examples/variational_inference/GLM-hierarchical-advi-minibatch.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# GLM: Mini-batch ADVI on hierarchical regression model\n",
    "\n",
    ":::{post} Sept 23, 2021\n",
    ":tags: generalized linear model, hierarchical model, variational inference\n",
    ":category: intermediate\n",
    ":::"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Unlike Gaussian mixture models, (hierarchical) regression models have independent variables. These variables affect the likelihood function, but are not random variables. When using mini-batch, we should take care of that."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "env: PYTENSOR_FLAGS=device=cpu, floatX=float32, warn_float64=ignore\n",
      "Running on PyMC v5.0.1\n"
     ]
    }
   ],
   "source": [
    "%env PYTENSOR_FLAGS=device=cpu, floatX=float32, warn_float64=ignore\n",
    "\n",
    "import os\n",
    "\n",
    "import arviz as az\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import pymc as pm\n",
    "import pytensor\n",
    "import pytensor.tensor as pt\n",
    "import seaborn as sns\n",
    "\n",
    "from scipy import stats\n",
    "\n",
    "print(f\"Running on PyMC v{pm.__version__}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%config InlineBackend.figure_format = 'retina'\n",
    "RANDOM_SEED = 8927\n",
    "rng = np.random.default_rng(RANDOM_SEED)\n",
    "az.style.use(\"arviz-darkgrid\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>idnum</th>\n",
       "      <th>state</th>\n",
       "      <th>state2</th>\n",
       "      <th>stfips</th>\n",
       "      <th>zip</th>\n",
       "      <th>region</th>\n",
       "      <th>typebldg</th>\n",
       "      <th>floor</th>\n",
       "      <th>room</th>\n",
       "      <th>...</th>\n",
       "      <th>pcterr</th>\n",
       "      <th>adjwt</th>\n",
       "      <th>dupflag</th>\n",
       "      <th>zipflag</th>\n",
       "      <th>cntyfips</th>\n",
       "      <th>county</th>\n",
       "      <th>fips</th>\n",
       "      <th>Uppm</th>\n",
       "      <th>county_code</th>\n",
       "      <th>log_radon</th>\n",
       "    </tr>\n",
       "  </thead>\n",
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       "      <td>1.0</td>\n",
       "      <td>AITKIN</td>\n",
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       "      <td>0.502054</td>\n",
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       "      <td>0.832909</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>...</td>\n",
       "      <td>14.5</td>\n",
       "      <td>471.366223</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>AITKIN</td>\n",
       "      <td>27001.0</td>\n",
       "      <td>0.502054</td>\n",
       "      <td>0</td>\n",
       "      <td>0.832909</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>5083.0</td>\n",
       "      <td>MN</td>\n",
       "      <td>MN</td>\n",
       "      <td>27.0</td>\n",
       "      <td>55748</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>...</td>\n",
       "      <td>9.6</td>\n",
       "      <td>433.316718</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>AITKIN</td>\n",
       "      <td>27001.0</td>\n",
       "      <td>0.502054</td>\n",
       "      <td>0</td>\n",
       "      <td>1.098612</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>5084.0</td>\n",
       "      <td>MN</td>\n",
       "      <td>MN</td>\n",
       "      <td>27.0</td>\n",
       "      <td>56469</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>...</td>\n",
       "      <td>24.3</td>\n",
       "      <td>461.623670</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>AITKIN</td>\n",
       "      <td>27001.0</td>\n",
       "      <td>0.502054</td>\n",
       "      <td>0</td>\n",
       "      <td>0.095310</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>5085.0</td>\n",
       "      <td>MN</td>\n",
       "      <td>MN</td>\n",
       "      <td>27.0</td>\n",
       "      <td>55011</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>...</td>\n",
       "      <td>13.8</td>\n",
       "      <td>433.316718</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>ANOKA</td>\n",
