notebooks/05_the_many_variables_and_the_spurious_waffles.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 5. The Many Variables & The Spurious Waffles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "!pip install -q numpyro arviz daft networkx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import collections\n",
    "import itertools\n",
    "import math\n",
    "import os\n",
    "\n",
    "import arviz as az\n",
    "import daft\n",
    "import matplotlib.pyplot as plt\n",
    "import networkx as nx\n",
    "import pandas as pd\n",
    "\n",
    "import jax.numpy as jnp\n",
    "from jax import random\n",
    "\n",
    "import numpyro\n",
    "import numpyro.distributions as dist\n",
    "import numpyro.optim as optim\n",
    "from numpyro.diagnostics import print_summary\n",
    "from numpyro.infer import Predictive, SVI, Trace_ELBO\n",
    "from numpyro.infer.autoguide import AutoLaplaceApproximation\n",
    "\n",
    "if \"SVG\" in os.environ:\n",
    "    %config InlineBackend.figure_formats = [\"svg\"]\n",
    "az.style.use(\"arviz-darkgrid\")\n",
    "numpyro.set_platform(\"cpu\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# load data and copy\n",
    "WaffleDivorce = pd.read_csv(\"../data/WaffleDivorce.csv\", sep=\";\")\n",
    "d = WaffleDivorce\n",
    "\n",
    "# standardize variables\n",
    "d[\"A\"] = d.MedianAgeMarriage.pipe(lambda x: (x - x.mean()) / x.std())\n",
    "d[\"D\"] = d.Divorce.pipe(lambda x: (x - x.mean()) / x.std())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.2436303013880823"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d.MedianAgeMarriage.std()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000/1000 [00:00<00:00, 1196.77it/s, init loss: 2138.6682, avg. loss [951-1000]: 59.4385]\n"
     ]
    }
   ],
   "source": [
    "def model(A, D=None):\n",
    "    a = numpyro.sample(\"a\", dist.Normal(0, 0.2))\n",
    "    bA = numpyro.sample(\"bA\", dist.Normal(0, 0.5))\n",
    "    sigma = numpyro.sample(\"sigma\", dist.Exponential(1))\n",
    "    mu = numpyro.deterministic(\"mu\", a + bA * A)\n",
    "    numpyro.sample(\"D\", dist.Normal(mu, sigma), obs=D)\n",
    "\n",
    "\n",
    "m5_1 = AutoLaplaceApproximation(model)\n",
    "svi = SVI(model, m5_1, optim.Adam(1), Trace_ELBO(), A=d.A.values, D=d.D.values)\n",
    "svi_result = svi.run(random.PRNGKey(0), 1000)\n",
    "p5_1 = svi_result.params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "predictive = Predictive(m5_1.model, num_samples=1000, return_sites=[\"mu\"])\n",
    "prior_pred = predictive(random.PRNGKey(10), A=jnp.array([-2, 2]))\n",
    "mu = prior_pred[\"mu\"]\n",
    "plt.subplot(xlim=(-2, 2), ylim=(-2, 2))\n",
    "for i in range(20):\n",
    "    plt.plot([-2, 2], mu[i], \"k\", alpha=0.4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# compute percentile interval of mean\n",
    "A_seq = jnp.linspace(start=-3, stop=3.2, num=30)\n",
    "post = m5_1.sample_posterior(random.PRNGKey(1), p5_1, sample_shape=(1000,))\n",
    "post.pop(\"mu\")\n",
    "post_pred = Predictive(m5_1.model, post)(random.PRNGKey(2), A=A_seq)\n",
    "mu = post_pred[\"mu\"]\n",
    "mu_mean = jnp.mean(mu, 0)\n",
    "mu_PI = jnp.percentile(mu, q=jnp.array([5.5, 94.5]), axis=0)\n",
    "\n",
    "# plot it all\n",
