\"sim_heights\")\n",
    "    # number of plants\n",
    "    N = 100\n",
    "    # simulate initial heights\n",
    "    h0 = tfd.Normal(loc=10.0, scale=2.0).sample(N, seed=seed())\n",
    "    # assign treatments and simulate fungus and growth\n",
    "    treatment = jnp.repeat(jnp.array([0.0, 1.0]), repeats=N // 2)\n",
    "    fungus = tfd.Binomial(total_count=1.0, probs=(0.5 - treatment * 0.4)).sample(seed=seed())\n",
    "    h1 = h0 + tfd.Normal(loc=5.0 - 3.0 * fungus, scale=1.0).sample(seed=seed())\n",
    "    # compose a clean data frame\n",
    "    return {\"h0\": h0, \"h1\": h1, \"treatment\": treatment, \"fungus\": fungus}\n",
    "\n",
    "d_dict = simulate()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 283,
   "metadata": {},
   "outputs": [],
   "source": [
    "d = pd.DataFrame.from_dict(d_dict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 285,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_66(h0):\n",
    "    def _generator():\n",
    "        p = yield tfd.LogNormal(loc=0.0, scale=0.25, name=\"p\")\n",
    "        sigma = yield tfd.Exponential(rate=1.0, name=\"sigma\")\n",
    "        mu = h0 * p\n",
    "        h1 = yield tfd.Normal(loc=mu, scale=sigma, name=\"h1\")\n",
    "\n",
    "    return tfd.JointDistributionCoroutineAutoBatched(_generator, validate_args=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 286,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_66 = model_66(d.h0.values)\n",
    "jd_66_pd = jd_66.experimental_pin(h1=d.h1.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 291,
   "metadata": {},
   "outputs": [],
   "source": [
    "def target_log_prob_66(*states):\n",
    "    return jd_66_pd.unnormalized_log_prob(states)\n",
    "\n",
    "def sample_post_66(init_state, seed):\n",
    "    kernel = tfp.mcmc.NoUTurnSampler(target_log_prob_66, 1e-3)\n",
    "  \n",
    "    return tfp.mcmc.sample_chain(\n",
    "            num_results=1000,\n",
    "            current_state=init_state,\n",
    "            kernel=kernel,\n",
    "            num_burnin_steps=2000,\n",
    "            trace_fn=None, seed=seed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 292,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_chains = 4\n",
    "init_state_66 = jd_66_pd.sample_unpinned(num_chains, seed=key())\n",
    "post_66 = sample_post_66(init_state_66, key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 293,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_66_dict = {k: jnp.moveaxis(v, 0, 1) for k, v in post_66._asdict().items()}\n",
    "dict_66 = dict(posterior=post_66_dict)\n",
    "idata_66 = az.from_dict(**dict_66)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 294,
   "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_3%</th>\n",
       "      <th>hdi_97%</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>p</th>\n",
       "      <td>1.411</td>\n",
       "      <td>0.018</td>\n",
       "      <td>1.377</td>\n",
       "      <td>1.444</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>2713.0</td>\n",
       "      <td>1816.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma</th>\n",
       "      <td>1.869</td>\n",
       "      <td>0.141</td>\n",
       "      <td>1.615</td>\n",
       "      <td>2.130</td>\n",
       "      <td>0.006</td>\n",
       "      <td>0.005</td>\n",
       "      <td>520.0</td>\n",
       "      <td>542.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  ess_bulk  ess_tail  \\\n",
       "p      1.411  0.018   1.377    1.444      0.000    0.000    2713.0    1816.0   \n",
       "sigma  1.869  0.141   1.615    2.130      0.006    0.005     520.0     542.0   \n",
       "\n",
       "       r_hat  \n",
       "p       1.00  \n",
       "sigma   1.01  "
      ]
     },
     "execution_count": 294,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata_66)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result shows that with height as the only predictor variable in the model there is about 40% growth on average."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 6.16\n",
    "\n",
    "In this model we include treatment & fungus variables as well"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 295,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_67(h0, treatment, fungus):\n",
    "    def _generator():\n",
    "        a = yield tfd.LogNormal(loc=0.0, scale=0.2, name=\"a\")\n",
    "        bt = yield tfd.Normal(loc=0.0, scale=0.5, name=\"bt\")\n",