       "      <td>27003.0</td>\n",
       "      <td>0.428565</td>\n",
       "      <td>1</td>\n",
       "      <td>1.163151</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
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       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <th>914</th>\n",
       "      <td>914</td>\n",
       "      <td>5995.0</td>\n",
       "      <td>MN</td>\n",
       "      <td>MN</td>\n",
       "      <td>27.0</td>\n",
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       "      <td>5.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>...</td>\n",
       "      <td>4.5</td>\n",
       "      <td>1146.499190</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>171.0</td>\n",
       "      <td>WRIGHT</td>\n",
       "      <td>27171.0</td>\n",
       "      <td>0.913909</td>\n",
       "      <td>83</td>\n",
       "      <td>1.871802</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>915</th>\n",
       "      <td>915</td>\n",
       "      <td>5996.0</td>\n",
       "      <td>MN</td>\n",
       "      <td>MN</td>\n",
       "      <td>27.0</td>\n",
       "      <td>55376</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>...</td>\n",
       "      <td>8.3</td>\n",
       "      <td>1105.956867</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>171.0</td>\n",
       "      <td>WRIGHT</td>\n",
       "      <td>27171.0</td>\n",
       "      <td>0.913909</td>\n",
       "      <td>83</td>\n",
       "      <td>1.526056</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>916</th>\n",
       "      <td>916</td>\n",
       "      <td>5997.0</td>\n",
       "      <td>MN</td>\n",
       "      <td>MN</td>\n",
       "      <td>27.0</td>\n",
       "      <td>55376</td>\n",
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       "      <td>0.0</td>\n",
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       "      <td>5.2</td>\n",
       "      <td>1214.922779</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>171.0</td>\n",
       "      <td>WRIGHT</td>\n",
       "      <td>27171.0</td>\n",
       "      <td>0.913909</td>\n",
       "      <td>83</td>\n",
       "      <td>1.629241</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>917</th>\n",
       "      <td>917</td>\n",
       "      <td>5998.0</td>\n",
       "      <td>MN</td>\n",
       "      <td>MN</td>\n",
       "      <td>27.0</td>\n",
       "      <td>56297</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>...</td>\n",
       "      <td>9.6</td>\n",
       "      <td>1177.377355</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>173.0</td>\n",
       "      <td>YELLOW MEDICINE</td>\n",
       "      <td>27173.0</td>\n",
       "      <td>1.426590</td>\n",
       "      <td>84</td>\n",
       "      <td>1.335001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>918</th>\n",
       "      <td>918</td>\n",
       "      <td>5999.0</td>\n",
       "      <td>MN</td>\n",
       "      <td>MN</td>\n",
       "      <td>27.0</td>\n",
       "      <td>56297</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>...</td>\n",
       "      <td>8.0</td>\n",
       "      <td>1214.922779</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>173.0</td>\n",
       "      <td>YELLOW MEDICINE</td>\n",
       "      <td>27173.0</td>\n",
       "      <td>1.426590</td>\n",
       "      <td>84</td>\n",
       "      <td>1.098612</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>919 rows × 30 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     Unnamed: 0   idnum state state2  stfips    zip  region  typebldg  floor  \\\n",
       "0             0  5081.0    MN     MN    27.0  55735     5.0       1.0    1.0   \n",
       "1             1  5082.0    MN     MN    27.0  55748     5.0       1.0    0.0   \n",
       "2             2  5083.0    MN     MN    27.0  55748     5.0       1.0    0.0   \n",
       "3             3  5084.0    MN     MN    27.0  56469     5.0       1.0    0.0   \n",
       "4             4  5085.0    MN     MN    27.0  55011     3.0       1.0    0.0   \n",
