14_adventures_in_covariance-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/14_adventures_in_covariance.ipynb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 14. Adventures in Covariance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "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 matplotlib.patches import Ellipse, transforms\n",
    "from collections import namedtuple\n",
    "\n",
    "import random\n",
    "import jax\n",
    "import jax.numpy as jnp\n",
    "\n",
    "import tensorflow as tf\n",
    "from tensorflow_probability.substrates import jax as tfp\n",
    "tfd = tfp.distributions\n",
    "tfb = tfp.bijectors\n",
    "# to use 'sample_distributions'\n",
    "import tensorflow_probability as xtfp\n",
    "xtfd = xtfp.distributions\n",
    "xtfb = xtfp.bijectors\n",
    "\n",
    "key = tfp.util.SeedStream(748, salt=\"ch-14\")\n",
    "plt.rcParams['figure.figsize'] = [6, 5]\n",
    "\n",
    "# TFP often requires 64-bit precision (float64) for certain computations \n",
    "# to ensure numerical stability and accuracy, e.g., tfd.Possion.\n",
    "# jax.config.update(\"jax_enable_x64\", True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 14.1 Varying slopes by construction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 14.1.1 Simulate the population"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 14.1\n",
    "\n",
    "Simulate the population"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = 3.5  # average morning wait time\n",
    "b = -1  # average difference afternoon wait time\n",
    "sigma_a = 1  # std dev in intercepts\n",
    "sigma_b = 0.5  # std dev in slopes\n",
    "rho = -0.7  # correlation between intercepts and slopes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 14.2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The value in a is the mean intercept, the wait in the morning. And the value in b is the mean slope, the difference in wait between afternoon and morning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 14.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "cov_ab = sigma_a * sigma_b * rho\n",
    "Sigma = [[sigma_a ** 2, cov_ab], [cov_ab, sigma_b ** 2]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 14.4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 14.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array([[ 1.  , -0.35],\n",
       "       [-0.35,  0.25]], dtype=float32)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sigmas = jnp.array([sigma_a, sigma_b])  # standard deviations\n",
    "Rho = jnp.array([[1, rho], [rho, 1]])  # correlation matrix\n",
    "\n",
    "# now matrix multiply to get covariance matrix\n",
    "Sigma = jnp.diag(sigmas) @ Rho @ jnp.diag(sigmas)\n",
    "Sigma"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 14.6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "N_cafes = 20"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 14.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def build_vary_effects(seed: int):\n",
    "\tkey = tfp.util.SeedStream(seed, salt=\"vary_effects\")\n",
    "\n",
    "\tvary_effects = tfd.MultivariateNormalTriL(\n",
    "\t\t\tloc=[a, b], scale_tril=jnp.linalg.cholesky(Sigma)\n",
    "\t).sample(N_cafes, seed=key())\n",
    "\n",
    "\treturn vary_effects"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "vary_effects = build_vary_effects(22)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 14.8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "a_cafe = vary_effects[:, 0]\n",
    "b_cafe = vary_effects[:, 1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 14.1.2 Simulate observations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 14.10\n",
    "\n",
    "The data we’re generating describes the waiting times in 20 different cafés. Each café has a different average waiting times in the morning and in the afternoon. The average morning waiting time is the intercept, and the difference between afternoon and morning average waiting times is the slope. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "N_visits = 10\n",
    "N_cafes = 20\n",
    "afternoon = np.tile(np.arange(2), N_visits * N_cafes // 2)\n",
    "cafe_id = np.repeat(np.arange(N_cafes), N_visits)\n",
    "\n",
    "def generate_data_frame(seed: int):\n",
    "\tsigma = 0.5  # std dev within cafes\n",
    "\tkey = tfp.util.SeedStream(seed, salt=\"generate_data_frame\")\n",
    "\n",
    "\tmu = jnp.take(a_cafe, cafe_id) + jnp.take(b_cafe, cafe_id) * afternoon\n",
    "\twait = tfd.Normal(loc=mu, scale=sigma).sample(seed=key())\n",
    "\n",
    "\treturn pd.DataFrame(dict(cafe=cafe_id, afternoon=afternoon, wait=wait))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>cafe</th>\n",
       "      <th>afternoon</th>\n",
       "      <th>wait</th>\n",
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       "<p>200 rows × 3 columns</p>\n",
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      "text/plain": [
       "     cafe  afternoon      wait\n",
       "0       0          0  5.839082\n",
       "1       0          1  4.106898\n",
       "2       0          0  5.268901\n",
       "3       0          1  3.337065\n",
       "4       0          0  5.572800\n",
       "..    ...        ...       ...\n",
       "195    19          1  3.235406\n",
       "196    19          0  4.392893\n",
       "197    19          1  3.825197\n",
       "198    19          0  4.253631\n",
       "199    19          1  3.438692\n",
       "\n",
       "[200 rows x 3 columns]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d = generate_data_frame(22)\n",
    "d"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 14.1.3 The vaying slopes model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 14.11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:283: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'> requested in zeros is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  minval = minval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:284: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'>  is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return jaxrand.randint(key=seed, shape=shape, minval=minval, maxval=maxval,\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 600x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R = tfd.LKJ(dimension=2, concentration=2).sample((int(1e4),), seed=key())\n",
    "az.plot_kde(R[:, 0, 1], bw=2, label=\"correlation\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10000, 2, 2)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 14.12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:283: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'> requested in zeros is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  minval = minval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:284: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'>  is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return jaxrand.randint(key=seed, shape=shape, minval=minval, maxval=maxval,\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Array([[1.       , 0.5246102],\n",
       "       [0.5246102, 1.       ]], dtype=float32)"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rr = tfd.CholeskyLKJ(dimension=2, concentration=2.0).sample(seed=key())\n",
    "rr @ rr.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_14_1(cafe, afternoon):\n",
    "\tdef _generator():\n",
    "\t\ta = yield tfd.Normal(loc=5.0, scale=2.0, name='a')\n",
    "\t\tb = yield tfd.Normal(loc=-1.0, scale=0.5, name='b')\n",
    "\t\tsigma = yield tfd.Exponential(rate=1.0, name='sigma')\n",
    "\t\tsigma_cafe = yield tfd.Sample(tfd.Exponential(rate=1.0), sample_shape=2, name='sigma_cafe')\n",
    "\t\tRho = yield tfd.LKJ(dimension=2, concentration=2.0, name='Rho')\n",
    "\n",
    "\t\tsd = jnp.diag(sigma_cafe)\n",
    "\t\t# corr = Rho @ Rho.T\n",
    "\t\tcov = sd @ Rho @ sd\n",
    "\t\tab_cafe = yield tfd.Sample(\n",
    "\t\t\ttfd.MultivariateNormalFullCovariance(loc=[a, b], covariance_matrix=cov),\n",
    "\t\t\tsample_shape=20, name='ab_cafe')\n",
    "\n",
    "\t\ta_cafe, b_cafe = ab_cafe[:, 0], ab_cafe[:, 1]\n",
    "\t\tmu = jnp.take(a_cafe, cafe) + jnp.take(b_cafe, cafe) * afternoon\n",
    "\t\tyield tfd.Normal(loc=mu, scale=sigma, name='wait')\n",
    "\n",
    "\treturn tfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_14_1 = model_14_1(d.cafe.values.astype(np.int32), d.afternoon.values.astype(np.float32))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:283: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'> requested in zeros is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  minval = minval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:284: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'>  is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return jaxrand.randint(key=seed, shape=shape, minval=minval, maxval=maxval,\n"
     ]
    }
   ],
   "source": [
    "jd_14_1_pin = jd_14_1.experimental_pin(wait=d.wait.values.astype(np.float32))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jax.jit\n",
    "def run_chain(init_state, seed, step_size=1e-3, num_steps=500, burnin=1000):\n",
    "\n",
    "  def target_log_prob(*states):\n",
    "    return jd_14_1_pin.unnormalized_log_prob(states)\n",
    "  \n",
    "  bijectors = [tfb.Identity(), tfb.Identity(), tfb.Exp(), tfb.Exp(),\n",
    "               tfb.CorrelationCholesky(), tfb.Identity()]\n",
    "\n",
    "  kernel = tfp.mcmc.NoUTurnSampler(\n",
    "      target_log_prob_fn=target_log_prob,\n",
    "      step_size=step_size)\n",
    "  \n",
    "  kernel = tfp.mcmc.TransformedTransitionKernel(\n",
    "    inner_kernel=kernel,\n",
    "    bijector=bijectors)\n",
    "\n",
    "  kernel = tfp.mcmc.DualAveragingStepSizeAdaptation(\n",
    "    inner_kernel=kernel,\n",
    "    num_adaptation_steps=burnin)\n",
    "\n",
    "  chain_state = tfp.mcmc.sample_chain(\n",
    "      num_results=num_steps,\n",
    "      num_burnin_steps=burnin,\n",
    "      current_state=init_state,\n",
    "      kernel=kernel,\n",
    "      seed=seed,\n",
    "      trace_fn=None)\n",
    "  \n",
    "  return chain_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:283: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'> requested in zeros is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  minval = minval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:284: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'>  is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return jaxrand.randint(key=seed, shape=shape, minval=minval, maxval=maxval,\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:283: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'> requested in zeros is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  minval = minval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:284: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'>  is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return jaxrand.randint(key=seed, shape=shape, minval=minval, maxval=maxval,\n"
     ]
    }
   ],
   "source": [
    "num_chains = 4\n",
    "init_state = jd_14_1_pin.sample_unpinned(num_chains, seed=key())\n",
    "post_1 = run_chain(init_state=init_state, seed=key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_1_dict = {k: jnp.moveaxis(v, 0, 1) for k, v in post_1._asdict().items()}\n",
    "dict_1 = dict(posterior=post_1_dict)\n",
    "idata_1 = az.from_dict(**dict_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/arviz/stats/diagnostics.py:596: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  (between_chain_variance / within_chain_variance + num_samples - 1) / (num_samples)\n"
     ]
    },
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_5.5%</th>\n",
       "      <th>hdi_94.5%</th>\n",
       "      <th>mcse_mean</th>\n",
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       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Rho[0, 0]</th>\n",
       "      <td>1.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>1.000</td>\n",
       "      <td>1.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>2000.0</td>\n",
       "      <td>2000.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rho[0, 1]</th>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>2000.0</td>\n",
       "      <td>2000.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rho[1, 0]</th>\n",
       "      <td>-0.774</td>\n",
       "      <td>0.200</td>\n",
       "      <td>-0.965</td>\n",
       "      <td>-0.515</td>\n",
       "      <td>0.008</td>\n",
       "      <td>0.006</td>\n",
       "      <td>352.0</td>\n",
       "      <td>194.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rho[1, 1]</th>\n",
       "      <td>0.569</td>\n",
       "      <td>0.193</td>\n",
       "      <td>0.279</td>\n",
       "      <td>0.873</td>\n",
       "      <td>0.009</td>\n",
       "      <td>0.007</td>\n",
       "      <td>351.0</td>\n",
       "      <td>194.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>a</th>\n",
       "      <td>3.438</td>\n",
       "      <td>0.215</td>\n",
       "      <td>3.086</td>\n",
       "      <td>3.753</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.003</td>\n",
       "      <td>2476.0</td>\n",
       "      <td>1396.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[0, 0]</th>\n",
       "      <td>5.040</td>\n",
       "      <td>0.209</td>\n",
       "      <td>4.720</td>\n",
       "      <td>5.382</td>\n",
       "      <td>0.005</td>\n",
       "      <td>0.003</td>\n",
       "      <td>1840.0</td>\n",
       "      <td>1556.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[0, 1]</th>\n",
       "      <td>-1.495</td>\n",
       "      <td>0.266</td>\n",
       "      <td>-1.902</td>\n",
       "      <td>-1.069</td>\n",
       "      <td>0.007</td>\n",
       "      <td>0.005</td>\n",
       "      <td>1517.0</td>\n",
       "      <td>1565.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[1, 0]</th>\n",
       "      <td>2.270</td>\n",
       "      <td>0.197</td>\n",
       "      <td>1.973</td>\n",
       "      <td>2.597</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.003</td>\n",
       "      <td>2270.0</td>\n",
       "      <td>1577.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[1, 1]</th>\n",
       "      <td>-0.821</td>\n",
       "      <td>0.245</td>\n",
       "      <td>-1.217</td>\n",
       "      <td>-0.433</td>\n",
       "      <td>0.006</td>\n",
       "      <td>0.004</td>\n",
       "      <td>1621.0</td>\n",
       "      <td>1543.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[2, 0]</th>\n",
       "      <td>5.040</td>\n",
       "      <td>0.207</td>\n",
       "      <td>4.673</td>\n",
       "      <td>5.334</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.003</td>\n",
       "      <td>2149.0</td>\n",
       "      <td>1431.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[2, 1]</th>\n",
       "      <td>-1.373</td>\n",
       "      <td>0.255</td>\n",
       "      <td>-1.761</td>\n",
       "      <td>-0.942</td>\n",
       "      <td>0.006</td>\n",
       "      <td>0.004</td>\n",
       "      <td>2012.0</td>\n",
       "      <td>1195.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[3, 0]</th>\n",
       "      <td>2.232</td>\n",
       "      <td>0.205</td>\n",
       "      <td>1.933</td>\n",
       "      <td>2.579</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.003</td>\n",
       "      <td>2746.0</td>\n",
       "      <td>1771.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[3, 1]</th>\n",
       "      <td>-0.777</td>\n",
       "      <td>0.253</td>\n",
       "      <td>-1.188</td>\n",
       "      <td>-0.397</td>\n",
       "      <td>0.006</td>\n",
       "      <td>0.004</td>\n",
       "      <td>1883.0</td>\n",
       "      <td>1364.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[4, 0]</th>\n",
       "      <td>3.485</td>\n",
       "      <td>0.194</td>\n",
       "      <td>3.170</td>\n",
       "      <td>3.787</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.003</td>\n",
       "      <td>2447.0</td>\n",
       "      <td>1589.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[4, 1]</th>\n",
       "      <td>-1.008</td>\n",
       "      <td>0.232</td>\n",
       "      <td>-1.379</td>\n",
       "      <td>-0.644</td>\n",
       "      <td>0.005</td>\n",
       "      <td>0.003</td>\n",
       "      <td>2382.0</td>\n",
       "      <td>1498.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[5, 0]</th>\n",
       "      <td>3.336</td>\n",
       "      <td>0.194</td>\n",
       "      <td>2.994</td>\n",
       "      <td>3.611</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.003</td>\n",
       "      <td>2146.0</td>\n",
       "      <td>1011.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[5, 1]</th>\n",
       "      <td>-0.988</td>\n",
       "      <td>0.234</td>\n",
       "      <td>-1.349</td>\n",
       "      <td>-0.607</td>\n",
       "      <td>0.005</td>\n",
       "      <td>0.004</td>\n",
       "      <td>2288.0</td>\n",
       "      <td>1580.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[6, 0]</th>\n",
       "      <td>2.715</td>\n",
       "      <td>0.209</td>\n",
       "      <td>2.390</td>\n",
       "      <td>3.043</td>\n",
       "      <td>0.005</td>\n",
       "      <td>0.004</td>\n",
       "      <td>1560.0</td>\n",
       "      <td>1569.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[6, 1]</th>\n",
       "      <td>-0.724</td>\n",
       "      <td>0.244</td>\n",
       "      <td>-1.117</td>\n",
       "      <td>-0.352</td>\n",
       "      <td>0.006</td>\n",
       "      <td>0.005</td>\n",
       "      <td>1552.0</td>\n",
       "      <td>1392.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[7, 0]</th>\n",