    "        bf = yield tfd.Normal(loc=0.0, scale=0.5, name=\"bf\")\n",
    "        sigma = yield tfd.Exponential(rate=1.0, name=\"sigma\")\n",
    "        p = a + bt * treatment + bf * fungus\n",
    "        mu = h0 * p\n",
    "        yield tfd.Normal(loc=mu, scale=sigma, name=\"h1\")\n",
    "\n",
    "    return tfd.JointDistributionCoroutineAutoBatched(_generator, validate_args=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 296,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_67 = model_67(d.h0.values, d.treatment.values, d.fungus.values)\n",
    "jd_67_pd = jd_67.experimental_pin(h1=d.h1.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 297,
   "metadata": {},
   "outputs": [],
   "source": [
    "def target_log_prob_67(*states):\n",
    "    return jd_67_pd.unnormalized_log_prob(states)\n",
    "\n",
    "def sample_post_67(init_state, seed):\n",
    "    kernel = tfp.mcmc.NoUTurnSampler(target_log_prob_67, 1e-2)\n",
    "  \n",
    "    return tfp.mcmc.sample_chain(\n",
    "            num_results=1000,\n",
    "            current_state=init_state,\n",
    "            kernel=kernel,\n",
    "            num_burnin_steps=1500,\n",
    "            trace_fn=None, seed=seed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# num_chains = 4\n",
    "# init_state_67 = jd_67_pd.sample_unpinned(num_chains, seed=key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 298,
   "metadata": {},
   "outputs": [],
   "source": [
    "state_name_67 = jd_67_pd.sample_unpinned(seed=key())._fields"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 299,
   "metadata": {},
   "outputs": [],
   "source": [
    "StateTuple = namedtuple(\"StateTuple\", state_name_67)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 300,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_chains = 4\n",
    "init_state_67 = [jnp.ones(num_chains), jnp.zeros(num_chains), \n",
    "                 jnp.zeros(num_chains), jnp.ones(num_chains)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 301,
   "metadata": {},
   "outputs": [],
   "source": [
    "init_state_67 = StateTuple(**dict(zip(state_name_67, init_state_67)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 302,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_67 = sample_post_67(init_state_67, key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 303,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_67_dict = {k: jnp.moveaxis(v, 0, 1) for k, v in post_67._asdict().items()}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 304,
   "metadata": {},
   "outputs": [],
   "source": [
    "dict_67 = dict(posterior=post_67_dict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 305,
   "metadata": {},
   "outputs": [],
   "source": [
    "idata_67 = az.from_dict(**dict_67)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 306,
   "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_3%</th>\n",
       "      <th>hdi_97%</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</th>\n",
       "      <td>1.493</td>\n",
       "      <td>0.023</td>\n",
       "      <td>1.451</td>\n",
       "      <td>1.536</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>2869.0</td>\n",
       "      <td>2715.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bf</th>\n",
       "      <td>-0.326</td>\n",
       "      <td>0.033</td>\n",
       "      <td>-0.389</td>\n",
       "      <td>-0.264</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.000</td>\n",
       "      <td>2774.0</td>\n",
       "      <td>2663.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bt</th>\n",
       "      <td>-0.015</td>\n",
       "      <td>0.028</td>\n",
       "      <td>-0.065</td>\n",
       "      <td>0.039</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.000</td>\n",
       "      <td>2888.0</td>\n",
       "      <td>2406.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma</th>\n",
       "      <td>1.257</td>\n",
       "      <td>0.089</td>\n",
       "      <td>1.100</td>\n",
       "      <td>1.433</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.002</td>\n",
       "      <td>874.0</td>\n",
       "      <td>1226.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  ess_bulk  ess_tail  \\\n",
       "a      1.493  0.023   1.451    1.536      0.000    0.000    2869.0    2715.0   \n",
       "bf    -0.326  0.033  -0.389   -0.264      0.001    0.000    2774.0    2663.0   \n",
       "bt    -0.015  0.028  -0.065    0.039      0.001    0.000    2888.0    2406.0   \n",