       "..          ...     ...   ...    ...     ...    ...     ...       ...    ...   \n",
       "914         914  5995.0    MN     MN    27.0  55363     5.0       1.0    0.0   \n",
       "915         915  5996.0    MN     MN    27.0  55376     5.0       1.0    0.0   \n",
       "916         916  5997.0    MN     MN    27.0  55376     5.0       1.0    0.0   \n",
       "917         917  5998.0    MN     MN    27.0  56297     5.0       1.0    0.0   \n",
       "918         918  5999.0    MN     MN    27.0  56297     5.0       1.0    0.0   \n",
       "\n",
       "     room  ... pcterr        adjwt  dupflag  zipflag  cntyfips  \\\n",
       "0     3.0  ...    9.7  1146.499190      1.0      0.0       1.0   \n",
       "1     4.0  ...   14.5   471.366223      0.0      0.0       1.0   \n",
       "2     4.0  ...    9.6   433.316718      0.0      0.0       1.0   \n",
       "3     4.0  ...   24.3   461.623670      0.0      0.0       1.0   \n",
       "4     4.0  ...   13.8   433.316718      0.0      0.0       3.0   \n",
       "..    ...  ...    ...          ...      ...      ...       ...   \n",
       "914   4.0  ...    4.5  1146.499190      0.0      0.0     171.0   \n",
       "915   7.0  ...    8.3  1105.956867      0.0      0.0     171.0   \n",
       "916   4.0  ...    5.2  1214.922779      0.0      0.0     171.0   \n",
       "917   4.0  ...    9.6  1177.377355      0.0      0.0     173.0   \n",
       "918   4.0  ...    8.0  1214.922779      0.0      0.0     173.0   \n",
       "\n",
       "              county     fips      Uppm  county_code  log_radon  \n",
       "0             AITKIN  27001.0  0.502054            0   0.832909  \n",
       "1             AITKIN  27001.0  0.502054            0   0.832909  \n",
       "2             AITKIN  27001.0  0.502054            0   1.098612  \n",
       "3             AITKIN  27001.0  0.502054            0   0.095310  \n",
       "4              ANOKA  27003.0  0.428565            1   1.163151  \n",
       "..               ...      ...       ...          ...        ...  \n",
       "914           WRIGHT  27171.0  0.913909           83   1.871802  \n",
       "915           WRIGHT  27171.0  0.913909           83   1.526056  \n",
       "916           WRIGHT  27171.0  0.913909           83   1.629241  \n",
       "917  YELLOW MEDICINE  27173.0  1.426590           84   1.335001  \n",
       "918  YELLOW MEDICINE  27173.0  1.426590           84   1.098612  \n",
       "\n",
       "[919 rows x 30 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "try:\n",
    "    data = pd.read_csv(os.path.join(\"..\", \"data\", \"radon.csv\"))\n",
    "except FileNotFoundError:\n",
    "    data = pd.read_csv(pm.get_data(\"radon.csv\"))\n",
    "\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "county_idx = data[\"county_code\"].values\n",
    "floor_idx = data[\"floor\"].values\n",
    "log_radon_idx = data[\"log_radon\"].values\n",
    "\n",
    "coords = {\"counties\": data.county.unique()}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, `log_radon_idx_t` is a dependent variable, while `floor_idx_t` and `county_idx_t` determine the independent variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "log_radon_idx_t = pm.Minibatch(log_radon_idx, batch_size=100)\n",
    "floor_idx_t = pm.Minibatch(floor_idx, batch_size=100)\n",
    "county_idx_t = pm.Minibatch(county_idx, batch_size=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "with pm.Model(coords=coords) as hierarchical_model:\n",
    "    # Hyperpriors for group nodes\n",
    "    mu_a = pm.Normal(\"mu_alpha\", mu=0.0, sigma=100**2)\n",
    "    sigma_a = pm.Uniform(\"sigma_alpha\", lower=0, upper=100)\n",
    "    mu_b = pm.Normal(\"mu_beta\", mu=0.0, sigma=100**2)\n",
    "    sigma_b = pm.Uniform(\"sigma_beta\", lower=0, upper=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Intercept for each county, distributed around group mean `mu_a`. Above we just set `mu` and `sd` to a fixed value while here we plug in a common group distribution for all `a` and `b` (which are vectors with the same length as the number of unique counties in our example)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "with hierarchical_model:\n",
    "\n",