       "      <td>1.917</td>\n",
       "      <td>0.212</td>\n",
       "      <td>1.579</td>\n",
       "      <td>2.257</td>\n",
       "      <td>0.006</td>\n",
       "      <td>0.004</td>\n",
       "      <td>1348.0</td>\n",
       "      <td>785.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[7, 1]</th>\n",
       "      <td>-0.094</td>\n",
       "      <td>0.279</td>\n",
       "      <td>-0.538</td>\n",
       "      <td>0.352</td>\n",
       "      <td>0.008</td>\n",
       "      <td>0.006</td>\n",
       "      <td>1105.0</td>\n",
       "      <td>1407.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[8, 0]</th>\n",
       "      <td>3.230</td>\n",
       "      <td>0.204</td>\n",
       "      <td>2.905</td>\n",
       "      <td>3.561</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.003</td>\n",
       "      <td>2143.0</td>\n",
       "      <td>1607.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[8, 1]</th>\n",
       "      <td>-1.147</td>\n",
       "      <td>0.249</td>\n",
       "      <td>-1.507</td>\n",
       "      <td>-0.744</td>\n",
       "      <td>0.006</td>\n",
       "      <td>0.004</td>\n",
       "      <td>1689.0</td>\n",
       "      <td>1539.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[9, 0]</th>\n",
       "      <td>3.702</td>\n",
       "      <td>0.204</td>\n",
       "      <td>3.366</td>\n",
       "      <td>4.014</td>\n",
       "      <td>0.005</td>\n",
       "      <td>0.004</td>\n",
       "      <td>1689.0</td>\n",
       "      <td>1475.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[9, 1]</th>\n",
       "      <td>-1.261</td>\n",
       "      <td>0.244</td>\n",
       "      <td>-1.653</td>\n",
       "      <td>-0.887</td>\n",
       "      <td>0.006</td>\n",
       "      <td>0.004</td>\n",
       "      <td>1795.0</td>\n",
       "      <td>1490.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[10, 0]</th>\n",
       "      <td>4.285</td>\n",
       "      <td>0.200</td>\n",
       "      <td>3.956</td>\n",
       "      <td>4.594</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.003</td>\n",
       "      <td>2060.0</td>\n",
       "      <td>1765.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[10, 1]</th>\n",
       "      <td>-0.853</td>\n",
       "      <td>0.252</td>\n",
       "      <td>-1.222</td>\n",
       "      <td>-0.422</td>\n",
       "      <td>0.007</td>\n",
       "      <td>0.005</td>\n",
       "      <td>1498.0</td>\n",
       "      <td>1485.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[11, 0]</th>\n",
       "      <td>3.262</td>\n",
       "      <td>0.210</td>\n",
       "      <td>2.951</td>\n",
       "      <td>3.614</td>\n",
       "      <td>0.005</td>\n",
       "      <td>0.004</td>\n",
       "      <td>1939.0</td>\n",
       "      <td>914.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[11, 1]</th>\n",
       "      <td>-0.949</td>\n",
       "      <td>0.239</td>\n",
       "      <td>-1.329</td>\n",
       "      <td>-0.577</td>\n",
       "      <td>0.005</td>\n",
       "      <td>0.004</td>\n",
       "      <td>2082.0</td>\n",
       "      <td>980.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[12, 0]</th>\n",
       "      <td>2.361</td>\n",
       "      <td>0.202</td>\n",
       "      <td>2.025</td>\n",
       "      <td>2.666</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.003</td>\n",
       "      <td>2158.0</td>\n",
       "      <td>1777.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[12, 1]</th>\n",
       "      <td>-0.472</td>\n",
       "      <td>0.248</td>\n",
       "      <td>-0.854</td>\n",
       "      <td>-0.065</td>\n",
       "      <td>0.005</td>\n",
       "      <td>0.004</td>\n",
       "      <td>2096.0</td>\n",
       "      <td>1759.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[13, 0]</th>\n",
       "      <td>3.073</td>\n",
       "      <td>0.211</td>\n",
       "      <td>2.747</td>\n",
       "      <td>3.425</td>\n",
       "      <td>0.005</td>\n",
       "      <td>0.004</td>\n",
       "      <td>1689.0</td>\n",
       "      <td>1130.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[13, 1]</th>\n",
       "      <td>-0.422</td>\n",
       "      <td>0.271</td>\n",
       "      <td>-0.881</td>\n",
       "      <td>-0.023</td>\n",
       "      <td>0.007</td>\n",
       "      <td>0.006</td>\n",
       "      <td>1311.0</td>\n",
       "      <td>1077.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[14, 0]</th>\n",
       "      <td>2.529</td>\n",
       "      <td>0.204</td>\n",
       "      <td>2.189</td>\n",
       "      <td>2.840</td>\n",
       "      <td>0.005</td>\n",
       "      <td>0.003</td>\n",
       "      <td>1873.0</td>\n",
       "      <td>1554.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[14, 1]</th>\n",
       "      <td>-0.843</td>\n",
       "      <td>0.245</td>\n",
       "      <td>-1.256</td>\n",
       "      <td>-0.473</td>\n",
       "      <td>0.006</td>\n",
       "      <td>0.005</td>\n",
       "      <td>1542.0</td>\n",
       "      <td>1255.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[15, 0]</th>\n",
       "      <td>3.344</td>\n",
       "      <td>0.207</td>\n",
       "      <td>3.010</td>\n",
       "      <td>3.660</td>\n",
       "      <td>0.005</td>\n",
       "      <td>0.004</td>\n",
       "      <td>1643.0</td>\n",
       "      <td>818.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[15, 1]</th>\n",
       "      <td>-0.817</td>\n",
       "      <td>0.241</td>\n",
       "      <td>-1.195</td>\n",
       "      <td>-0.426</td>\n",
       "      <td>0.005</td>\n",
       "      <td>0.004</td>\n",
       "      <td>1991.0</td>\n",
       "      <td>758.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[16, 0]</th>\n",
       "      <td>3.512</td>\n",
       "      <td>0.195</td>\n",
       "      <td>3.194</td>\n",
       "      <td>3.807</td>\n",
       "      <td>0.005</td>\n",
       "      <td>0.004</td>\n",
       "      <td>1448.0</td>\n",
       "      <td>1037.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[16, 1]</th>\n",
       "      <td>-0.884</td>\n",
       "      <td>0.223</td>\n",
       "      <td>-1.243</td>\n",
       "      <td>-0.542</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.003</td>\n",
       "      <td>2607.0</td>\n",
       "      <td>1843.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[17, 0]</th>\n",
       "      <td>4.692</td>\n",
       "      <td>0.204</td>\n",
       "      <td>4.357</td>\n",
       "      <td>4.999</td>\n",
       "      <td>0.005</td>\n",
       "      <td>0.003</td>\n",
       "      <td>1759.0</td>\n",
       "      <td>1430.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[17, 1]</th>\n",
       "      <td>-1.194</td>\n",
       "      <td>0.245</td>\n",
       "      <td>-1.602</td>\n",
       "      <td>-0.828</td>\n",
       "      <td>0.006</td>\n",
       "      <td>0.004</td>\n",
       "      <td>1817.0</td>\n",
       "      <td>1181.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[18, 0]</th>\n",
       "      <td>4.271</td>\n",
       "      <td>0.203</td>\n",
       "      <td>3.981</td>\n",
       "      <td>4.620</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.003</td>\n",
       "      <td>2304.0</td>\n",
       "      <td>1648.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[18, 1]</th>\n",
       "      <td>-1.322</td>\n",
       "      <td>0.249</td>\n",
       "      <td>-1.761</td>\n",
       "      <td>-0.957</td>\n",
       "      <td>0.006</td>\n",
       "      <td>0.004</td>\n",
       "      <td>2028.0</td>\n",
       "      <td>1508.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[19, 0]</th>\n",
       "      <td>4.007</td>\n",
       "      <td>0.196</td>\n",
       "      <td>3.701</td>\n",
       "      <td>4.325</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.003</td>\n",
       "      <td>2268.0</td>\n",
       "      <td>1284.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ab_cafe[19, 1]</th>\n",
       "      <td>-0.902</td>\n",
       "      <td>0.242</td>\n",
       "      <td>-1.282</td>\n",
       "      <td>-0.522</td>\n",
       "      <td>0.005</td>\n",
       "      <td>0.004</td>\n",
       "      <td>2079.0</td>\n",
       "      <td>1691.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b</th>\n",
       "      <td>-0.926</td>\n",
       "      <td>0.116</td>\n",
       "      <td>-1.107</td>\n",
       "      <td>-0.743</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.002</td>\n",
       "      <td>1916.0</td>\n",
       "      <td>1633.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma</th>\n",
       "      <td>0.493</td>\n",
       "      <td>0.027</td>\n",
       "      <td>0.448</td>\n",
       "      <td>0.534</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>1308.0</td>\n",
       "      <td>1414.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma_cafe[0]</th>\n",
       "      <td>0.952</td>\n",
       "      <td>0.167</td>\n",
       "      <td>0.715</td>\n",
       "      <td>1.211</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.003</td>\n",
       "      <td>1733.0</td>\n",
       "      <td>1287.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma_cafe[1]</th>\n",
       "      <td>0.575</td>\n",
       "      <td>0.192</td>\n",
       "      <td>0.281</td>\n",
       "      <td>0.850</td>\n",
       "      <td>0.007</td>\n",
       "      <td>0.005</td>\n",
       "      <td>699.0</td>\n",
       "      <td>1095.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 mean     sd  hdi_5.5%  hdi_94.5%  mcse_mean  mcse_sd  \\\n",
       "Rho[0, 0]       1.000  0.000     1.000      1.000      0.000    0.000   \n",
       "Rho[0, 1]       0.000  0.000     0.000      0.000      0.000    0.000   \n",
       "Rho[1, 0]      -0.774  0.200    -0.965     -0.515      0.008    0.006   \n",
       "Rho[1, 1]       0.569  0.193     0.279      0.873      0.009    0.007   \n",
       "a               3.438  0.215     3.086      3.753      0.004    0.003   \n",
       "ab_cafe[0, 0]   5.040  0.209     4.720      5.382      0.005    0.003   \n",
       "ab_cafe[0, 1]  -1.495  0.266    -1.902     -1.069      0.007    0.005   \n",
       "ab_cafe[1, 0]   2.270  0.197     1.973      2.597      0.004    0.003   \n",
       "ab_cafe[1, 1]  -0.821  0.245    -1.217     -0.433      0.006    0.004   \n",
       "ab_cafe[2, 0]   5.040  0.207     4.673      5.334      0.004    0.003   \n",
       "ab_cafe[2, 1]  -1.373  0.255    -1.761     -0.942      0.006    0.004   \n",
       "ab_cafe[3, 0]   2.232  0.205     1.933      2.579      0.004    0.003   \n",
       "ab_cafe[3, 1]  -0.777  0.253    -1.188     -0.397      0.006    0.004   \n",
       "ab_cafe[4, 0]   3.485  0.194     3.170      3.787      0.004    0.003   \n",
       "ab_cafe[4, 1]  -1.008  0.232    -1.379     -0.644      0.005    0.003   \n",
       "ab_cafe[5, 0]   3.336  0.194     2.994      3.611      0.004    0.003   \n",
       "ab_cafe[5, 1]  -0.988  0.234    -1.349     -0.607      0.005    0.004   \n",
       "ab_cafe[6, 0]   2.715  0.209     2.390      3.043      0.005    0.004   \n",
       "ab_cafe[6, 1]  -0.724  0.244    -1.117     -0.352      0.006    0.005   \n",
       "ab_cafe[7, 0]   1.917  0.212     1.579      2.257      0.006    0.004   \n",
       "ab_cafe[7, 1]  -0.094  0.279    -0.538      0.352      0.008    0.006   \n",
       "ab_cafe[8, 0]   3.230  0.204     2.905      3.561      0.004    0.003   \n",
       "ab_cafe[8, 1]  -1.147  0.249    -1.507     -0.744      0.006    0.004   \n",
       "ab_cafe[9, 0]   3.702  0.204     3.366      4.014      0.005    0.004   \n",
       "ab_cafe[9, 1]  -1.261  0.244    -1.653     -0.887      0.006    0.004   \n",
       "ab_cafe[10, 0]  4.285  0.200     3.956      4.594      0.004    0.003   \n",
       "ab_cafe[10, 1] -0.853  0.252    -1.222     -0.422      0.007    0.005   \n",
       "ab_cafe[11, 0]  3.262  0.210     2.951      3.614      0.005    0.004   \n",
       "ab_cafe[11, 1] -0.949  0.239    -1.329     -0.577      0.005    0.004   \n",
       "ab_cafe[12, 0]  2.361  0.202     2.025      2.666      0.004    0.003   \n",
       "ab_cafe[12, 1] -0.472  0.248    -0.854     -0.065      0.005    0.004   \n",
       "ab_cafe[13, 0]  3.073  0.211     2.747      3.425      0.005    0.004   \n",
       "ab_cafe[13, 1] -0.422  0.271    -0.881     -0.023      0.007    0.006   \n",
       "ab_cafe[14, 0]  2.529  0.204     2.189      2.840      0.005    0.003   \n",
       "ab_cafe[14, 1] -0.843  0.245    -1.256     -0.473      0.006    0.005   \n",
       "ab_cafe[15, 0]  3.344  0.207     3.010      3.660      0.005    0.004   \n",
       "ab_cafe[15, 1] -0.817  0.241    -1.195     -0.426      0.005    0.004   \n",
       "ab_cafe[16, 0]  3.512  0.195     3.194      3.807      0.005    0.004   \n",
       "ab_cafe[16, 1] -0.884  0.223    -1.243     -0.542      0.004    0.003   \n",
       "ab_cafe[17, 0]  4.692  0.204     4.357      4.999      0.005    0.003   \n",
       "ab_cafe[17, 1] -1.194  0.245    -1.602     -0.828      0.006    0.004   \n",
       "ab_cafe[18, 0]  4.271  0.203     3.981      4.620      0.004    0.003   \n",
       "ab_cafe[18, 1] -1.322  0.249    -1.761     -0.957      0.006    0.004   \n",
       "ab_cafe[19, 0]  4.007  0.196     3.701      4.325      0.004    0.003   \n",
       "ab_cafe[19, 1] -0.902  0.242    -1.282     -0.522      0.005    0.004   \n",
       "b              -0.926  0.116    -1.107     -0.743      0.003    0.002   \n",
       "sigma           0.493  0.027     0.448      0.534      0.001    0.001   \n",
       "sigma_cafe[0]   0.952  0.167     0.715      1.211      0.004    0.003   \n",
       "sigma_cafe[1]   0.575  0.192     0.281      0.850      0.007    0.005   \n",
       "\n",
       "                ess_bulk  ess_tail  r_hat  \n",
       "Rho[0, 0]         2000.0    2000.0    NaN  \n",
       "Rho[0, 1]         2000.0    2000.0    NaN  \n",
       "Rho[1, 0]          352.0     194.0   1.01  \n",
       "Rho[1, 1]          351.0     194.0   1.01  \n",
       "a                 2476.0    1396.0   1.00  \n",
       "ab_cafe[0, 0]     1840.0    1556.0   1.00  \n",
       "ab_cafe[0, 1]     1517.0    1565.0   1.00  \n",
       "ab_cafe[1, 0]     2270.0    1577.0   1.00  \n",
       "ab_cafe[1, 1]     1621.0    1543.0   1.00  \n",
       "ab_cafe[2, 0]     2149.0    1431.0   1.00  \n",
       "ab_cafe[2, 1]     2012.0    1195.0   1.00  \n",
       "ab_cafe[3, 0]     2746.0    1771.0   1.00  \n",
       "ab_cafe[3, 1]     1883.0    1364.0   1.00  \n",
       "ab_cafe[4, 0]     2447.0    1589.0   1.00  \n",
       "ab_cafe[4, 1]     2382.0    1498.0   1.00  \n",
       "ab_cafe[5, 0]     2146.0    1011.0   1.00  \n",
       "ab_cafe[5, 1]     2288.0    1580.0   1.01  \n",
       "ab_cafe[6, 0]     1560.0    1569.0   1.00  \n",
       "ab_cafe[6, 1]     1552.0    1392.0   1.00  \n",
       "ab_cafe[7, 0]     1348.0     785.0   1.00  \n",
       "ab_cafe[7, 1]     1105.0    1407.0   1.00  \n",
       "ab_cafe[8, 0]     2143.0    1607.0   1.00  \n",
       "ab_cafe[8, 1]     1689.0    1539.0   1.00  \n",
       "ab_cafe[9, 0]     1689.0    1475.0   1.00  \n",
       "ab_cafe[9, 1]     1795.0    1490.0   1.00  \n",
       "ab_cafe[10, 0]    2060.0    1765.0   1.00  \n",
       "ab_cafe[10, 1]    1498.0    1485.0   1.00  \n",
       "ab_cafe[11, 0]    1939.0     914.0   1.00  \n",
       "ab_cafe[11, 1]    2082.0     980.0   1.00  \n",
       "ab_cafe[12, 0]    2158.0    1777.0   1.00  \n",
       "ab_cafe[12, 1]    2096.0    1759.0   1.00  \n",
       "ab_cafe[13, 0]    1689.0    1130.0   1.00  \n",
       "ab_cafe[13, 1]    1311.0    1077.0   1.00  \n",
       "ab_cafe[14, 0]    1873.0    1554.0   1.01  \n",
       "ab_cafe[14, 1]    1542.0    1255.0   1.00  \n",
       "ab_cafe[15, 0]    1643.0     818.0   1.01  \n",
       "ab_cafe[15, 1]    1991.0     758.0   1.00  \n",
       "ab_cafe[16, 0]    1448.0    1037.0   1.00  \n",
       "ab_cafe[16, 1]    2607.0    1843.0   1.00  \n",
       "ab_cafe[17, 0]    1759.0    1430.0   1.00  \n",
       "ab_cafe[17, 1]    1817.0    1181.0   1.00  \n",
       "ab_cafe[18, 0]    2304.0    1648.0   1.00  \n",
       "ab_cafe[18, 1]    2028.0    1508.0   1.00  \n",
       "ab_cafe[19, 0]    2268.0    1284.0   1.00  \n",
       "ab_cafe[19, 1]    2079.0    1691.0   1.00  \n",
       "b                 1916.0    1633.0   1.00  \n",
       "sigma             1308.0    1414.0   1.00  \n",
       "sigma_cafe[0]     1733.0    1287.0   1.00  \n",
       "sigma_cafe[1]      699.0    1095.0   1.00  "
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata_1, hdi_prob=0.89)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 14.13"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_kde(post_1_dict['Rho'][:, :, 1, 0], bw=2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 14.14"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4, 500, 20, 2)"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "post_1_dict[\"ab_cafe\"].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a1 = np.array(\n",
    "    [np.mean(d.wait[(cafe_id == i) & (afternoon == 0)]) for i in range(N_cafes)]\n",
    ")\n",
    "b1 = (\n",
    "    np.array(\n",
    "        [np.mean(d.wait[(cafe_id == i) & (afternoon == 1)]) for i in range(N_cafes)]\n",
    "    )\n",
    "    - a1\n",
    ")\n",
    "\n",
    "# extract posterior means of partially pooled estimates\n",
    "a2 = np.mean(post_1_dict[\"ab_cafe\"][..., 0], axis=(0, 1))\n",
    "b2 = np.mean(post_1_dict[\"ab_cafe\"][..., 1], axis=(0, 1))\n",
    "\n",
    "# plot both and connect with lines\n",
    "plt.plot(a1, b1, \"o\")\n",
    "plt.gca().set(\n",
    "    xlabel=\"intercept\",\n",
    "    ylabel=\"slope\",\n",
    "    ylim=(np.min(b1) - 0.1, np.max(b1) + 0.1),\n",