       "sigma  1.257  0.089   1.100    1.433      0.003    0.002     874.0    1226.0   \n",
       "\n",
       "       r_hat  \n",
       "a        1.0  \n",
       "bf       1.0  \n",
       "bt       1.0  \n",
       "sigma    1.0  "
      ]
     },
     "execution_count": 306,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata_67)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 307,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_68(h0, treatment):\n",
    "    def _generator():\n",
    "        a = yield tfd.LogNormal(loc=0.0, scale=0.2, name=\"a\")\n",
    "        bt = yield tfd.Normal(loc=0.0, scale=0.5, name=\"bt\")\n",
    "        sigma = yield tfd.Exponential(rate=1.0, name=\"sigma\")\n",
    "        p = a + bt * treatment\n",
    "        mu = h0 * p\n",
    "        yield tfd.Normal(loc=mu, scale=sigma, name=\"h1\")\n",
    "\n",
    "    return tfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 308,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_68 = model_68(d.h0.values, d.treatment.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 309,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_68_pd = jd_68.experimental_pin(h1=d.h1.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 310,
   "metadata": {},
   "outputs": [],
   "source": [
    "def target_log_prob_68(*states):\n",
    "    return jd_68_pd.unnormalized_log_prob(states)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 311,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sample_post_68(init_state, seed):\n",
    "    kernel = tfp.mcmc.NoUTurnSampler(target_log_prob_68, 1e-3)\n",
    "  \n",
    "    return tfp.mcmc.sample_chain(\n",
    "            num_results=1000,\n",
    "            current_state=init_state,\n",
    "            kernel=kernel,\n",
    "            num_burnin_steps=1500,\n",
    "            trace_fn=None, seed=seed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 316,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_chains = 4\n",
    "init_state_68 = jd_68_pd.sample_unpinned(num_chains, seed=key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 317,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_68 = sample_post_68(init_state_68, key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 318,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_68_dict = {k: jnp.moveaxis(v, 0, 1) for k, v in post_68._asdict().items()}\n",
    "dict_68 = dict(posterior=post_68_dict)\n",
    "idata_68 = az.from_dict(**dict_68)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 319,
   "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_3%</th>\n",
       "      <th>hdi_97%</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</th>\n",
       "      <td>1.350</td>\n",
       "      <td>0.025</td>\n",
       "      <td>1.300</td>\n",
       "      <td>1.395</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.000</td>\n",
       "      <td>2540.0</td>\n",
       "      <td>2509.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bt</th>\n",
       "      <td>0.119</td>\n",
       "      <td>0.035</td>\n",
       "      <td>0.053</td>\n",
       "      <td>0.188</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>2146.0</td>\n",
       "      <td>1969.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma</th>\n",
       "      <td>1.772</td>\n",
       "      <td>0.126</td>\n",
       "      <td>1.554</td>\n",
       "      <td>2.029</td>\n",
       "      <td>0.005</td>\n",
       "      <td>0.004</td>\n",
       "      <td>625.0</td>\n",
       "      <td>683.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  ess_bulk  ess_tail  \\\n",
       "a      1.350  0.025   1.300    1.395      0.001    0.000    2540.0    2509.0   \n",
       "bt     0.119  0.035   0.053    0.188      0.001    0.001    2146.0    1969.0   \n",
       "sigma  1.772  0.126   1.554    2.029      0.005    0.004     625.0     683.0   \n",
       "\n",
       "       r_hat  \n",
       "a       1.00  \n",
       "bt      1.00  \n",
       "sigma   1.01  "
      ]
     },
     "execution_count": 319,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata_68)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 320,
   "metadata": {},
   "outputs": [],
   "source": [
    "mu_66 = idata_66.posterior['p'] * xr.DataArray(d.h0.values)\n",
    "mu_66 = mu_66.to_numpy()\n",
    "# add newaxis to braodcast through obs\n",
    "sigma_66 = idata_66.posterior['sigma'].to_numpy()[..., np.newaxis]\n",