    "    a = pm.Normal(\"alpha\", mu=mu_a, sigma=sigma_a, dims=\"counties\")\n",
    "    # Intercept for each county, distributed around group mean mu_a\n",
    "    b = pm.Normal(\"beta\", mu=mu_b, sigma=sigma_b, dims=\"counties\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Model prediction of radon level `a[county_idx]` translates to `a[0, 0, 0, 1, 1, ...]`, we thus link multiple household measures of a county to its coefficients."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "with hierarchical_model:\n",
    "\n",
    "    radon_est = a[county_idx_t] + b[county_idx_t] * floor_idx_t"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we specify the likelihood:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "with hierarchical_model:\n",
    "\n",
    "    # Model error\n",
    "    eps = pm.Uniform(\"eps\", lower=0, upper=100)\n",
    "\n",
    "    # Data likelihood\n",
    "    radon_like = pm.Normal(\n",
    "        \"radon_like\", mu=radon_est, sigma=eps, observed=log_radon_idx_t, total_size=len(data)\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Random variables `radon_like`, associated with `log_radon_idx_t`, should be given to the function for ADVI to denote that as observations in the likelihood term."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On the other hand, `minibatches` should include the three variables above."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then, run ADVI with mini-batch."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/fonnesbeck/mambaforge/envs/pie/lib/python3.9/site-packages/pymc/logprob/joint_logprob.py:167: UserWarning: Found a random variable that was neither among the observations nor the conditioned variables: [integers_rv{0, (0, 0), int64, False}.0, integers_rv{0, (0, 0), int64, False}.out]\n",
      "  warnings.warn(\n",
      "/home/fonnesbeck/mambaforge/envs/pie/lib/python3.9/site-packages/pymc/logprob/joint_logprob.py:167: UserWarning: Found a random variable that was neither among the observations nor the conditioned variables: [integers_rv{0, (0, 0), int64, False}.0, integers_rv{0, (0, 0), int64, False}.out]\n",
      "  warnings.warn(\n",
      "/home/fonnesbeck/mambaforge/envs/pie/lib/python3.9/site-packages/pymc/logprob/joint_logprob.py:167: UserWarning: Found a random variable that was neither among the observations nor the conditioned variables: [integers_rv{0, (0, 0), int64, False}.0, integers_rv{0, (0, 0), int64, False}.out]\n",
      "  warnings.warn(\n",
      "/home/fonnesbeck/mambaforge/envs/pie/lib/python3.9/site-packages/pymc/logprob/joint_logprob.py:167: UserWarning: Found a random variable that was neither among the observations nor the conditioned variables: [integers_rv{0, (0, 0), int64, False}.0, integers_rv{0, (0, 0), int64, False}.out]\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       "    /* Turns off some styling */\n",
       "    progress {\n",
       "        /* gets rid of default border in Firefox and Opera. */\n",
       "        border: none;\n",
       "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
       "        background-size: auto;\n",
       "    }\n",
       "    progress:not([value]), progress:not([value])::-webkit-progress-bar {\n",
       "        background: repeating-linear-gradient(45deg, #7e7e7e, #7e7e7e 10px, #5c5c5c 10px, #5c5c5c 20px);\n",
       "    }\n",
       "    .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
       "        background: #F44336;\n",
       "    }\n",
       "</style>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "    <div>\n",
       "      <progress value='11499' class='' max='100000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
       "      11.50% [11499/100000 00:03&lt;00:27 Average Loss = 263.87]\n",
       "    </div>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with hierarchical_model:\n",
    "    approx = pm.fit(100_000, callbacks=[pm.callbacks.CheckParametersConvergence(tolerance=1e-4)])\n",
    "\n",
    "idata_advi = approx.sample(500)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check the trace of ELBO and compare the result with MCMC."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 491,