    "    xlim=(np.min(a1) - 0.1, np.max(a1) + 0.1),\n",
    ")\n",
    "plt.plot(a2, b2, \"ko\", mfc=\"none\")\n",
    "\n",
    "for i in range(N_cafes):\n",
    "    plt.plot([a1[i], a2[i]], [b1[i], b2[i]], \"k\", lw=0.5)\n",
    "fig, ax = plt.gcf(), plt.gca()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 14.15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x500 with 1 Axes>"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compute posterior mean bivariate Gaussian\n",
    "Mu_est = np.array([np.mean(post_1_dict[\"a\"]), np.mean(post_1_dict[\"b\"])])\n",
    "rho_est = np.mean(post_1_dict[\"Rho\"][..., 1, 0])\n",
    "\n",
    "sa_est = np.mean(post_1_dict[\"sigma\"][..., 0])\n",
    "sb_est = np.mean(post_1_dict[\"sigma\"][..., 1])\n",
    "\n",
    "cov_ab = sa_est * sb_est * rho_est\n",
    "Sigma_est = np.array([[sa_est ** 2, cov_ab], [cov_ab, sb_est ** 2]])\n",
    "\n",
    "# draw contours\n",
    "for l in [0.1, 0.3, 0.5, 0.8, 0.99]:\n",
    "    pearson = Sigma_est[0, 1] / np.sqrt(Sigma_est[0, 0] * Sigma_est[1, 1])\n",
    "    ellipse = Ellipse(\n",
    "        (0, 0),\n",
    "        np.sqrt(1 + pearson),\n",
    "        np.sqrt(1 - pearson),\n",
    "        edgecolor=\"k\",\n",
    "        alpha=0.2,\n",
    "        facecolor=\"none\",\n",
    "    )\n",
    "\n",
    "    std_dev = tfd.Normal(loc=0.0, scale=1.0).quantile((1 + np.sqrt(l)) / 2)\n",
    "\n",
    "    scale_x = 2 * std_dev * np.sqrt(Sigma_est[0, 0])\n",
    "    scale_y = 2 * std_dev * np.sqrt(Sigma_est[1, 1])\n",
    "    scale = transforms.Affine2D().rotate_deg(45).scale(scale_x, scale_y)\n",
    "    ellipse.set_transform(scale.translate(Mu_est[0], Mu_est[1]) + ax.transData)\n",
    "    ax.add_patch(ellipse)\n",
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 14.16"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# convert varying effects to waiting times\n",
    "wait_morning_1 = a1\n",
    "wait_afternoon_1 = a1 + b1\n",
    "wait_morning_2 = a2\n",
    "wait_afternoon_2 = a2 + b2\n",
    "\n",
    "# plot both and connect with lines\n",
    "plt.plot(wait_morning_1, wait_afternoon_1, \"o\")\n",
    "plt.gca().set(\n",
    "    xlabel=\"morning wait\",\n",
    "    ylabel=\"afternoon wait\",\n",
    "    ylim=(np.min(wait_afternoon_1) - 0.1, np.max(wait_afternoon_1) + 0.1),\n",
    "    xlim=(np.min(wait_morning_1) - 0.1, np.max(wait_morning_1) + 0.1),\n",
    ")\n",
    "plt.plot(wait_morning_2, wait_afternoon_2, \"ko\", mfc=\"none\")\n",
    "for i in range(N_cafes):\n",
    "    plt.plot(\n",
    "        [wait_morning_1[i], wait_morning_2[i]],\n",
    "        [wait_afternoon_1[i], wait_afternoon_2[i]],\n",
    "        \"k\",\n",
    "        lw=0.5,\n",
    "    )\n",
    "x = np.linspace(np.min(wait_morning_1), np.max(wait_morning_1), 101)\n",
    "plt.plot(x, x, \"k--\", lw=1)\n",
    "fig, ax = plt.gcf(), plt.gca()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 14.17"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x500 with 1 Axes>"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# now shrinkage distribution by simulation\n",
    "v = (\n",
    "    tfd.MultivariateNormalFullCovariance(loc=Mu_est, covariance_matrix=Sigma_est)\n",
    "    .sample(10000, seed=key())\n",
    ")\n",
    "\n",
    "# v[:, 1] = v[:, 0] + v[:, 1]  # calculate afternoon wait\n",
    "v = jnp.stack([v[:, 0], v[:, 0] + v[:, 1]], axis=1)\n",
    "\n",
    "Sigma_est2 = np.cov(v, rowvar=False)\n",
    "\n",
    "Mu_est2 = Mu_est\n",
    "\n",
    "Mu_est2[1] = Mu_est2[0] + Mu_est2[1]\n",
    "\n",
    "# draw contours\n",
    "for l in [0.1, 0.3, 0.5, 0.8, 0.99]:\n",
    "    pearson = Sigma_est2[0, 1] / np.sqrt(Sigma_est2[0, 0] * Sigma_est2[1, 1])\n",
    "    ellipse = Ellipse(\n",
    "        (0, 0),\n",
    "        np.sqrt(1 + pearson),\n",
    "        np.sqrt(1 - pearson),\n",
    "        edgecolor=\"k\",\n",
    "        alpha=0.2,\n",
    "        facecolor=\"none\",\n",
    "    )\n",
    "\n",
    "    std_dev = tfd.Normal(loc=0.0, scale=1.0).quantile((1 + np.sqrt(l)) / 2)\n",
    "\n",
    "    scale_x = 2 * std_dev * np.sqrt(Sigma_est2[0, 0])\n",
    "    scale_y = 2 * std_dev * np.sqrt(Sigma_est2[1, 1])\n",
    "    scale = transforms.Affine2D().rotate_deg(45).scale(scale_x, scale_y)\n",
    "    ellipse.set_transform(scale.translate(Mu_est2[0], Mu_est2[1]) + ax.transData)\n",
    "    ax.add_patch(ellipse)\n",
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 14.2 Advanced varying slopes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 14.18"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [],
   "source": [
    "d = pd.read_csv(\"./data/Chimpanzees.csv\", sep=\";\")\n",
    "d[\"block_id\"] = d.block\n",
    "d[\"treatment\"] = 1 + d.prosoc_left + 2 * d.condition\n",
    "\n",
    "dat = dict(\n",
    "    L=d.pulled_left.values,\n",
    "    tid=d.treatment.values - 1,\n",
    "    actor=d.actor.values - 1,\n",
    "    block_id=d.block_id.values - 1,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_14_2(tid, actor, block_id):\n",
    "\tdef _generator():\n",
    "\t\t# fixed priors\n",
    "\t\tg = yield tfd.Sample(tfd.Normal(loc=0.0, scale=1.0), sample_shape=4, name='g')\n",
    "\t\tsigma_actor = yield tfd.Sample(tfd.Exponential(rate=1.0), sample_shape=4, name='sigma_actor')\n",
    "\t\tRho_actor = yield tfd.LKJ(dimension=4, concentration=2.0, name='Rho_actor')\n",
    "\t\tsigma_block = yield tfd.Sample(tfd.Exponential(rate=1.0), sample_shape=4, name='sigma_block')\n",
    "\t\tRho_block = yield tfd.LKJ(dimension=4, concentration=2.0, name='Rho_block')\n",
    "\n",
    "\t\t# adaptive priors\n",
    "\t\tsd_actor = jnp.diag(sigma_actor)\n",
    "\t\tcov_actor = sd_actor @ Rho_actor @ sd_actor\n",
    "\t\talpha = yield tfd.Sample(\n",
    "\t\t\ttfd.MultivariateNormalFullCovariance(loc=0, covariance_matrix=cov_actor),\n",
    "\t\t\tsample_shape=7, name='alpha')\n",
    "\t\t\n",
    "\t\tsd_block = jnp.diag(sigma_block)\n",
    "\t\tcov_block = sd_block @ Rho_block @ sd_block\n",
    "\t\tbeta = yield tfd.Sample(\n",
    "\t\t\ttfd.MultivariateNormalFullCovariance(loc=0, covariance_matrix=cov_block),\n",
    "\t\t\tsample_shape=6, name='beta')\n",
    "\n",
    "\t\tlogit = jnp.take(g, tid) + alpha.at[actor, tid].get() + beta.at[block_id, tid].get()\n",
    "\t\tyield tfd.Bernoulli(logits=logit, name='L')\n",
    "\n",
    "\treturn tfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_14_2 = model_14_2(dat[\"tid\"], dat[\"actor\"], dat[\"block_id\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:283: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'> requested in zeros is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  minval = minval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:284: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'>  is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return jaxrand.randint(key=seed, shape=shape, minval=minval, maxval=maxval,\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:283: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'> requested in zeros is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  minval = minval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:284: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'>  is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return jaxrand.randint(key=seed, shape=shape, minval=minval, maxval=maxval,\n"
     ]
    }
   ],
   "source": [
    "jd_14_2_pin = jd_14_2.experimental_pin(L=dat[\"L\"].astype(np.float32))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jax.jit\n",
    "def run_chain(init_state, seed, step_size=1e-3, num_steps=500, burnin=1000):\n",
    "\n",
    "  def target_log_prob(*states):\n",
    "    return jd_14_2_pin.unnormalized_log_prob(states)\n",
    "  \n",
    "  bijectors = [tfb.Identity(), tfb.Exp(), tfb.CorrelationCholesky(), tfb.Exp(),\n",
    "               tfb.CorrelationCholesky(), tfb.Identity(), tfb.Identity()]\n",
    "\n",
    "  kernel = tfp.mcmc.NoUTurnSampler(\n",
    "      target_log_prob_fn=target_log_prob,\n",
    "      step_size=step_size)\n",
    "  \n",
    "  kernel = tfp.mcmc.TransformedTransitionKernel(\n",
    "    inner_kernel=kernel,\n",
    "    bijector=bijectors)\n",
    "\n",
    "  kernel = tfp.mcmc.DualAveragingStepSizeAdaptation(\n",
    "    inner_kernel=kernel,\n",
    "    num_adaptation_steps=burnin)\n",
    "\n",
    "  chain_state = tfp.mcmc.sample_chain(\n",
    "      num_results=num_steps,\n",
    "      num_burnin_steps=burnin,\n",
    "      current_state=init_state,\n",
    "      kernel=kernel,\n",
    "      seed=seed,\n",
    "      trace_fn=None)\n",
    "  \n",
    "  return chain_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:283: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'> requested in zeros is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  minval = minval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:284: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'>  is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return jaxrand.randint(key=seed, shape=shape, minval=minval, maxval=maxval,\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:283: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'> requested in zeros is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  minval = minval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:284: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'>  is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return jaxrand.randint(key=seed, shape=shape, minval=minval, maxval=maxval,\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:283: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'> requested in zeros is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  minval = minval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:284: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'>  is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return jaxrand.randint(key=seed, shape=shape, minval=minval, maxval=maxval,\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:283: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'> requested in zeros is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  minval = minval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:284: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'>  is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return jaxrand.randint(key=seed, shape=shape, minval=minval, maxval=maxval,\n"
     ]
    }
   ],
   "source": [
    "num_chains = 4\n",
    "init_state = jd_14_2_pin.sample_unpinned(num_chains, seed=key())\n",
    "post_2 = run_chain(init_state=init_state, seed=key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_2_dict = {k: jnp.moveaxis(v, 0, 1) for k, v in post_2._asdict().items()}\n",
    "dict_2 = dict(posterior=post_2_dict)\n",
    "idata_2 = az.from_dict(**dict_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/arviz/stats/diagnostics.py:596: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  (between_chain_variance / within_chain_variance + num_samples - 1) / (num_samples)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/arviz/stats/diagnostics.py:596: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  (between_chain_variance / within_chain_variance + num_samples - 1) / (num_samples)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/arviz/stats/diagnostics.py:596: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  (between_chain_variance / within_chain_variance + num_samples - 1) / (num_samples)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/arviz/stats/diagnostics.py:596: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  (between_chain_variance / within_chain_variance + num_samples - 1) / (num_samples)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/arviz/stats/diagnostics.py:596: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  (between_chain_variance / within_chain_variance + num_samples - 1) / (num_samples)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/arviz/stats/diagnostics.py:596: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  (between_chain_variance / within_chain_variance + num_samples - 1) / (num_samples)\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>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_5.5%</th>\n",
       "      <th>hdi_94.5%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Rho_actor[0, 0]</th>\n",
       "      <td>1.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>1.000</td>\n",
       "      <td>1.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>2000.0</td>\n",
       "      <td>2000.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rho_actor[0, 1]</th>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>2000.0</td>\n",
       "      <td>2000.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rho_actor[0, 2]</th>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>2000.0</td>\n",
       "      <td>2000.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rho_actor[0, 3]</th>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>2000.0</td>\n",
       "      <td>2000.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rho_actor[1, 0]</th>\n",
       "      <td>0.354</td>\n",
       "      <td>0.436</td>\n",
       "      <td>-0.277</td>\n",
       "      <td>0.960</td>\n",
       "      <td>0.024</td>\n",
       "      <td>0.018</td>\n",
       "      <td>305.0</td>\n",
       "      <td>379.0</td>\n",
       "      <td>1.02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma_actor[3]</th>\n",
       "      <td>2.091</td>\n",
       "      <td>0.768</td>\n",
       "      <td>1.056</td>\n",
       "      <td>3.209</td>\n",
       "      <td>0.042</td>\n",
       "      <td>0.030</td>\n",
       "      <td>364.0</td>\n",
       "      <td>349.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma_block[0]</th>\n",
       "      <td>0.383</td>\n",
       "      <td>0.286</td>\n",
       "      <td>0.020</td>\n",
       "      <td>0.760</td>\n",
       "      <td>0.021</td>\n",
       "      <td>0.015</td>\n",
       "      <td>154.0</td>\n",
       "      <td>208.0</td>\n",
       "      <td>1.04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma_block[1]</th>\n",
       "      <td>0.464</td>\n",
       "      <td>0.384</td>\n",
       "      <td>0.018</td>\n",
       "      <td>0.919</td>\n",
       "      <td>0.032</td>\n",
       "      <td>0.023</td>\n",
       "      <td>112.0</td>\n",
       "      <td>187.0</td>\n",
       "      <td>1.02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma_block[2]</th>\n",
       "      <td>0.359</td>\n",
       "      <td>0.314</td>\n",
       "      <td>0.018</td>\n",
       "      <td>0.700</td>\n",
       "      <td>0.024</td>\n",
       "      <td>0.017</td>\n",
       "      <td>133.0</td>\n",
       "      <td>169.0</td>\n",
       "      <td>1.02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma_block[3]</th>\n",
       "      <td>0.541</td>\n",
       "      <td>0.412</td>\n",
       "      <td>0.020</td>\n",
       "      <td>1.023</td>\n",
       "      <td>0.039</td>\n",
       "      <td>0.027</td>\n",
       "      <td>96.0</td>\n",
       "      <td>240.0</td>\n",
       "      <td>1.04</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>96 rows × 9 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                  mean     sd  hdi_5.5%  hdi_94.5%  mcse_mean  mcse_sd  \\\n",
       "Rho_actor[0, 0]  1.000  0.000     1.000      1.000      0.000    0.000   \n",
       "Rho_actor[0, 1]  0.000  0.000     0.000      0.000      0.000    0.000   \n",
       "Rho_actor[0, 2]  0.000  0.000     0.000      0.000      0.000    0.000   \n",
       "Rho_actor[0, 3]  0.000  0.000     0.000      0.000      0.000    0.000   \n",
       "Rho_actor[1, 0]  0.354  0.436    -0.277      0.960      0.024    0.018   \n",
       "...                ...    ...       ...        ...        ...      ...   \n",
       "sigma_actor[3]   2.091  0.768     1.056      3.209      0.042    0.030   \n",
       "sigma_block[0]   0.383  0.286     0.020      0.760      0.021    0.015   \n",
       "sigma_block[1]   0.464  0.384     0.018      0.919      0.032    0.023   \n",
       "sigma_block[2]   0.359  0.314     0.018      0.700      0.024    0.017   \n",
       "sigma_block[3]   0.541  0.412     0.020      1.023      0.039    0.027   \n",
       "\n",
       "                 ess_bulk  ess_tail  r_hat  \n",
       "Rho_actor[0, 0]    2000.0    2000.0    NaN  \n",
       "Rho_actor[0, 1]    2000.0    2000.0    NaN  \n",
       "Rho_actor[0, 2]    2000.0    2000.0    NaN  \n",
       "Rho_actor[0, 3]    2000.0    2000.0    NaN  \n",
       "Rho_actor[1, 0]     305.0     379.0   1.02  \n",
       "...                   ...       ...    ...  \n",
       "sigma_actor[3]      364.0     349.0   1.01  \n",
       "sigma_block[0]      154.0     208.0   1.04  \n",
       "sigma_block[1]      112.0     187.0   1.02  \n",
       "sigma_block[2]      133.0     169.0   1.02  \n",
       "sigma_block[3]       96.0     240.0   1.04  \n",
       "\n",
       "[96 rows x 9 columns]"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata_2, hdi_prob=0.89)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 14.19"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_14_3(tid, actor, block_id):\n",
    "\tdef _generator():\n",
    "\t\t# fixed priors\n",
    "\t\tg = yield tfd.Sample(tfd.Normal(loc=0.0, scale=1.0), sample_shape=4, name='g')\n",
    "\t\tsigma_actor = yield tfd.Sample(tfd.Exponential(rate=1.0), sample_shape=4, name='sigma_actor')\n",
    "\t\trho_chol_actor = yield tfd.CholeskyLKJ(dimension=4, concentration=2.0, name='rho_chol_actor')\n",
    "\t\tsigma_block = yield tfd.Sample(tfd.Exponential(rate=1.0), sample_shape=4, name='sigma_block')\n",
    "\t\trho_chol_block = yield tfd.CholeskyLKJ(dimension=4, concentration=2.0, name='rho_chol_block')\n",