    "az.plot_pair(d[[\"D\", \"A\"]].to_dict(orient=\"list\"))\n",
    "plt.plot(A_seq, mu_mean, \"k\")\n",
    "plt.fill_between(A_seq, mu_PI[0], mu_PI[1], color=\"k\", alpha=0.2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000/1000 [00:00<00:00, 1218.38it/s, init loss: 962.7464, avg. loss [951-1000]: 66.1313]\n"
     ]
    }
   ],
   "source": [
    "d[\"M\"] = d.Marriage.pipe(lambda x: (x - x.mean()) / x.std())\n",
    "\n",
    "\n",
    "def model(M, D=None):\n",
    "    a = numpyro.sample(\"a\", dist.Normal(0, 0.2))\n",
    "    bM = numpyro.sample(\"bM\", dist.Normal(0, 0.5))\n",
    "    sigma = numpyro.sample(\"sigma\", dist.Exponential(1))\n",
    "    mu = a + bM * M\n",
    "    numpyro.sample(\"D\", dist.Normal(mu, sigma), obs=D)\n",
    "\n",
    "\n",
    "m5_2 = AutoLaplaceApproximation(model)\n",
    "svi = SVI(model, m5_2, optim.Adam(1), Trace_ELBO(), M=d.M.values, D=d.D.values)\n",
    "svi_result = svi.run(random.PRNGKey(0), 1000)\n",
    "p5_2 = svi_result.params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 212.598x133.858 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dag5_1 = nx.DiGraph()\n",
    "dag5_1.add_edges_from([(\"A\", \"D\"), (\"A\", \"M\"), (\"M\", \"D\")])\n",
    "pgm = daft.PGM()\n",
    "coordinates = {\"A\": (0, 0), \"D\": (1, 1), \"M\": (2, 0)}\n",
    "for node in dag5_1.nodes:\n",
    "    pgm.add_node(node, node, *coordinates[node])\n",
    "for edge in dag5_1.edges:\n",
    "    pgm.add_edge(*edge)\n",
    "with plt.rc_context({\"figure.constrained_layout.use\": False}):\n",
    "    pgm.render()\n",
    "plt.gca().invert_yaxis()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "D _||_ M | A\n"
     ]
    }
   ],
   "source": [
    "DMA_dag2 = nx.DiGraph()\n",
    "DMA_dag2.add_edges_from([(\"A\", \"D\"), (\"A\", \"M\")])\n",
    "conditional_independencies = collections.defaultdict(list)\n",
    "for edge in itertools.combinations(sorted(DMA_dag2.nodes), 2):\n",
    "    remaining = sorted(set(DMA_dag2.nodes) - set(edge))\n",
    "    for size in range(len(remaining) + 1):\n",
    "        for subset in itertools.combinations(remaining, size):\n",
    "            if any(cond.issubset(set(subset)) for cond in conditional_independencies[edge]):\n",
    "                continue\n",
    "            if nx.d_separated(DMA_dag2, {edge[0]}, {edge[1]}, set(subset)):\n",
    "                conditional_independencies[edge].append(set(subset))\n",
    "                print(f\"{edge[0]} _||_ {edge[1]}\" + (f\" | {' '.join(subset)}\" if subset else \"\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "DMA_dag1 = nx.DiGraph()\n",
    "DMA_dag1.add_edges_from([(\"A\", \"D\"), (\"A\", \"M\"), (\"M\", \"D\")])\n",
    "conditional_independencies = collections.defaultdict(list)\n",
    "for edge in itertools.combinations(sorted(DMA_dag1.nodes), 2):\n",
    "    remaining = sorted(set(DMA_dag1.nodes) - set(edge))\n",
    "    for size in range(len(remaining) + 1):\n",
    "        for subset in itertools.combinations(remaining, size):\n",
    "            if any(cond.issubset(set(subset)) for cond in conditional_independencies[edge]):\n",
    "                continue\n",
    "            if nx.d_separated(DMA_dag1, {edge[0]}, {edge[1]}, set(subset)):\n",
    "                conditional_independencies[edge].append(set(subset))\n",