       "width": 731
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(approx.hist);"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can extract the covariance matrix from the mean field approximation and use it as the scaling matrix for the NUTS algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "scaling = approx.cov.eval()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Also, we can generate samples (one for each chain) to use as the starting points for the sampler."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_chains = 4\n",
    "sample = approx.sample(return_inferencedata=False, size=n_chains)\n",
    "start_dict = list(sample[i] for i in range(n_chains))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [mu_alpha, sigma_alpha, mu_beta, sigma_beta, alpha, beta, eps]\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       "    /* Turns off some styling */\n",
       "    progress {\n",
       "        /* gets rid of default border in Firefox and Opera. */\n",
       "        border: none;\n",
       "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
       "        background-size: auto;\n",
       "    }\n",
       "    progress:not([value]), progress:not([value])::-webkit-progress-bar {\n",
       "        background: repeating-linear-gradient(45deg, #7e7e7e, #7e7e7e 10px, #5c5c5c 10px, #5c5c5c 20px);\n",
       "    }\n",
       "    .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
       "        background: #F44336;\n",
       "    }\n",
       "</style>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "    <div>\n",
       "      <progress value='8000' class='' max='8000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
       "      100.00% [8000/8000 08:57&lt;00:00 Sampling 4 chains, 0 divergences]\n",
       "    </div>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 538 seconds.\n"
     ]
    }
   ],
   "source": [
    "# Inference button (TM)!\n",
    "with pm.Model(coords=coords):\n",
    "\n",
    "    mu_a = pm.Normal(\"mu_alpha\", mu=0.0, sigma=100**2)\n",
    "    sigma_a = pm.Uniform(\"sigma_alpha\", lower=0, upper=100)\n",
    "    mu_b = pm.Normal(\"mu_beta\", mu=0.0, sigma=100**2)\n",
    "    sigma_b = pm.Uniform(\"sigma_beta\", lower=0, upper=100)\n",
    "\n",
    "    a = pm.Normal(\"alpha\", mu=mu_a, sigma=sigma_a, dims=\"counties\")\n",
    "    b = pm.Normal(\"beta\", mu=mu_b, sigma=sigma_b, dims=\"counties\")\n",
    "\n",
    "    # Model error\n",
    "    eps = pm.Uniform(\"eps\", lower=0, upper=100)\n",
    "\n",
    "    radon_est = a[county_idx] + b[county_idx] * floor_idx\n",
    "\n",
    "    radon_like = pm.Normal(\"radon_like\", mu=radon_est, sigma=eps, observed=log_radon_idx)\n",
    "\n",
    "    # essentially, this is what init='advi' does\n",
    "    step = pm.NUTS(scaling=scaling, is_cov=True)\n",
    "    hierarchical_trace = pm.sample(draws=2000, step=step, chains=n_chains, initvals=start_dict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2484x1104 with 6 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 1115,
       "width": 2495
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_density(\n",
    "    data=[idata_advi, hierarchical_trace],\n",
    "    var_names=[\"~alpha\", \"~beta\"],\n",
    "    data_labels=[\"ADVI\", \"NUTS\"],\n",
    ");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Watermark"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Last updated: Thu Sep 23 2021\n",
      "\n",
      "Python implementation: CPython\n",
      "Python version       : 3.8.10\n",
      "IPython version      : 7.25.0\n",
      "\n",
      "xarray: 0.17.0\n",
      "\n",
      "numpy     : 1.21.0\n",
      "seaborn   : 0.11.1\n",
      "pandas    : 1.2.1\n",
      "matplotlib: 3.3.4\n",
      "theano    : 1.1.2\n",
      "pymc3     : 3.11.2\n",
      "scipy     : 1.7.1\n",
      "arviz     : 0.11.2\n",
      "\n",
      "Watermark: 2.2.0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -n -u -v -iv -w -p xarray"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
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    ":::"
   ]
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