    "\n",
    "\t\t# adaptive priors\n",
    "\t\tsd_actor = jnp.diag(sigma_actor)\n",
    "\t\tz_actor = yield tfd.Sample(\n",
    "\t\t\ttfd.MultivariateNormalDiag(loc=0., scale_diag=jnp.ones(4)),\n",
    "\t\t\tsample_shape=7, name='z_actor')\n",
    "\t\talpha = z_actor @ rho_chol_actor.T @ sd_actor\n",
    "\n",
    "\t\tsd_block = jnp.diag(sigma_block)\n",
    "\t\tz_block = yield tfd.Sample(\n",
    "\t\t\ttfd.MultivariateNormalDiag(loc=0., scale_diag=jnp.ones(4)),\n",
    "\t\t\tsample_shape=6, name='z_block')\n",
    "\t\tbeta = z_block @ rho_chol_block.T @ sd_block\n",
    "\n",
    "\t\tlogit = jnp.take(g, tid) + alpha.at[actor, tid].get() + beta.at[block_id, tid].get()\n",
    "\t\tyield tfd.Bernoulli(logits=logit, name='L')\n",
    "\n",
    "\treturn tfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_14_3 = model_14_3(dat[\"tid\"], dat[\"actor\"], dat[\"block_id\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:283: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'> requested in zeros is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  minval = minval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:284: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'>  is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return jaxrand.randint(key=seed, shape=shape, minval=minval, maxval=maxval,\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:283: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'> requested in zeros is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  minval = minval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:284: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'>  is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return jaxrand.randint(key=seed, shape=shape, minval=minval, maxval=maxval,\n"
     ]
    }
   ],
   "source": [
    "jd_14_3_pin = jd_14_3.experimental_pin(L=dat[\"L\"].astype(np.float32))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jax.jit\n",
    "def run_chain(init_state, seed, step_size=1e-3, num_steps=500, burnin=1000):\n",
    "\n",
    "  def target_log_prob(*states):\n",
    "    return jd_14_3_pin.unnormalized_log_prob(states)\n",
    "  \n",
    "  bijectors = [tfb.Identity(), tfb.Exp(), tfb.CorrelationCholesky(), tfb.Exp(),\n",
    "               tfb.CorrelationCholesky(), tfb.Identity(), tfb.Identity()]\n",
    "\n",
    "  kernel = tfp.mcmc.NoUTurnSampler(\n",
    "      target_log_prob_fn=target_log_prob,\n",
    "      step_size=step_size)\n",
    "  \n",
    "  kernel = tfp.mcmc.TransformedTransitionKernel(\n",
    "    inner_kernel=kernel,\n",
    "    bijector=bijectors)\n",
    "\n",
    "  kernel = tfp.mcmc.DualAveragingStepSizeAdaptation(\n",
    "    inner_kernel=kernel,\n",
    "    num_adaptation_steps=burnin)\n",
    "\n",
    "  chain_state = tfp.mcmc.sample_chain(\n",
    "      num_results=num_steps,\n",
    "      num_burnin_steps=burnin,\n",
    "      current_state=init_state,\n",
    "      kernel=kernel,\n",
    "      seed=seed,\n",
    "      trace_fn=None)\n",
    "  \n",
    "  return chain_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:283: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'> requested in zeros is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  minval = minval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:284: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'>  is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return jaxrand.randint(key=seed, shape=shape, minval=minval, maxval=maxval,\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:283: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'> requested in zeros is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  minval = minval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:284: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'>  is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return jaxrand.randint(key=seed, shape=shape, minval=minval, maxval=maxval,\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:283: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'> requested in zeros is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  minval = minval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:284: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'>  is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return jaxrand.randint(key=seed, shape=shape, minval=minval, maxval=maxval,\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:283: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'> requested in zeros is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  minval = minval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:284: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'>  is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return jaxrand.randint(key=seed, shape=shape, minval=minval, maxval=maxval,\n"
     ]
    }
   ],
   "source": [
    "num_chains = 4\n",
    "init_state = jd_14_3_pin.sample_unpinned(num_chains, seed=key())\n",
    "post_3 = run_chain(init_state=init_state, seed=key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_3_dict = {k: jnp.moveaxis(v, 0, 1) for k, v in post_3._asdict().items()}\n",
    "dict_3 = dict(posterior=post_3_dict)\n",
    "idata_3 = az.from_dict(**dict_3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/arviz/stats/diagnostics.py:596: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  (between_chain_variance / within_chain_variance + num_samples - 1) / (num_samples)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/arviz/stats/diagnostics.py:596: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  (between_chain_variance / within_chain_variance + num_samples - 1) / (num_samples)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/arviz/stats/diagnostics.py:596: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  (between_chain_variance / within_chain_variance + num_samples - 1) / (num_samples)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/arviz/stats/diagnostics.py:596: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  (between_chain_variance / within_chain_variance + num_samples - 1) / (num_samples)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/arviz/stats/diagnostics.py:596: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  (between_chain_variance / within_chain_variance + num_samples - 1) / (num_samples)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/arviz/stats/diagnostics.py:596: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  (between_chain_variance / within_chain_variance + num_samples - 1) / (num_samples)\n"
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       "      <td>-0.945</td>\n",
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       "      <th>g[3]</th>\n",
       "      <td>0.649</td>\n",
       "      <td>0.535</td>\n",
       "      <td>-0.172</td>\n",
       "      <td>1.521</td>\n",
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       "    <tr>\n",
       "      <th>rho_chol_actor[0, 0]</th>\n",
       "      <td>1.000</td>\n",
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       "      <td>1.262</td>\n",
       "      <td>0.017</td>\n",
       "      <td>0.022</td>\n",
       "      <td>2753.0</td>\n",
       "      <td>1314.0</td>\n",
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       "      <td>-0.263</td>\n",
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       "<p>96 rows × 9 columns</p>\n",
       "</div>"
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      "text/plain": [
       "                       mean     sd  hdi_5.5%  hdi_94.5%  mcse_mean  mcse_sd  \\\n",
       "g[0]                  0.224  0.487    -0.498      1.023      0.011    0.009   \n",
       "g[1]                  0.653  0.409    -0.019      1.249      0.010    0.008   \n",
       "g[2]                 -0.008  0.591    -0.945      0.926      0.012    0.012   \n",
       "g[3]                  0.649  0.535    -0.172      1.521      0.012    0.010   \n",
       "rho_chol_actor[0, 0]  1.000  0.000     1.000      1.000      0.000    0.000   \n",
       "...                     ...    ...       ...        ...        ...      ...   \n",
       "z_block[4, 3]        -0.060  0.890    -1.525      1.262      0.017    0.022   \n",
       "z_block[5, 0]        -0.263  0.843    -1.577      1.148      0.018    0.017   \n",
       "z_block[5, 1]         0.751  0.939    -0.710      2.296      0.022    0.017   \n",
       "z_block[5, 2]        -0.104  0.931    -1.710      1.244      0.019    0.020   \n",
       "z_block[5, 3]         0.445  0.952    -1.042      1.926      0.022    0.022   \n",
       "\n",
       "                      ess_bulk  ess_tail  r_hat  \n",
       "g[0]                    1990.0    1672.0    1.0  \n",
       "g[1]                    1802.0    1463.0    1.0  \n",
       "g[2]                    2337.0    1754.0    1.0  \n",
       "g[3]                    2015.0    1544.0    1.0  \n",
       "rho_chol_actor[0, 0]    2000.0    2000.0    NaN  \n",
       "...                        ...       ...    ...  \n",
       "z_block[4, 3]           2753.0    1314.0    1.0  \n",
       "z_block[5, 0]           2185.0    1523.0    1.0  \n",
       "z_block[5, 1]           1862.0    1494.0    1.0  \n",
       "z_block[5, 2]           2330.0    1441.0    1.0  \n",
       "z_block[5, 3]           1939.0    1277.0    1.0  \n",
       "\n",
       "[96 rows x 9 columns]"
      ]
     },
     "execution_count": 158,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata_3, hdi_prob=0.89)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/arviz/stats/diagnostics.py:596: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  (between_chain_variance / within_chain_variance + num_samples - 1) / (num_samples)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/arviz/stats/diagnostics.py:596: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  (between_chain_variance / within_chain_variance + num_samples - 1) / (num_samples)\n",
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      "  (between_chain_variance / within_chain_variance + num_samples - 1) / (num_samples)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/arviz/stats/diagnostics.py:596: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  (between_chain_variance / within_chain_variance + num_samples - 1) / (num_samples)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/arviz/stats/diagnostics.py:596: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  (between_chain_variance / within_chain_variance + num_samples - 1) / (num_samples)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/arviz/stats/diagnostics.py:596: RuntimeWarning: invalid value encountered in scalar divide\n",
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       "      <td>0.754</td>\n",
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       "      <td>1084.0</td>\n",
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       "    <tr>\n",
       "      <th>sigma_block[0]</th>\n",
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       "      <td>0.296</td>\n",
       "      <td>0.283</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.631</td>\n",
       "      <td>0.007</td>\n",
       "      <td>0.005</td>\n",
       "      <td>964.0</td>\n",
       "      <td>583.0</td>\n",
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       "                 mean     sd  hdi_5.5%  hdi_94.5%  mcse_mean  mcse_sd  \\\n",
       "sigma_actor[0]  1.394  0.495     0.672      2.074      0.012    0.008   \n",
       "sigma_actor[1]  0.909  0.407     0.325      1.477      0.011    0.008   \n",
       "sigma_actor[2]  1.877  0.595     1.001      2.647      0.014    0.010   \n",
       "sigma_actor[3]  1.577  0.591     0.754      2.456      0.017    0.013   \n",
       "sigma_block[0]  0.426  0.339     0.001      0.840      0.010    0.007   \n",
       "sigma_block[1]  0.429  0.345     0.000      0.844      0.011    0.008   \n",
       "sigma_block[2]  0.296  0.283     0.001      0.631      0.007    0.005   \n",
       "sigma_block[3]  0.467  0.372     0.001      0.943      0.011    0.007   \n",
       "\n",
       "                ess_bulk  ess_tail  r_hat  \n",
       "sigma_actor[0]    1655.0    1678.0    1.0  \n",
       "sigma_actor[1]    1220.0    1500.0    1.0  \n",
       "sigma_actor[2]    2104.0    1682.0    1.0  \n",
       "sigma_actor[3]    1339.0    1084.0    1.0  \n",
       "sigma_block[0]     836.0     711.0    1.0  \n",
       "sigma_block[1]     746.0     745.0    1.0  \n",
       "sigma_block[2]     964.0     583.0    1.0  \n",
       "sigma_block[3]     971.0     935.0    1.0  "
      ]
     },
     "execution_count": 163,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "precis_3 = az.summary(idata_3, hdi_prob=0.89)\n",
    "precis_3[precis_3.index.str.startswith(('sigma_actor', 'sigma_block'))]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 14.3 Instruments and causal designs (TODO)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 14.23"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 500\n",
    "U_sim = tfd.Normal(loc=0., scale=1.).sample(N, seed=key())\n",
    "Q_sim = tfd.Categorical(logits=jnp.ones(4)).sample(N, seed=key())\n",
    "E_sim = tfd.Normal(loc=U_sim + Q_sim, scale=1.).sample(seed=key())\n",
    "W_sim = tfd.Normal(loc=U_sim, scale=1.).sample(seed=key())\n",
    "dat_sim = dict(\n",
    "\t\tW=(W_sim - W_sim.mean()) / W_sim.std(),\n",
    "\t\tE=(E_sim - E_sim.mean()) / E_sim.std(),\n",
    "\t\tQ=(Q_sim - Q_sim.mean()) / Q_sim.std(),\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 14.24"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_14_4(E):\n",
    "\tdef _generator():\n",
    "\t\tsigma = yield tfd.Exponential(rate=1., name='sigma')\n",
    "\t\tbEW = yield tfd.Normal(loc=0., scale=.5, name='bEW')\n",
    "\t\taW = yield tfd.Normal(loc=0., scale=.2, name='aW')\n",
    "\t\tmu = aW + bEW * E\n",
    "\t\tyield tfd.Normal(loc=mu, scale=sigma, name='W')\n",
    "\t\t\n",
    "\treturn tfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_14_4 = model_14_4(dat_sim[\"E\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_14_4_pin = jd_14_4.experimental_pin(W=dat_sim[\"W\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jax.jit\n",
    "def run_chain(init_state, seed, step_size=1e-3, num_steps=500, burnin=500):\n",
    "\n",
    "  def target_log_prob(*states):\n",
    "    return jd_14_4_pin.unnormalized_log_prob(states)\n",
    "  \n",
    "  bijectors = [tfb.Exp(), tfb.Identity(), tfb.Identity()]\n",
    "\n",
    "  kernel = tfp.mcmc.NoUTurnSampler(\n",
    "      target_log_prob_fn=target_log_prob,\n",
    "      step_size=step_size)\n",
    "  \n",
    "  kernel = tfp.mcmc.TransformedTransitionKernel(\n",
    "    inner_kernel=kernel,\n",
    "    bijector=bijectors)\n",
    "\n",
    "  kernel = tfp.mcmc.DualAveragingStepSizeAdaptation(\n",
    "    inner_kernel=kernel,\n",
    "    num_adaptation_steps=burnin)\n",
    "\n",
    "  chain_state = tfp.mcmc.sample_chain(\n",
    "      num_results=num_steps,\n",
    "      num_burnin_steps=burnin,\n",
    "      current_state=init_state,\n",
    "      kernel=kernel,\n",
    "      seed=seed,\n",
    "      trace_fn=None)\n",
    "  \n",
    "  return chain_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_chains = 4\n",
    "init_state = jd_14_4_pin.sample_unpinned(num_chains, seed=key())\n",
    "post_4 = run_chain(init_state=init_state, seed=key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_4_dict = {k: jnp.moveaxis(v, 0, 1) for k, v in post_4._asdict().items()}\n",
    "dict_4 = dict(posterior=post_4_dict)\n",
    "idata_4 = az.from_dict(**dict_4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_5.5%</th>\n",
       "      <th>hdi_94.5%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>aW</th>\n",
       "      <td>0.000</td>\n",
       "      <td>0.040</td>\n",
       "      <td>-0.069</td>\n",
       "      <td>0.061</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>2811.0</td>\n",
       "      <td>1458.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bEW</th>\n",
       "      <td>0.432</td>\n",
       "      <td>0.042</td>\n",
       "      <td>0.363</td>\n",
       "      <td>0.493</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>2940.0</td>\n",
       "      <td>1547.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma</th>\n",
       "      <td>0.904</td>\n",
       "      <td>0.029</td>\n",
       "      <td>0.857</td>\n",
       "      <td>0.948</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.000</td>\n",
       "      <td>2686.0</td>\n",
       "      <td>1600.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        mean     sd  hdi_5.5%  hdi_94.5%  mcse_mean  mcse_sd  ess_bulk  \\\n",
       "aW     0.000  0.040    -0.069      0.061      0.001    0.001    2811.0   \n",
       "bEW    0.432  0.042     0.363      0.493      0.001    0.001    2940.0   \n",
       "sigma  0.904  0.029     0.857      0.948      0.001    0.000    2686.0   \n",
       "\n",
       "       ess_tail  r_hat  \n",
       "aW       1458.0   1.01  \n",
       "bEW      1547.0   1.00  \n",
       "sigma    1600.0   1.01  "
      ]
     },
     "execution_count": 182,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata_4, hdi_prob=0.89)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 14.25"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_14_5(E, Q):\n",
    "\tdef _generator():\n",
    "\t\tsigma = yield tfd.Exponential(rate=1., name='sigma')\n",
    "\t\tbQW = yield tfd.Normal(loc=0., scale=.5, name='bQW')\n",
    "\t\tbEW = yield tfd.Normal(loc=0., scale=.5, name='bEW')\n",
    "\t\taW = yield tfd.Normal(loc=0., scale=.2, name='aW')\n",
    "\t\tmu = aW + bEW * E + bQW * Q\n",
    "\t\tyield tfd.Normal(loc=mu, scale=sigma, name='W')\n",