    "                print(f\"{edge[0]} _||_ {edge[1]}\" + (f\" | {' '.join(subset)}\" if subset else \"\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000/1000 [00:00<00:00, 1002.82it/s, init loss: 3201.7393, avg. loss [951-1000]: 59.5721]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                mean       std    median      5.5%     94.5%     n_eff     r_hat\n",
      "         a     -0.00      0.10     -0.01     -0.16      0.14   1049.96      1.00\n",
      "        bA     -0.61      0.16     -0.61     -0.86     -0.36    822.38      1.00\n",
      "        bM     -0.06      0.16     -0.06     -0.31      0.19    984.99      1.00\n",
      "     mu[0]      0.36      0.13      0.37      0.15      0.57    921.63      1.00\n",
      "     mu[1]      0.32      0.21      0.32     -0.01      0.66    900.77      1.00\n",
      "     mu[2]      0.12      0.10      0.12     -0.03      0.28    995.35      1.00\n",
      "     mu[3]      0.76      0.21      0.75      0.43      1.10    911.65      1.00\n",
      "     mu[4]     -0.35      0.12     -0.35     -0.52     -0.14   1070.56      1.00\n",
      "     mu[5]      0.12      0.15      0.12     -0.13      0.35    861.01      1.00\n",
      "     mu[6]     -0.71      0.17     -0.70     -0.95     -0.42   1053.26      1.00\n",
      "     mu[7]     -0.31      0.20     -0.32     -0.63      0.03    865.14      1.00\n",
      "     mu[8]     -1.74      0.40     -1.74     -2.28     -1.00    804.96      1.00\n",
      "     mu[9]     -0.12      0.14     -0.12     -0.37      0.08   1072.06      1.00\n",
      "    mu[10]      0.04      0.12      0.04     -0.14      0.23    858.83      1.00\n",
      "    mu[11]     -0.49      0.30     -0.49     -0.91      0.05    872.77      1.00\n",
      "    mu[12]      1.30      0.27      1.30      0.87      1.72    867.10      1.00\n",
      "    mu[13]     -0.43      0.13     -0.43     -0.61     -0.21   1125.00      1.00\n",
      "    mu[14]      0.18      0.11      0.18      0.00      0.35    987.73      1.00\n",
      "    mu[15]      0.30      0.11      0.30      0.11      0.47    909.55      1.00\n",
      "    mu[16]      0.48      0.13      0.49      0.27      0.70    875.38      1.00\n",
      "    mu[17]      0.58      0.15      0.58      0.35      0.82    867.29      1.00\n",
      "    mu[18]      0.07      0.10      0.06     -0.09      0.21   1002.97      1.00\n",
      "    mu[19]     -0.07      0.27     -0.07     -0.50      0.34   1018.90      1.00\n",
      "    mu[20]     -0.58      0.15     -0.58     -0.80     -0.32   1013.12      1.00\n",
      "    mu[21]     -1.13      0.24     -1.13     -1.47     -0.74    928.11      1.00\n",
      "    mu[22]     -0.11      0.16     -0.11     -0.38      0.12   1058.69      1.00\n",
      "    mu[23]     -0.05      0.21     -0.05     -0.38      0.27   1029.22      1.00\n",
      "    mu[24]      0.13      0.11      0.13     -0.05      0.30   1018.21      1.00\n",
      "    mu[25]      0.24      0.15      0.24      0.03      0.50    987.36      1.00\n",
      "    mu[26]      0.20      0.14      0.19     -0.04      0.42   1004.82      1.00\n",
      "    mu[27]      0.33      0.14      0.32      0.10      0.53    944.68      1.00\n",
      "    mu[28]     -0.31      0.14     -0.31     -0.53     -0.09   1106.73      1.00\n",