    "\n",
    "normal_66 = tfd.Normal(loc=mu_66, scale=sigma_66)\n",
    "ll_i_66 = normal_66.log_prob(d.h1.values)\n",
    "\n",
    "dict_66 = dict(log_likelihood={'ll': ll_i_66},\n",
    "               dims={\"ll\": [\"obs\"]},\n",
    "               coords={\"obs\": jnp.arange(len(d.h1.values))})\n",
    "idata_66 = az.from_dict(**dict_66)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 329,
   "metadata": {},
   "outputs": [],
   "source": [
    "mu_67 = (idata_67.posterior['a'] + \\\n",
    "         idata_67.posterior['bt'] * xr.DataArray(d.treatment.values) + \\\n",
    "         idata_67.posterior['bf'] * xr.DataArray(d.fungus.values)) * xr.DataArray(d.h0.values)\n",
    "mu_67 = mu_67.to_numpy()\n",
    "sigma_67 = idata_67.posterior['sigma'].to_numpy()[..., np.newaxis]\n",
    "\n",
    "normal_67 = tfd.Normal(loc=mu_67, scale=sigma_67)\n",
    "ll_i_67 = normal_67.log_prob(d.h1.values)\n",
    "\n",
    "dict_67 = dict(log_likelihood={'ll': ll_i_67},\n",
    "               dims={\"ll\": [\"obs\"]},\n",
    "               coords={\"obs\": jnp.arange(len(d.h1.values))})\n",
    "idata_67 = az.from_dict(**dict_67)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 330,
   "metadata": {},
   "outputs": [],
   "source": [
    "mu_68 = (idata_68.posterior['a'] + \\\n",
    "         idata_68.posterior['bt'] * xr.DataArray(d.treatment.values)) * xr.DataArray(d.h0.values)\n",
    "mu_68 = mu_68.to_numpy()\n",
    "sigma_68 = idata_68.posterior['sigma'].to_numpy()[..., np.newaxis]\n",
    "\n",
    "normal_68 = tfd.Normal(loc=mu_68, scale=sigma_68)\n",
    "ll_i_68 = normal_68.log_prob(d.h1.values)\n",
    "\n",
    "dict_68 = dict(log_likelihood={'ll': ll_i_68},\n",
    "               dims={\"ll\": [\"obs\"]},\n",
    "               coords={\"obs\": jnp.arange(len(d.h1.values))})\n",
    "idata_68 = az.from_dict(**dict_68)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 7.26"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 336,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jun/miniforge3/envs/dl/lib/python3.12/site-packages/arviz/stats/stats.py:1632: UserWarning: For one or more samples the posterior variance of the log predictive densities exceeds 0.4. This could be indication of WAIC starting to fail. \n",
      "See http://arxiv.org/abs/1507.04544 for details\n",
      "  warnings.warn(\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.12/site-packages/arviz/stats/stats.py:1632: UserWarning: For one or more samples the posterior variance of the log predictive densities exceeds 0.4. This could be indication of WAIC starting to fail. \n",
      "See http://arxiv.org/abs/1507.04544 for details\n",
      "  warnings.warn(\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.12/site-packages/arviz/stats/stats.py:1632: UserWarning: For one or more samples the posterior variance of the log predictive densities exceeds 0.4. This could be indication of WAIC starting to fail. \n",
      "See http://arxiv.org/abs/1507.04544 for details\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "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>rank</th>\n",
       "      <th>elpd_waic</th>\n",
       "      <th>p_waic</th>\n",
       "      <th>elpd_diff</th>\n",
       "      <th>weight</th>\n",
       "      <th>se</th>\n",
       "      <th>dse</th>\n",
       "      <th>warning</th>\n",
       "      <th>scale</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>m6.7</th>\n",
       "      <td>0</td>\n",
       "      <td>334.520512</td>\n",
       "      <td>4.425648</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.954797</td>\n",
       "      <td>17.387366</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>True</td>\n",
       "      <td>deviance</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>m6.8</th>\n",
       "      <td>1</td>\n",
       "      <td>402.415840</td>\n",
       "      <td>3.385741</td>\n",
       "      <td>67.895328</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>14.534156</td>\n",
       "      <td>14.636170</td>\n",
       "      <td>True</td>\n",
       "      <td>deviance</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>m6.6</th>\n",
       "      <td>2</td>\n",
       "      <td>411.123234</td>\n",
       "      <td>2.299253</td>\n",
       "      <td>76.602721</td>\n",
       "      <td>0.045203</td>\n",
       "      <td>15.366604</td>\n",
       "      <td>18.044349</td>\n",
       "      <td>True</td>\n",