    "\t\t\n",
    "\treturn tfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_14_5 = model_14_5(dat_sim[\"E\"], dat_sim[\"Q\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_14_5_pin = jd_14_5.experimental_pin(W=dat_sim[\"W\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jax.jit\n",
    "def run_chain(init_state, seed, step_size=1e-3, num_steps=500, burnin=500):\n",
    "\n",
    "  def target_log_prob(*states):\n",
    "    return jd_14_5_pin.unnormalized_log_prob(states)\n",
    "  \n",
    "  bijectors = [tfb.Exp(), tfb.Identity(), tfb.Identity(), tfb.Identity()]\n",
    "\n",
    "  kernel = tfp.mcmc.NoUTurnSampler(\n",
    "      target_log_prob_fn=target_log_prob,\n",
    "      step_size=step_size)\n",
    "  \n",
    "  kernel = tfp.mcmc.TransformedTransitionKernel(\n",
    "    inner_kernel=kernel,\n",
    "    bijector=bijectors)\n",
    "\n",
    "  kernel = tfp.mcmc.DualAveragingStepSizeAdaptation(\n",
    "    inner_kernel=kernel,\n",
    "    num_adaptation_steps=burnin)\n",
    "\n",
    "  chain_state = tfp.mcmc.sample_chain(\n",
    "      num_results=num_steps,\n",
    "      num_burnin_steps=burnin,\n",
    "      current_state=init_state,\n",
    "      kernel=kernel,\n",
    "      seed=seed,\n",
    "      trace_fn=None)\n",
    "  \n",
    "  return chain_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_chains = 4\n",
    "init_state = jd_14_5_pin.sample_unpinned(num_chains, seed=key())\n",
    "post_5 = run_chain(init_state=init_state, seed=key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_5_dict = {k: jnp.moveaxis(v, 0, 1) for k, v in post_5._asdict().items()}\n",
    "dict_5 = dict(posterior=post_5_dict)\n",
    "idata_5 = az.from_dict(**dict_5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_5.5%</th>\n",
       "      <th>hdi_94.5%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>aW</th>\n",
       "      <td>0.001</td>\n",
       "      <td>0.039</td>\n",
       "      <td>-0.056</td>\n",
       "      <td>0.068</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>3116.0</td>\n",
       "      <td>1774.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bEW</th>\n",
       "      <td>0.633</td>\n",
       "      <td>0.046</td>\n",
       "      <td>0.561</td>\n",
       "      <td>0.705</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>1346.0</td>\n",
       "      <td>1523.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bQW</th>\n",
       "      <td>-0.336</td>\n",
       "      <td>0.046</td>\n",
       "      <td>-0.406</td>\n",
       "      <td>-0.257</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>1364.0</td>\n",
       "      <td>1479.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma</th>\n",
       "      <td>0.862</td>\n",
       "      <td>0.028</td>\n",
       "      <td>0.816</td>\n",
       "      <td>0.903</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.000</td>\n",
       "      <td>2803.0</td>\n",
       "      <td>1486.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        mean     sd  hdi_5.5%  hdi_94.5%  mcse_mean  mcse_sd  ess_bulk  \\\n",
       "aW     0.001  0.039    -0.056      0.068      0.001    0.001    3116.0   \n",
       "bEW    0.633  0.046     0.561      0.705      0.001    0.001    1346.0   \n",
       "bQW   -0.336  0.046    -0.406     -0.257      0.001    0.001    1364.0   \n",
       "sigma  0.862  0.028     0.816      0.903      0.001    0.000    2803.0   \n",
       "\n",
       "       ess_tail  r_hat  \n",
       "aW       1774.0    1.0  \n",
       "bEW      1523.0    1.0  \n",
       "bQW      1479.0    1.0  \n",
       "sigma    1486.0    1.0  "
      ]
     },
     "execution_count": 189,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata_5, hdi_prob=0.89)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 14.26"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_14_6(E, Q):\n",
    "\tdef _generator():\n",
    "\t\tSigma = yield tfd.Sample(tfd.Exponential(rate=1.), sample_shape=2, name='Sigma')\n",
    "\t\tRho = yield tfd.CholeskyLKJ(dimension=2, concentration=2.0, name='Rho')\n",
    "\t\tbQE = yield tfd.Normal(loc=0., scale=.5, name='bQE')\n",
    "\t\tbEW = yield tfd.Normal(loc=0., scale=.5, name='bEW')\n",
    "\t\taE = yield tfd.Normal(loc=0., scale=.2, name='aE')\n",
    "\t\taW = yield tfd.Normal(loc=0., scale=.2, name='aW')\n",
    "\t\tmuE = aE + bQE * Q\n",
    "\t\tmuW = aW + bEW * E\n",
    "\t\tmu = jnp.stack([muW, muE], axis=1)\n",
    "\t\tcov_tril = jnp.diag(Sigma) @ Rho\n",
    "\t\tyield tfd.MultivariateNormalTriL(loc=mu, scale_tril=cov_tril, name='WE')\n",
    "\t\t\n",
    "\treturn tfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_14_6 = model_14_6(dat_sim[\"E\"], dat_sim[\"Q\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:283: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'> requested in zeros is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  minval = minval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:284: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'>  is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return jaxrand.randint(key=seed, shape=shape, minval=minval, maxval=maxval,\n"
     ]
    }
   ],
   "source": [
    "jd_14_6_pin = jd_14_6.experimental_pin(WE=jnp.stack([dat_sim[\"W\"], dat_sim[\"E\"]], axis=1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 213,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jax.jit\n",
    "def run_chain(init_state, seed, step_size=1e-3, num_steps=500, burnin=600):\n",
    "\n",
    "  def target_log_prob(*states):\n",
    "    return jd_14_6_pin.unnormalized_log_prob(states)\n",
    "  \n",
    "  bijectors = [tfb.Exp(), tfb.CorrelationCholesky(), \n",
    "               tfb.Identity(), tfb.Identity(), tfb.Identity(), tfb.Identity()]\n",
    "\n",
    "  kernel = tfp.mcmc.NoUTurnSampler(\n",
    "      target_log_prob_fn=target_log_prob,\n",
    "      step_size=step_size)\n",
    "  \n",
    "  kernel = tfp.mcmc.TransformedTransitionKernel(\n",
    "    inner_kernel=kernel,\n",
    "    bijector=bijectors)\n",
    "\n",
    "  kernel = tfp.mcmc.DualAveragingStepSizeAdaptation(\n",
    "    inner_kernel=kernel,\n",
    "    num_adaptation_steps=burnin)\n",
    "\n",
    "  chain_state = tfp.mcmc.sample_chain(\n",
    "      num_results=num_steps,\n",
    "      num_burnin_steps=burnin,\n",
    "      current_state=init_state,\n",
    "      kernel=kernel,\n",
    "      seed=seed,\n",
    "      trace_fn=None)\n",
    "  \n",
    "  return chain_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 214,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:283: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'> requested in zeros is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  minval = minval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:284: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'>  is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return jaxrand.randint(key=seed, shape=shape, minval=minval, maxval=maxval,\n"
     ]
    }
   ],
   "source": [
    "num_chains = 4\n",
    "init_state = jd_14_6_pin.sample_unpinned(num_chains, seed=key())\n",
    "post_6 = run_chain(init_state=init_state, seed=key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 215,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_6_dict = {k: jnp.moveaxis(v, 0, 1) for k, v in post_6._asdict().items()}\n",
    "dict_6 = dict(posterior=post_6_dict)\n",
    "idata_6 = az.from_dict(**dict_6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/arviz/stats/diagnostics.py:596: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  (between_chain_variance / within_chain_variance + num_samples - 1) / (num_samples)\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_5.5%</th>\n",
       "      <th>hdi_94.5%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Rho[0, 0]</th>\n",
       "      <td>1.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>1.000</td>\n",
       "      <td>1.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>2000.0</td>\n",
       "      <td>2000.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rho[0, 1]</th>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>2000.0</td>\n",
       "      <td>2000.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rho[1, 0]</th>\n",
       "      <td>0.465</td>\n",
       "      <td>0.055</td>\n",
       "      <td>0.385</td>\n",
       "      <td>0.556</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>603.0</td>\n",
       "      <td>833.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rho[1, 1]</th>\n",
       "      <td>0.883</td>\n",
       "      <td>0.029</td>\n",
       "      <td>0.833</td>\n",
       "      <td>0.924</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>603.0</td>\n",
       "      <td>833.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Sigma[0]</th>\n",
       "      <td>0.976</td>\n",
       "      <td>0.040</td>\n",
       "      <td>0.914</td>\n",
       "      <td>1.039</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>891.0</td>\n",
       "      <td>1272.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Sigma[1]</th>\n",
       "      <td>0.806</td>\n",
       "      <td>0.025</td>\n",
       "      <td>0.763</td>\n",
       "      <td>0.842</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.000</td>\n",
       "      <td>2529.0</td>\n",
       "      <td>1782.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>aE</th>\n",
       "      <td>0.000</td>\n",
       "      <td>0.034</td>\n",
       "      <td>-0.055</td>\n",
       "      <td>0.055</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>2122.0</td>\n",
       "      <td>1807.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>aW</th>\n",
       "      <td>0.001</td>\n",
       "      <td>0.042</td>\n",
       "      <td>-0.064</td>\n",
       "      <td>0.068</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>1643.0</td>\n",
       "      <td>1368.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bEW</th>\n",
       "      <td>0.068</td>\n",
       "      <td>0.068</td>\n",
       "      <td>-0.039</td>\n",
       "      <td>0.179</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.002</td>\n",
       "      <td>654.0</td>\n",
       "      <td>915.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bQE</th>\n",
       "      <td>0.593</td>\n",
       "      <td>0.035</td>\n",
       "      <td>0.537</td>\n",
       "      <td>0.648</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>1386.0</td>\n",
       "      <td>1402.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            mean     sd  hdi_5.5%  hdi_94.5%  mcse_mean  mcse_sd  ess_bulk  \\\n",
       "Rho[0, 0]  1.000  0.000     1.000      1.000      0.000    0.000    2000.0   \n",
       "Rho[0, 1]  0.000  0.000     0.000      0.000      0.000    0.000    2000.0   \n",
       "Rho[1, 0]  0.465  0.055     0.385      0.556      0.002    0.002     603.0   \n",
       "Rho[1, 1]  0.883  0.029     0.833      0.924      0.001    0.001     603.0   \n",
       "Sigma[0]   0.976  0.040     0.914      1.039      0.001    0.001     891.0   \n",
       "Sigma[1]   0.806  0.025     0.763      0.842      0.001    0.000    2529.0   \n",
       "aE         0.000  0.034    -0.055      0.055      0.001    0.001    2122.0   \n",
       "aW         0.001  0.042    -0.064      0.068      0.001    0.001    1643.0   \n",
       "bEW        0.068  0.068    -0.039      0.179      0.003    0.002     654.0   \n",
       "bQE        0.593  0.035     0.537      0.648      0.001    0.001    1386.0   \n",
       "\n",
       "           ess_tail  r_hat  \n",
       "Rho[0, 0]    2000.0    NaN  \n",
       "Rho[0, 1]    2000.0    NaN  \n",
       "Rho[1, 0]     833.0    1.0  \n",
       "Rho[1, 1]     833.0    1.0  \n",
       "Sigma[0]     1272.0    1.0  \n",
       "Sigma[1]     1782.0    1.0  \n",
       "aE           1807.0    1.0  \n",
       "aW           1368.0    1.0  \n",
       "bEW           915.0    1.0  \n",
       "bQE          1402.0    1.0  "
      ]
     },
     "execution_count": 216,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata_6, hdi_prob=0.89)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 14.4 Social relations as correlated varying effects (TODO)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 14.30"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "odict_keys(['kl_dyads', 'kl_households'])"
      ]
     },
     "execution_count": 219,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pyreadr\n",
    "KosterLeckie = pyreadr.read_r('./data/KosterLeckie.rda')\n",
    "KosterLeckie.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
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       "      <td>2</td>\n",
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       "      <td>0</td>\n",
       "      <td>-3.499</td>\n",
       "      <td>0.022</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "    <tr>\n",
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       "      <td>0</td>\n",
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       "      <td>0.000</td>\n",
       "      <td>0</td>\n",
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       "      <td>0</td>\n",
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       "      <td>24</td>\n",
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       "      <td>-0.092</td>\n",
       "      <td>0</td>\n",
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       "      <td>0</td>\n",
       "      <td>-1.798</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0</td>\n",
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       "      <td>0</td>\n",
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       "      <th>299</th>\n",
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       "      <td>-0.637</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-1.723</td>\n",
       "      <td>0.042</td>\n",
       "      <td>0</td>\n",
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       "  </tbody>\n",
       "</table>\n",
       "<p>300 rows × 13 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     hidA  hidB  did  giftsAB  giftsBA  offset  drel1  drel2  drel3  drel4  \\\n",
       "0       1     2    1        0        4   0.000      0      0      1      0   \n",
       "1       1     3    2        6       31  -0.003      0      1      0      0   \n",
       "2       1     4    3        2        5  -0.019      0      1      0      0   \n",
       "3       1     5    4        4        2   0.000      0      1      0      0   \n",
       "4       1     6    5        8        2  -0.003      1      0      0      0   \n",
       "..    ...   ...  ...      ...      ...     ...    ...    ...    ...    ...   \n",
       "295    22    24  296        0        1   0.000      0      0      1      0   \n",
       "296    22    25  297        2        0  -0.637      0      0      0      1   \n",
       "297    23    24  298        2        0  -0.092      0      0      0      0   \n",
       "298    23    25  299        4        0  -0.818      0      0      1      0   \n",
       "299    24    25  300        2        0  -0.637      0      0      0      0   \n",
       "\n",
       "     dlndist   dass  d0125  \n",
       "0     -2.790  0.000      0  \n",
       "1     -2.817  0.044      0  \n",
       "2     -1.886  0.025      0  \n",
       "3     -1.892  0.011      0  \n",
       "4     -3.499  0.022      0  \n",
       "..       ...    ...    ...  \n",
       "295   -2.442  0.000      0  \n",
       "296   -1.747  0.026      0  \n",
       "297   -1.798  0.000      0  \n",
       "298   -1.848  0.031      0  \n",
       "299   -1.723  0.042      0  \n",
       "\n",
       "[300 rows x 13 columns]"
      ]
     },
     "execution_count": 220,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kl_dyads = KosterLeckie['kl_dyads']\n",
    "kl_dyads"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 14.31"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 221,
   "metadata": {},
   "outputs": [],
   "source": [
    "kl_data = dict(\n",
    "    N=kl_dyads.shape[0],\n",
    "    N_households=kl_dyads.hidB.max(),\n",
    "    did=kl_dyads.did.values - 1,\n",
    "    hidA=kl_dyads.hidA.values - 1,\n",
    "    hidB=kl_dyads.hidB.values - 1,\n",
    "    giftsAB=kl_dyads.giftsAB.values,\n",
    "    giftsBA=kl_dyads.giftsBA.values,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 249,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_14_7(N_households, N, did, hidA, hidB):\n",
    "\tdef _generator():\n",
    "\t\t# gr matrix of varying effects\n",
    "\t\tL_Rho_gr = yield tfd.CholeskyLKJ(dimension=2, concentration=4., name='L_Rho_gr')\n",
    "\t\tsigma_gr = yield tfd.Sample(tfd.Exponential(rate=1.), sample_shape=2, name='sigma_gr')\n",
    "\t\tcov_tril = jnp.diag(sigma_gr) @ L_Rho_gr\n",
    "\t\tgr = yield tfd.Sample(\n",
    "\t\t\ttfd.MultivariateNormalTriL(loc=0., scale_tril=cov_tril, name='gr'),\n",
    "\t\t\tsample_shape=N_households, name='gr')\n",
    "\n",
    "\t\t# dyad effects\n",
    "\t\tsigma_d = yield tfd.Exponential(rate=1., name='sigma_d')\n",
    "\t\tL_Rho_d = yield tfd.CholeskyLKJ(dimension=2, concentration=8., name='L_Rho_d')\n",
    "\t\tcov_tril = jnp.diag(jnp.repeat(sigma_d, 2)) @ L_Rho_d\n",
    "\t\tz = yield tfd.Sample(\n",
    "\t\t\ttfd.MultivariateNormalDiag(loc=0., scale_diag=[1., 1.]),\n",
    "\t\t\tsample_shape=N, name='z')\n",
    "\t\td = z @ L_Rho_d.T @ jnp.diag(jnp.repeat(sigma_d, 2))\n",
    "\n",
    "\t\ta = yield tfd.Normal(loc=0., scale=1., name='a')\n",
    "\t\tlog_lambdaAB = a + gr.at[hidA, 0].get() + gr.at[hidB, 1].get() + d.at[did, 0].get()\n",
    "\t\tlog_lambdaBA = a + gr.at[hidB, 0].get() + gr.at[hidA, 1].get() + d.at[did, 1].get()\n",
    "\t\tyield tfd.Poisson(log_rate=log_lambdaAB, name='giftsAB')\n",
    "\t\tyield tfd.Poisson(log_rate=log_lambdaBA, name='giftsBA')\n",
    "\n",
    "\treturn tfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 250,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_14_7 = model_14_7(kl_data[\"N_households\"], kl_data[\"N\"], \n",
    "                     kl_data[\"did\"], kl_data[\"hidA\"], kl_data[\"hidB\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 251,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:283: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'> requested in zeros is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  minval = minval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:284: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'>  is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return jaxrand.randint(key=seed, shape=shape, minval=minval, maxval=maxval,\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:283: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'> requested in zeros is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  minval = minval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:284: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'>  is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return jaxrand.randint(key=seed, shape=shape, minval=minval, maxval=maxval,\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/jax/_src/numpy/array_methods.py:69: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in astype is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return lax_numpy.astype(arr, dtype, copy=copy, device=device)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/ops.py:339: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in array is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return np.array(value, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:290: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in zeros is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  minval = minval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:291: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in zeros is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  maxval = maxval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:292: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'>  is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return jaxrand.uniform(key=seed, shape=shape, dtype=dtype, minval=minval,\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/numpy_array.py:450: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in ones is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  lambda shape, dtype=np.float32, name=None, layout=None: np.ones(  # pylint: disable=g-long-lambda\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/ops.py:339: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in array is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return np.array(value, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:290: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in zeros is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  minval = minval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:291: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in zeros is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  maxval = maxval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:292: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'>  is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return jaxrand.uniform(key=seed, shape=shape, dtype=dtype, minval=minval,\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/jax/_src/numpy/array_methods.py:69: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in astype is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return lax_numpy.astype(arr, dtype, copy=copy, device=device)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/ops.py:339: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in array is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return np.array(value, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:290: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in zeros is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  minval = minval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:291: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in zeros is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  maxval = maxval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:292: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'>  is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return jaxrand.uniform(key=seed, shape=shape, dtype=dtype, minval=minval,\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/numpy_array.py:450: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in ones is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  lambda shape, dtype=np.float32, name=None, layout=None: np.ones(  # pylint: disable=g-long-lambda\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/ops.py:339: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in array is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return np.array(value, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:290: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in zeros is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  minval = minval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:291: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in zeros is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  maxval = maxval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:292: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'>  is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return jaxrand.uniform(key=seed, shape=shape, dtype=dtype, minval=minval,\n"
     ]
    }
   ],
   "source": [
    "jd_14_7_pin = jd_14_7.experimental_pin(giftsAB=kl_data[\"giftsAB\"], giftsBA=kl_data[\"giftsBA\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 252,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jax.jit\n",
    "def run_chain(init_state, seed, step_size=1e-3, num_steps=500, burnin=600):\n",
    "\n",
    "  def target_log_prob(*states):\n",
    "    return jd_14_7_pin.unnormalized_log_prob(states)\n",
    "  \n",
    "  bijectors = [tfb.CorrelationCholesky(), tfb.Exp(), tfb.Identity(),\n",
    "               tfb.Exp(), tfb.CorrelationCholesky(), tfb.Identity(),\n",
    "               tfb.Identity()]\n",
    "\n",
    "  kernel = tfp.mcmc.NoUTurnSampler(\n",
    "      target_log_prob_fn=target_log_prob,\n",
    "      step_size=step_size)\n",
    "  \n",
    "  kernel = tfp.mcmc.TransformedTransitionKernel(\n",
    "    inner_kernel=kernel,\n",
    "    bijector=bijectors)\n",
    "\n",
    "  kernel = tfp.mcmc.DualAveragingStepSizeAdaptation(\n",
    "    inner_kernel=kernel,\n",
    "    num_adaptation_steps=burnin)\n",
    "\n",
    "  chain_state = tfp.mcmc.sample_chain(\n",
    "      num_results=num_steps,\n",
    "      num_burnin_steps=burnin,\n",
    "      current_state=init_state,\n",
    "      kernel=kernel,\n",
    "      seed=seed,\n",
    "      trace_fn=None)\n",
    "  \n",
    "  return chain_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 253,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:283: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'> requested in zeros is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  minval = minval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:284: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'>  is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return jaxrand.randint(key=seed, shape=shape, minval=minval, maxval=maxval,\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:283: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'> requested in zeros is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  minval = minval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:284: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'>  is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return jaxrand.randint(key=seed, shape=shape, minval=minval, maxval=maxval,\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/jax/_src/numpy/array_methods.py:69: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in astype is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return lax_numpy.astype(arr, dtype, copy=copy, device=device)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/ops.py:339: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in array is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return np.array(value, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:290: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in zeros is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  minval = minval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:291: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in zeros is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  maxval = maxval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:292: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'>  is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return jaxrand.uniform(key=seed, shape=shape, dtype=dtype, minval=minval,\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/numpy_array.py:450: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in ones is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  lambda shape, dtype=np.float32, name=None, layout=None: np.ones(  # pylint: disable=g-long-lambda\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/ops.py:339: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in array is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return np.array(value, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:290: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in zeros is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  minval = minval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:291: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in zeros is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  maxval = maxval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:292: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'>  is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return jaxrand.uniform(key=seed, shape=shape, dtype=dtype, minval=minval,\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/jax/_src/numpy/array_methods.py:69: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in astype is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return lax_numpy.astype(arr, dtype, copy=copy, device=device)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/ops.py:339: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in array is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return np.array(value, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:290: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in zeros is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  minval = minval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:291: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in zeros is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  maxval = maxval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:292: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'>  is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return jaxrand.uniform(key=seed, shape=shape, dtype=dtype, minval=minval,\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/numpy_array.py:450: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in ones is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  lambda shape, dtype=np.float32, name=None, layout=None: np.ones(  # pylint: disable=g-long-lambda\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/ops.py:339: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in array is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return np.array(value, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:290: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in zeros is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  minval = minval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:291: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in zeros is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  maxval = maxval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:292: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'>  is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return jaxrand.uniform(key=seed, shape=shape, dtype=dtype, minval=minval,\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:283: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'> requested in zeros is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  minval = minval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:284: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'>  is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return jaxrand.randint(key=seed, shape=shape, minval=minval, maxval=maxval,\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:283: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'> requested in zeros is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  minval = minval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:284: UserWarning: Explicitly requested dtype <class 'jax.numpy.int64'>  is not available, and will be truncated to dtype int32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return jaxrand.randint(key=seed, shape=shape, minval=minval, maxval=maxval,\n"
     ]
    }
   ],
   "source": [
    "num_chains = 4\n",
    "init_state = jd_14_7_pin.sample_unpinned(num_chains, seed=key())\n",
    "post_7 = run_chain(init_state=init_state, seed=key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 254,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_7_dict = {k: jnp.moveaxis(v, 0, 1) for k, v in post_7._asdict().items()}\n",
    "dict_7 = dict(posterior=post_7_dict)\n",
    "idata_7 = az.from_dict(**dict_7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 255,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/arviz/stats/diagnostics.py:596: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  (between_chain_variance / within_chain_variance + num_samples - 1) / (num_samples)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/arviz/stats/diagnostics.py:596: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  (between_chain_variance / within_chain_variance + num_samples - 1) / (num_samples)\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>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_5.5%</th>\n",
       "      <th>hdi_94.5%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>L_Rho_gr[0, 0]</th>\n",
       "      <td>1.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>1.000</td>\n",
       "      <td>1.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>2000.0</td>\n",
       "      <td>2000.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L_Rho_gr[0, 1]</th>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>2000.0</td>\n",
       "      <td>2000.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L_Rho_gr[1, 0]</th>\n",
       "      <td>-0.408</td>\n",
       "      <td>0.202</td>\n",
       "      <td>-0.729</td>\n",
       "      <td>-0.097</td>\n",
       "      <td>0.005</td>\n",
       "      <td>0.004</td>\n",
       "      <td>1626.0</td>\n",
       "      <td>1845.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L_Rho_gr[1, 1]</th>\n",
       "      <td>0.885</td>\n",
       "      <td>0.093</td>\n",
       "      <td>0.760</td>\n",
       "      <td>1.000</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>1655.0</td>\n",
       "      <td>1845.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma_gr[0]</th>\n",
       "      <td>0.833</td>\n",
       "      <td>0.145</td>\n",
       "      <td>0.606</td>\n",
       "      <td>1.042</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.002</td>\n",
       "      <td>1910.0</td>\n",
       "      <td>1845.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma_gr[1]</th>\n",
       "      <td>0.423</td>\n",
       "      <td>0.092</td>\n",
       "      <td>0.284</td>\n",
       "      <td>0.566</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>1412.0</td>\n",
       "      <td>1571.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 mean     sd  hdi_5.5%  hdi_94.5%  mcse_mean  mcse_sd  \\\n",
       "L_Rho_gr[0, 0]  1.000  0.000     1.000      1.000      0.000    0.000   \n",
       "L_Rho_gr[0, 1]  0.000  0.000     0.000      0.000      0.000    0.000   \n",
       "L_Rho_gr[1, 0] -0.408  0.202    -0.729     -0.097      0.005    0.004   \n",
       "L_Rho_gr[1, 1]  0.885  0.093     0.760      1.000      0.002    0.002   \n",
       "sigma_gr[0]     0.833  0.145     0.606      1.042      0.003    0.002   \n",
       "sigma_gr[1]     0.423  0.092     0.284      0.566      0.002    0.002   \n",
       "\n",
       "                ess_bulk  ess_tail  r_hat  \n",
       "L_Rho_gr[0, 0]    2000.0    2000.0    NaN  \n",
       "L_Rho_gr[0, 1]    2000.0    2000.0    NaN  \n",
       "L_Rho_gr[1, 0]    1626.0    1845.0    1.0  \n",
       "L_Rho_gr[1, 1]    1655.0    1845.0    1.0  \n",
       "sigma_gr[0]       1910.0    1845.0    1.0  \n",
       "sigma_gr[1]       1412.0    1571.0    1.0  "
      ]
     },
     "execution_count": 255,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "precis_7 = az.summary(idata_7, hdi_prob=0.89)\n",
    "precis_7[precis_7.index.str.startswith(('L_Rho_gr', 'sigma_gr'))]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 14.35"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 266,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_5.5%</th>\n",
       "      <th>hdi_94.5%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>L_Rho_d[0, 0]</th>\n",
       "      <td>1.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>1.000</td>\n",