       "      <td>deviance</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      rank   elpd_waic    p_waic  elpd_diff    weight         se        dse  \\\n",
       "m6.7     0  334.520512  4.425648   0.000000  0.954797  17.387366   0.000000   \n",
       "m6.8     1  402.415840  3.385741  67.895328  0.000000  14.534156  14.636170   \n",
       "m6.6     2  411.123234  2.299253  76.602721  0.045203  15.366604  18.044349   \n",
       "\n",
       "      warning     scale  \n",
       "m6.7     True  deviance  \n",
       "m6.8     True  deviance  \n",
       "m6.6     True  deviance  "
      ]
     },
     "execution_count": 336,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "compare_df =az.compare(\n",
    "    {\"m6.6\": idata_66, \"m6.7\": idata_67, \"m6.8\": idata_68},\n",
    "    ic=\"waic\", scale=\"deviance\")\n",
    "compare_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 7.27 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 341,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jun/miniforge3/envs/dl/lib/python3.12/site-packages/arviz/stats/stats.py:1632: UserWarning: For one or more samples the posterior variance of the log predictive densities exceeds 0.4. This could be indication of WAIC starting to fail. \n",
      "See http://arxiv.org/abs/1507.04544 for details\n",
      "  warnings.warn(\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.12/site-packages/arviz/stats/stats.py:1632: UserWarning: For one or more samples the posterior variance of the log predictive densities exceeds 0.4. This could be indication of WAIC starting to fail. \n",
      "See http://arxiv.org/abs/1507.04544 for details\n",
      "  warnings.warn(\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.12/site-packages/arviz/stats/stats.py:1632: UserWarning: For one or more samples the posterior variance of the log predictive densities exceeds 0.4. This could be indication of WAIC starting to fail. \n",
      "See http://arxiv.org/abs/1507.04544 for details\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Array(14.636169, dtype=float32)"
      ]
     },
     "execution_count": 341,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "waic_66 = az.waic(idata_66, pointwise=True, scale=\"deviance\")\n",
    "waic_67 = az.waic(idata_67, pointwise=True, scale=\"deviance\")\n",
    "waic_68 = az.waic(idata_68, pointwise=True, scale=\"deviance\")\n",
    "\n",
    "diff_78 = waic_67.waic_i - waic_68.waic_i\n",
    "jnp.sqrt(len(diff_78) * jnp.var(diff_78.to_numpy()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 7.29"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 337,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 600x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_compare(compare_df);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 7.31"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 342,
   "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>m6.6</th>\n",
       "      <th>m6.7</th>\n",
       "      <th>m6.8</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>m6.6</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>18.044349</td>\n",
       "      <td>7.020422</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>m6.7</th>\n",
       "      <td>18.044349</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>14.636170</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>m6.8</th>\n",
       "      <td>7.020422</td>\n",
       "      <td>14.636170</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           m6.6       m6.7       m6.8\n",
       "m6.6   0.000000  18.044349   7.020422\n",
       "m6.7  18.044349   0.000000  14.636170\n",
       "m6.8   7.020422  14.636170   0.000000"
      ]
     },
     "execution_count": 342,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dSE = lambda waic1, waic2: np.sqrt(\n",
    "    len(waic1.waic_i) * np.var(waic1.waic_i.to_numpy() - waic2.waic_i.to_numpy())\n",
    ")\n",
    "data = {\"m6.6\": waic_66, \"m6.7\": waic_67, \"m6.8\": waic_68}\n",
    "pd.DataFrame(\n",
    "    {\n",
    "        row: {col: dSE(row_val, col_val) for col, col_val in data.items()}\n",
    "        for row, row_val in data.items()\n",
    "    }\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 7.5.2 Outliers and other illusions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "# az.compare(compare_dict, ic=\"loo\", scale=\"deviance\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.12.4"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}