       "      <td>1.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>2000.0</td>\n",
       "      <td>2000.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L_Rho_d[0, 1]</th>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>2000.0</td>\n",
       "      <td>2000.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L_Rho_d[1, 0]</th>\n",
       "      <td>0.881</td>\n",
       "      <td>0.034</td>\n",
       "      <td>0.832</td>\n",
       "      <td>0.935</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>1001.0</td>\n",
       "      <td>1499.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L_Rho_d[1, 1]</th>\n",
       "      <td>0.468</td>\n",
       "      <td>0.063</td>\n",
       "      <td>0.373</td>\n",
       "      <td>0.569</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.001</td>\n",
       "      <td>1001.0</td>\n",
       "      <td>1499.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma_d</th>\n",
       "      <td>1.102</td>\n",
       "      <td>0.057</td>\n",
       "      <td>1.009</td>\n",
       "      <td>1.191</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.001</td>\n",
       "      <td>983.0</td>\n",
       "      <td>1471.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                mean     sd  hdi_5.5%  hdi_94.5%  mcse_mean  mcse_sd  \\\n",
       "L_Rho_d[0, 0]  1.000  0.000     1.000      1.000      0.000    0.000   \n",
       "L_Rho_d[0, 1]  0.000  0.000     0.000      0.000      0.000    0.000   \n",
       "L_Rho_d[1, 0]  0.881  0.034     0.832      0.935      0.001    0.001   \n",
       "L_Rho_d[1, 1]  0.468  0.063     0.373      0.569      0.002    0.001   \n",
       "sigma_d        1.102  0.057     1.009      1.191      0.002    0.001   \n",
       "\n",
       "               ess_bulk  ess_tail  r_hat  \n",
       "L_Rho_d[0, 0]    2000.0    2000.0    NaN  \n",
       "L_Rho_d[0, 1]    2000.0    2000.0    NaN  \n",
       "L_Rho_d[1, 0]    1001.0    1499.0    1.0  \n",
       "L_Rho_d[1, 1]    1001.0    1499.0    1.0  \n",
       "sigma_d           983.0    1471.0    1.0  "
      ]
     },
     "execution_count": 266,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "precis_7[precis_7.index.str.startswith(('L_Rho_d', 'sigma_d'))]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 14.5 Continuous categories and the Gaussian process (TODO)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 14.35"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 295,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "odict_keys(['islandsDistMatrix'])"
      ]
     },
     "execution_count": 295,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "idm = pyreadr.read_r('./data/islandsDistMatrix.rda')\n",
    "idm.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 297,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
       "    .dataframe thead th {\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Ml</th>\n",
       "      <th>Ti</th>\n",
       "      <th>SC</th>\n",
       "      <th>Ya</th>\n",
       "      <th>Fi</th>\n",
       "      <th>Tr</th>\n",
       "      <th>Ch</th>\n",
       "      <th>Mn</th>\n",
       "      <th>To</th>\n",
       "      <th>Ha</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Malekula</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.6</td>\n",
       "      <td>4.4</td>\n",
       "      <td>1.2</td>\n",
       "      <td>2.0</td>\n",
       "      <td>3.2</td>\n",
       "      <td>2.8</td>\n",
       "      <td>1.9</td>\n",
       "      <td>5.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Tikopia</th>\n",
       "      <td>0.5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.3</td>\n",
       "      <td>4.2</td>\n",
       "      <td>1.2</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2.9</td>\n",
       "      <td>2.7</td>\n",
       "      <td>2.0</td>\n",
       "      <td>5.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Santa Cruz</th>\n",
       "      <td>0.6</td>\n",
       "      <td>0.3</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3.9</td>\n",
       "      <td>1.6</td>\n",
       "      <td>1.7</td>\n",
       "      <td>2.6</td>\n",
       "      <td>2.4</td>\n",
       "      <td>2.3</td>\n",
       "      <td>5.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Yap</th>\n",
       "      <td>4.4</td>\n",
       "      <td>4.2</td>\n",
       "      <td>3.9</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5.4</td>\n",
       "      <td>2.5</td>\n",
       "      <td>1.6</td>\n",
       "      <td>1.6</td>\n",
       "      <td>6.1</td>\n",
       "      <td>7.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Lau Fiji</th>\n",
       "      <td>1.2</td>\n",
       "      <td>1.2</td>\n",
       "      <td>1.6</td>\n",
       "      <td>5.4</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3.2</td>\n",
       "      <td>4.0</td>\n",
       "      <td>3.9</td>\n",
       "      <td>0.8</td>\n",
       "      <td>4.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Trobriand</th>\n",
       "      <td>2.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.7</td>\n",
       "      <td>2.5</td>\n",
       "      <td>3.2</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.8</td>\n",
       "      <td>0.8</td>\n",
       "      <td>3.9</td>\n",
       "      <td>6.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Chuuk</th>\n",
       "      <td>3.2</td>\n",
       "      <td>2.9</td>\n",
       "      <td>2.6</td>\n",
       "      <td>1.6</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.8</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.2</td>\n",
       "      <td>4.8</td>\n",
       "      <td>5.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Manus</th>\n",
       "      <td>2.8</td>\n",
       "      <td>2.7</td>\n",
       "      <td>2.4</td>\n",
       "      <td>1.6</td>\n",
       "      <td>3.9</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1.2</td>\n",
       "      <td>0.0</td>\n",
       "      <td>4.6</td>\n",
       "      <td>6.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Tonga</th>\n",
       "      <td>1.9</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2.3</td>\n",
       "      <td>6.1</td>\n",
       "      <td>0.8</td>\n",
       "      <td>3.9</td>\n",
       "      <td>4.8</td>\n",
       "      <td>4.6</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Hawaii</th>\n",
       "      <td>5.7</td>\n",
       "      <td>5.3</td>\n",
       "      <td>5.4</td>\n",
       "      <td>7.2</td>\n",
       "      <td>4.9</td>\n",
       "      <td>6.7</td>\n",
       "      <td>5.8</td>\n",
       "      <td>6.7</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             Ml   Ti   SC   Ya   Fi   Tr   Ch   Mn   To   Ha\n",
       "Malekula    0.0  0.5  0.6  4.4  1.2  2.0  3.2  2.8  1.9  5.7\n",
       "Tikopia     0.5  0.0  0.3  4.2  1.2  2.0  2.9  2.7  2.0  5.3\n",
       "Santa Cruz  0.6  0.3  0.0  3.9  1.6  1.7  2.6  2.4  2.3  5.4\n",
       "Yap         4.4  4.2  3.9  0.0  5.4  2.5  1.6  1.6  6.1  7.2\n",
       "Lau Fiji    1.2  1.2  1.6  5.4  0.0  3.2  4.0  3.9  0.8  4.9\n",
       "Trobriand   2.0  2.0  1.7  2.5  3.2  0.0  1.8  0.8  3.9  6.7\n",
       "Chuuk       3.2  2.9  2.6  1.6  4.0  1.8  0.0  1.2  4.8  5.8\n",
       "Manus       2.8  2.7  2.4  1.6  3.9  0.8  1.2  0.0  4.6  6.7\n",
       "Tonga       1.9  2.0  2.3  6.1  0.8  3.9  4.8  4.6  0.0  5.0\n",
       "Hawaii      5.7  5.3  5.4  7.2  4.9  6.7  5.8  6.7  5.0  0.0"
      ]
     },
     "execution_count": 297,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Dmat = idm['islandsDistMatrix']\n",
    "Dmat.columns = [\"Ml\", \"Ti\", \"SC\", \"Ya\", \"Fi\", \"Tr\", \"Ch\", \"Mn\", \"To\", \"Ha\"]\n",
    "Dmat.round(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 14.39"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 289,
   "metadata": {},
   "outputs": [],
   "source": [
    "d = pd.read_csv(\"./data/Kline2.csv\", sep=\";\")\n",
    "d[\"society\"] = range(0, 10)  # index observations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 286,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cov_GPL2(x, sq_alpha, sq_rho, delta):\n",
    "\tN = x.shape[0]\n",
    "\tK = sq_alpha * jnp.exp(-sq_rho * jnp.square(x))\n",
    "\tK = K.at[jnp.diag_indices(N)].add(delta)\n",
    "\treturn K"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 299,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_14_8(Dmat, P, society):\n",
    "\tdef _generator():\n",
    "\t\ta = yield tfd.Exponential(rate=1., name='a')\n",
    "\t\tb = yield tfd.Exponential(rate=1., name='b')\n",
    "\t\tg = yield tfd.Exponential(rate=1., name='g')\n",
    "\t\trhosq = yield tfd.Exponential(rate=.5, name='rhosq')\n",
    "\t\tetasq = yield tfd.Exponential(rate=2., name='etasq')\n",
    "\t\tSIGMA = cov_GPL2(Dmat, etasq, rhosq, 0.01)\n",
    "\t\tk = yield tfd.MultivariateNormalFullCovariance(loc=0., covariance_matrix=SIGMA, name='k')\n",
    "\t\tlambda_ = a * P**b / g * jnp.exp(k[society])\n",
    "\t\tyield tfd.Poisson(rate=lambda_, name='T')\n",
    "\n",
    "\treturn tfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 300,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_14_8 = model_14_8(Dmat.to_numpy(), \n",
    "                     d.population.values.astype(np.float32), \n",
    "                     d.society.values.astype(np.int32))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 301,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/jax/_src/numpy/array_methods.py:69: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in astype is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return lax_numpy.astype(arr, dtype, copy=copy, device=device)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/ops.py:339: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in array is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return np.array(value, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:290: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in zeros is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  minval = minval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:291: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in zeros is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  maxval = maxval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:292: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'>  is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return jaxrand.uniform(key=seed, shape=shape, dtype=dtype, minval=minval,\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/ops.py:339: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in array is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return np.array(value, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:290: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in zeros is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  minval = minval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:291: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in zeros is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  maxval = maxval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:292: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'>  is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return jaxrand.uniform(key=seed, shape=shape, dtype=dtype, minval=minval,\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/numpy_array.py:450: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in ones is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  lambda shape, dtype=np.float32, name=None, layout=None: np.ones(  # pylint: disable=g-long-lambda\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/ops.py:339: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in array is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return np.array(value, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:290: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in zeros is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  minval = minval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:291: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in zeros is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  maxval = maxval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:292: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'>  is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return jaxrand.uniform(key=seed, shape=shape, dtype=dtype, minval=minval,\n"
     ]
    }
   ],
   "source": [
    "jd_14_8_pin = jd_14_8.experimental_pin(T=d.total_tools.values.astype(np.float32))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 302,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jax.jit\n",
    "def run_chain(init_state, seed, step_size=1e-3, num_steps=500, burnin=600):\n",
    "\n",
    "  def target_log_prob(*states):\n",
    "    return jd_14_8_pin.unnormalized_log_prob(states)\n",
    "  \n",
    "  bijectors = [tfb.Exp(), tfb.Exp(), tfb.Exp(), \n",
    "               tfb.Exp(), tfb.Exp(), tfb.Identity()]\n",
    "\n",
    "  kernel = tfp.mcmc.NoUTurnSampler(\n",
    "      target_log_prob_fn=target_log_prob,\n",
    "      step_size=step_size)\n",
    "  \n",
    "  kernel = tfp.mcmc.TransformedTransitionKernel(\n",
    "    inner_kernel=kernel,\n",
    "    bijector=bijectors)\n",
    "\n",
    "  kernel = tfp.mcmc.DualAveragingStepSizeAdaptation(\n",
    "    inner_kernel=kernel,\n",
    "    num_adaptation_steps=burnin)\n",
    "\n",
    "  chain_state = tfp.mcmc.sample_chain(\n",
    "      num_results=num_steps,\n",
    "      num_burnin_steps=burnin,\n",
    "      current_state=init_state,\n",
    "      kernel=kernel,\n",
    "      seed=seed,\n",
    "      trace_fn=None)\n",
    "  \n",
    "  return chain_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 303,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/jax/_src/numpy/array_methods.py:69: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in astype is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return lax_numpy.astype(arr, dtype, copy=copy, device=device)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/ops.py:339: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in array is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return np.array(value, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:290: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in zeros is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  minval = minval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:291: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in zeros is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  maxval = maxval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:292: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'>  is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return jaxrand.uniform(key=seed, shape=shape, dtype=dtype, minval=minval,\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/numpy_array.py:450: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in ones is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  lambda shape, dtype=np.float32, name=None, layout=None: np.ones(  # pylint: disable=g-long-lambda\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/ops.py:339: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in array is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return np.array(value, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:290: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in zeros is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  minval = minval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:291: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'> requested in zeros is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  maxval = maxval + np.zeros([1] * final_rank, dtype=dtype)\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.10/site-packages/tensorflow_probability/python/internal/backend/jax/random_generators.py:292: UserWarning: Explicitly requested dtype <class 'jax.numpy.float64'>  is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  return jaxrand.uniform(key=seed, shape=shape, dtype=dtype, minval=minval,\n"
     ]
    }
   ],
   "source": [
    "num_chains = 4\n",
    "init_state = jd_14_8_pin.sample_unpinned(num_chains, seed=key())\n",
    "post_8 = run_chain(init_state=init_state, seed=key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 304,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_8_dict = {k: jnp.moveaxis(v, 0, 1) for k, v in post_8._asdict().items()}\n",
    "dict_8 = dict(posterior=post_8_dict)\n",
    "idata_8 = az.from_dict(**dict_8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 305,
   "metadata": {},
   "outputs": [
    {
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_5.5%</th>\n",
       "      <th>hdi_94.5%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>a</th>\n",
       "      <td>1.384</td>\n",
       "      <td>1.060</td>\n",
       "      <td>0.026</td>\n",
       "      <td>2.705</td>\n",
       "      <td>0.046</td>\n",
       "      <td>0.033</td>\n",
       "      <td>358.0</td>\n",
       "      <td>282.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b</th>\n",
       "      <td>0.269</td>\n",
       "      <td>0.078</td>\n",
       "      <td>0.140</td>\n",
       "      <td>0.384</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.003</td>\n",
       "      <td>392.0</td>\n",
       "      <td>293.0</td>\n",
       "      <td>1.02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>etasq</th>\n",
       "      <td>0.184</td>\n",
       "      <td>0.204</td>\n",
       "      <td>0.005</td>\n",
       "      <td>0.364</td>\n",
       "      <td>0.009</td>\n",
       "      <td>0.007</td>\n",
       "      <td>432.0</td>\n",
       "      <td>785.0</td>\n",
       "      <td>1.02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>g</th>\n",
       "      <td>0.515</td>\n",
       "      <td>0.433</td>\n",
       "      <td>0.007</td>\n",
       "      <td>1.017</td>\n",
       "      <td>0.020</td>\n",
       "      <td>0.014</td>\n",
       "      <td>318.0</td>\n",
       "      <td>322.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>k[0]</th>\n",
       "      <td>-0.183</td>\n",
       "      <td>0.289</td>\n",
       "      <td>-0.616</td>\n",
       "      <td>0.274</td>\n",
       "      <td>0.012</td>\n",
       "      <td>0.008</td>\n",
       "      <td>615.0</td>\n",
       "      <td>630.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>k[1]</th>\n",
       "      <td>-0.037</td>\n",
       "      <td>0.282</td>\n",
       "      <td>-0.480</td>\n",
       "      <td>0.403</td>\n",
       "      <td>0.012</td>\n",
       "      <td>0.009</td>\n",
       "      <td>571.0</td>\n",
       "      <td>592.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>k[2]</th>\n",
       "      <td>-0.081</td>\n",
       "      <td>0.274</td>\n",
       "      <td>-0.490</td>\n",
       "      <td>0.357</td>\n",
       "      <td>0.011</td>\n",
       "      <td>0.008</td>\n",
       "      <td>643.0</td>\n",
       "      <td>686.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>k[3]</th>\n",
       "      <td>0.341</td>\n",
       "      <td>0.254</td>\n",
       "      <td>-0.047</td>\n",
       "      <td>0.725</td>\n",
       "      <td>0.010</td>\n",
       "      <td>0.008</td>\n",
       "      <td>682.0</td>\n",
       "      <td>638.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>k[4]</th>\n",
       "      <td>0.073</td>\n",
       "      <td>0.254</td>\n",
       "      <td>-0.285</td>\n",
       "      <td>0.471</td>\n",
       "      <td>0.010</td>\n",
       "      <td>0.009</td>\n",
       "      <td>719.0</td>\n",
       "      <td>676.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>k[5]</th>\n",
       "      <td>-0.383</td>\n",
       "      <td>0.273</td>\n",
       "      <td>-0.811</td>\n",
       "      <td>0.017</td>\n",
       "      <td>0.010</td>\n",
       "      <td>0.008</td>\n",
       "      <td>832.0</td>\n",
       "      <td>654.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>k[6]</th>\n",
       "      <td>0.141</td>\n",
       "      <td>0.255</td>\n",
       "      <td>-0.253</td>\n",
       "      <td>0.528</td>\n",
       "      <td>0.010</td>\n",
       "      <td>0.009</td>\n",
       "      <td>688.0</td>\n",
       "      <td>652.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>k[7]</th>\n",
       "      <td>-0.205</td>\n",
       "      <td>0.262</td>\n",
       "      <td>-0.587</td>\n",
       "      <td>0.183</td>\n",
       "      <td>0.010</td>\n",
       "      <td>0.009</td>\n",
       "      <td>724.0</td>\n",
       "      <td>538.0</td>\n",
       "      <td>1.02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>k[8]</th>\n",
       "      <td>0.263</td>\n",
       "      <td>0.250</td>\n",
       "      <td>-0.089</td>\n",
       "      <td>0.655</td>\n",
       "      <td>0.010</td>\n",
       "      <td>0.008</td>\n",
       "      <td>681.0</td>\n",
       "      <td>561.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>k[9]</th>\n",
       "      <td>-0.137</td>\n",
       "      <td>0.333</td>\n",
       "      <td>-0.598</td>\n",
       "      <td>0.423</td>\n",
       "      <td>0.016</td>\n",
       "      <td>0.013</td>\n",
       "      <td>454.0</td>\n",
       "      <td>281.0</td>\n",
       "      <td>1.02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rhosq</th>\n",
       "      <td>1.399</td>\n",
       "      <td>1.686</td>\n",
       "      <td>0.018</td>\n",
       "      <td>3.377</td>\n",
       "      <td>0.084</td>\n",
       "      <td>0.059</td>\n",
       "      <td>282.0</td>\n",
       "      <td>650.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        mean     sd  hdi_5.5%  hdi_94.5%  mcse_mean  mcse_sd  ess_bulk  \\\n",
       "a      1.384  1.060     0.026      2.705      0.046    0.033     358.0   \n",
       "b      0.269  0.078     0.140      0.384      0.004    0.003     392.0   \n",
       "etasq  0.184  0.204     0.005      0.364      0.009    0.007     432.0   \n",
       "g      0.515  0.433     0.007      1.017      0.020    0.014     318.0   \n",
       "k[0]  -0.183  0.289    -0.616      0.274      0.012    0.008     615.0   \n",
       "k[1]  -0.037  0.282    -0.480      0.403      0.012    0.009     571.0   \n",
       "k[2]  -0.081  0.274    -0.490      0.357      0.011    0.008     643.0   \n",
       "k[3]   0.341  0.254    -0.047      0.725      0.010    0.008     682.0   \n",
       "k[4]   0.073  0.254    -0.285      0.471      0.010    0.009     719.0   \n",
       "k[5]  -0.383  0.273    -0.811      0.017      0.010    0.008     832.0   \n",
       "k[6]   0.141  0.255    -0.253      0.528      0.010    0.009     688.0   \n",
       "k[7]  -0.205  0.262    -0.587      0.183      0.010    0.009     724.0   \n",
       "k[8]   0.263  0.250    -0.089      0.655      0.010    0.008     681.0   \n",
       "k[9]  -0.137  0.333    -0.598      0.423      0.016    0.013     454.0   \n",
       "rhosq  1.399  1.686     0.018      3.377      0.084    0.059     282.0   \n",
       "\n",
       "       ess_tail  r_hat  \n",
       "a         282.0   1.01  \n",
       "b         293.0   1.02  \n",
       "etasq     785.0   1.02  \n",
       "g         322.0   1.01  \n",
       "k[0]      630.0   1.01  \n",
       "k[1]      592.0   1.01  \n",
       "k[2]      686.0   1.00  \n",
       "k[3]      638.0   1.01  \n",
       "k[4]      676.0   1.00  \n",
       "k[5]      654.0   1.01  \n",
       "k[6]      652.0   1.01  \n",
       "k[7]      538.0   1.02  \n",
       "k[8]      561.0   1.01  \n",
       "k[9]      281.0   1.02  \n",
       "rhosq     650.0   1.01  "
      ]
     },
     "execution_count": 305,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata_8, hdi_prob=0.89)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 14.48"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 403,
   "metadata": {},
   "outputs": [],
   "source": [
    "Primates301 = pd.read_csv(\"./data/Primates301.csv\", sep=\";\")\n",
    "d = Primates301.loc[Primates301[[\"group_size\", \"body\", \"brain\"]].dropna().index]\n",
    "spp_obs = d['name']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 14.49"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 343,
   "metadata": {},
   "outputs": [],
   "source": [
    "dat_list = dict(\n",
    "    N_spp=d.shape[0],\n",
    "    M=d.body.apply(np.log).pipe(lambda x: (x - x.mean()) / x.std()).values,\n",
    "    B=d.brain.apply(np.log).pipe(lambda x: (x - x.mean()) / x.std()).values,\n",
    "    G=d.group_size.apply(np.log).pipe(lambda x: (x - x.mean()) / x.std()).values,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 365,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_14_9(M, G, N_spp):\n",
    "  def _generator():\n",
    "    a = yield tfd.Normal(loc=0., scale=1., name='a')\n",
    "    bM = yield tfd.Normal(loc=0., scale=.5, name='bM')\n",
    "    bG = yield tfd.Normal(loc=0., scale=.5, name='bG')\n",
    "    sigma_sq = yield tfd.Exponential(rate=1., name='sigma_sq')\n",
    "    sigma = jnp.sqrt(sigma_sq)\n",
    "    mu = a + bM * M + bG * G\n",
    "    yield tfd.MultivariateNormalDiag(loc=mu, scale_diag=[sigma]*N_spp, name='B')\n",
    "    \n",
    "  return tfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 366,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_14_9 = model_14_9(dat_list['M'], dat_list['G'], dat_list['N_spp'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 367,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_14_9_pin = jd_14_9.experimental_pin(B=dat_list['B'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 368,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jax.jit\n",
    "def run_chain(init_state, seed, step_size=1e-3, num_steps=500, burnin=500):\n",
    "\n",
    "  def target_log_prob(*states):\n",
    "    return jd_14_9_pin.unnormalized_log_prob(states)\n",
    "  \n",
    "  bijectors = [tfb.Identity(), tfb.Identity(), tfb.Identity(), tfb.Exp()]\n",
    "\n",
    "  kernel = tfp.mcmc.NoUTurnSampler(\n",
    "      target_log_prob_fn=target_log_prob,\n",
    "      step_size=step_size)\n",
    "  \n",
    "  kernel = tfp.mcmc.TransformedTransitionKernel(\n",
    "    inner_kernel=kernel,\n",
    "    bijector=bijectors)\n",
    "\n",
    "  kernel = tfp.mcmc.DualAveragingStepSizeAdaptation(\n",
    "    inner_kernel=kernel,\n",
    "    num_adaptation_steps=burnin)\n",
    "\n",
    "  chain_state = tfp.mcmc.sample_chain(\n",
    "      num_results=num_steps,\n",
    "      num_burnin_steps=burnin,\n",
    "      current_state=init_state,\n",
    "      kernel=kernel,\n",
    "      seed=seed,\n",
    "      trace_fn=None)\n",
    "  \n",
    "  return chain_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 369,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_chains = 4\n",
    "init_state = jd_14_9_pin.sample_unpinned(num_chains, seed=key())\n",
    "post_9 = run_chain(init_state=init_state, seed=key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 370,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_9_dict = {k: jnp.moveaxis(v, 0, 1) for k, v in post_9._asdict().items()}\n",
    "dict_9 = dict(posterior=post_9_dict)\n",
    "idata_9 = az.from_dict(**dict_9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 371,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_5.5%</th>\n",
       "      <th>hdi_94.5%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>a</th>\n",
       "      <td>-0.000</td>\n",
       "      <td>0.017</td>\n",
       "      <td>-0.024</td>\n",
       "      <td>0.030</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2377.0</td>\n",
       "      <td>1520.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bG</th>\n",
       "      <td>0.123</td>\n",
       "      <td>0.023</td>\n",
       "      <td>0.085</td>\n",
       "      <td>0.158</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1680.0</td>\n",
       "      <td>1196.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bM</th>\n",
       "      <td>0.894</td>\n",
       "      <td>0.023</td>\n",
       "      <td>0.856</td>\n",
       "      <td>0.931</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1565.0</td>\n",
       "      <td>1279.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma_sq</th>\n",
       "      <td>0.047</td>\n",
       "      <td>0.005</td>\n",
       "      <td>0.039</td>\n",
       "      <td>0.055</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>493.0</td>\n",
       "      <td>608.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           mean     sd  hdi_5.5%  hdi_94.5%  mcse_mean  mcse_sd  ess_bulk  \\\n",
       "a        -0.000  0.017    -0.024      0.030      0.000      0.0    2377.0   \n",
       "bG        0.123  0.023     0.085      0.158      0.001      0.0    1680.0   \n",
       "bM        0.894  0.023     0.856      0.931      0.001      0.0    1565.0   \n",
       "sigma_sq  0.047  0.005     0.039      0.055      0.000      0.0     493.0   \n",
       "\n",
       "          ess_tail  r_hat  \n",
       "a           1520.0   1.00  \n",
       "bG          1196.0   1.00  \n",
       "bM          1279.0   1.00  \n",
       "sigma_sq     608.0   1.01  "
      ]
     },
     "execution_count": 371,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata_9, hdi_prob=0.89)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 14.50"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 384,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "odict_keys(['Primates301_vcov_matrix'])"
      ]
     },
     "execution_count": 384,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vv = pyreadr.read_r('./data/Primates301_vcov_matrix.rda')\n",
    "vv.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 385,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "odict_keys(['Primates301_distance_matrix'])"
      ]
     },
     "execution_count": 385,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dd = pyreadr.read_r('./data/Primates301_distance_matrix.rda')\n",
    "dd.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 392,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "V = vv['Primates301_vcov_matrix']\n",
    "Dmat = dd['Primates301_distance_matrix']\n",
    "\n",
    "plt.plot(Dmat.values.reshape(-1), V.values.reshape(-1), \"o\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 14.51"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 404,
   "metadata": {},
   "outputs": [],
   "source": [
    "# put species in right order\n",
    "dat_list[\"V\"] = V.loc[spp_obs, spp_obs].values\n",
    "# convert to correlation matrix\n",
    "dat_list[\"R\"] = dat_list[\"V\"] / np.max(V.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 405,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_14_10(M, G, R):\n",
    "  def _generator():\n",
    "    a = yield tfd.Normal(loc=0., scale=1., name='a')\n",
    "    bM = yield tfd.Normal(loc=0., scale=.5, name='bM')\n",
    "    bG = yield tfd.Normal(loc=0., scale=.5, name='bG')\n",
    "    sigma_sq = yield tfd.Exponential(rate=1., name='sigma_sq')\n",
    "    mu = a + bM * M + bG * G\n",
    "    SIGMA = R * sigma_sq\n",
    "    yield tfd.MultivariateNormalFullCovariance(\n",
    "      loc=mu, covariance_matrix=SIGMA, name='B')\n",
    "    \n",
    "  return tfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 407,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_14_10 = model_14_10(dat_list['M'], dat_list['G'], dat_list['R'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 408,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_14_10_pin = jd_14_10.experimental_pin(B=dat_list['B'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 409,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jax.jit\n",
    "def run_chain(init_state, seed, step_size=1e-3, num_steps=500, burnin=500):\n",
    "\n",
    "  def target_log_prob(*states):\n",
    "    return jd_14_10_pin.unnormalized_log_prob(states)\n",
    "  \n",
    "  bijectors = [tfb.Identity(), tfb.Identity(), tfb.Identity(), tfb.Exp()]\n",
    "\n",
    "  kernel = tfp.mcmc.NoUTurnSampler(\n",
    "      target_log_prob_fn=target_log_prob,\n",
    "      step_size=step_size)\n",
    "  \n",
    "  kernel = tfp.mcmc.TransformedTransitionKernel(\n",
    "    inner_kernel=kernel,\n",
    "    bijector=bijectors)\n",
    "\n",
    "  kernel = tfp.mcmc.DualAveragingStepSizeAdaptation(\n",
    "    inner_kernel=kernel,\n",
    "    num_adaptation_steps=burnin)\n",
    "\n",
    "  chain_state = tfp.mcmc.sample_chain(\n",
    "      num_results=num_steps,\n",
    "      num_burnin_steps=burnin,\n",
    "      current_state=init_state,\n",
    "      kernel=kernel,\n",
    "      seed=seed,\n",
    "      trace_fn=None)\n",
    "  \n",
    "  return chain_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 410,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_chains = 4\n",
    "init_state = jd_14_10_pin.sample_unpinned(num_chains, seed=key())\n",
    "post_10 = run_chain(init_state=init_state, seed=key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 411,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_10_dict = {k: jnp.moveaxis(v, 0, 1) for k, v in post_10._asdict().items()}\n",
    "dict_10 = dict(posterior=post_10_dict)\n",
    "idata_10 = az.from_dict(**dict_10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 412,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_5.5%</th>\n",
       "      <th>hdi_94.5%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>a</th>\n",
       "      <td>-0.186</td>\n",
       "      <td>0.178</td>\n",
       "      <td>-0.451</td>\n",
       "      <td>0.112</td>\n",
       "      <td>0.007</td>\n",
       "      <td>0.005</td>\n",
       "      <td>747.0</td>\n",
       "      <td>630.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bG</th>\n",
       "      <td>-0.013</td>\n",
       "      <td>0.020</td>\n",
       "      <td>-0.045</td>\n",
       "      <td>0.019</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>2044.0</td>\n",
       "      <td>1582.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bM</th>\n",
       "      <td>0.700</td>\n",
       "      <td>0.036</td>\n",
       "      <td>0.639</td>\n",
       "      <td>0.754</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>1948.0</td>\n",
       "      <td>1459.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma_sq</th>\n",
       "      <td>0.162</td>\n",
       "      <td>0.019</td>\n",
       "      <td>0.133</td>\n",
       "      <td>0.190</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.000</td>\n",
       "      <td>1263.0</td>\n",
       "      <td>988.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           mean     sd  hdi_5.5%  hdi_94.5%  mcse_mean  mcse_sd  ess_bulk  \\\n",
       "a        -0.186  0.178    -0.451      0.112      0.007    0.005     747.0   \n",
       "bG       -0.013  0.020    -0.045      0.019      0.000    0.000    2044.0   \n",
       "bM        0.700  0.036     0.639      0.754      0.001    0.001    1948.0   \n",
       "sigma_sq  0.162  0.019     0.133      0.190      0.001    0.000    1263.0   \n",
       "\n",
       "          ess_tail  r_hat  \n",
       "a            630.0   1.00  \n",
       "bG          1582.0   1.00  \n",
       "bM          1459.0   1.00  \n",
       "sigma_sq     988.0   1.01  "
      ]
     },
     "execution_count": 412,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata_10, hdi_prob=0.89)"
   ]
  }
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