      "    mu[29]     -0.72      0.19     -0.72     -1.03     -0.42   1099.72      1.00\n",
      "    mu[30]      0.12      0.10      0.12     -0.03      0.28    992.25      1.00\n",
      "    mu[31]     -1.09      0.24     -1.10     -1.44     -0.70    891.79      1.00\n",
      "    mu[32]      0.17      0.10      0.17      0.00      0.33    973.21      1.00\n",
      "    mu[33]      0.26      0.24      0.26     -0.13      0.63    903.59      1.00\n",
      "    mu[34]     -0.07      0.15     -0.07     -0.34      0.14   1057.21      1.00\n",
      "    mu[35]      0.75      0.18      0.75      0.49      1.05    865.16      1.00\n",
      "    mu[36]      0.04      0.11      0.04     -0.15      0.20   1071.57      1.00\n",
      "    mu[37]     -0.44      0.17     -0.44     -0.70     -0.17   1096.13      1.00\n",
      "    mu[38]     -0.97      0.21     -0.97     -1.31     -0.63   1057.69      1.00\n",
      "    mu[39]     -0.14      0.11     -0.14     -0.32      0.04   1109.30      1.00\n",
      "    mu[40]      0.22      0.11      0.22      0.04      0.39    962.55      1.00\n",
      "    mu[41]      0.43      0.16      0.42      0.18      0.69    929.76      1.00\n",
      "    mu[42]      0.39      0.12      0.40      0.18      0.57    890.80      1.00\n",
      "    mu[43]      1.19      0.30      1.20      0.72      1.70    930.35      1.00\n",
      "    mu[44]     -0.36      0.15     -0.35     -0.59     -0.12   1105.88      1.00\n",
      "    mu[45]     -0.18      0.11     -0.18     -0.34      0.01    937.86      1.00\n",
      "    mu[46]      0.05      0.10      0.05     -0.12      0.21    891.13      1.00\n",
      "    mu[47]      0.48      0.13      0.48      0.27      0.70    875.38      1.00\n",
      "    mu[48]     -0.08      0.14     -0.08     -0.32      0.13   1065.16      1.00\n",
      "    mu[49]      0.74      0.34      0.73      0.16      1.22    951.13      1.00\n",
      "     sigma      0.80      0.08      0.79      0.68      0.92    971.25      1.00\n",
      "\n"
     ]
    }
   ],
   "source": [
    "def model(M, A, D=None):\n",
    "    a = numpyro.sample(\"a\", dist.Normal(0, 0.2))\n",
    "    bM = numpyro.sample(\"bM\", dist.Normal(0, 0.5))\n",
    "    bA = numpyro.sample(\"bA\", dist.Normal(0, 0.5))\n",
    "    sigma = numpyro.sample(\"sigma\", dist.Exponential(1))\n",
    "    mu = numpyro.deterministic(\"mu\", a + bM * M + bA * A)\n",
    "    numpyro.sample(\"D\", dist.Normal(mu, sigma), obs=D)\n",
    "\n",
    "\n",
    "m5_3 = AutoLaplaceApproximation(model)\n",
    "svi = SVI(\n",
    "    model, m5_3, optim.Adam(1), Trace_ELBO(), M=d.M.values, A=d.A.values, D=d.D.values\n",
    ")\n",
    "svi_result = svi.run(random.PRNGKey(0), 1000)\n",
    "p5_3 = svi_result.params\n",
    "post = m5_3.sample_posterior(random.PRNGKey(1), p5_3, sample_shape=(1000,))\n",
    "print_summary(post, 0.89, False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x940 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "coeftab = {\n",
    "    \"m5.1\": m5_1.sample_posterior(random.PRNGKey(1), p5_1, sample_shape=(1, 1000)),\n",
    "    \"m5.2\": m5_2.sample_posterior(random.PRNGKey(2), p5_2, sample_shape=(1, 1000)),\n",
    "    \"m5.3\": m5_3.sample_posterior(random.PRNGKey(3), p5_3, sample_shape=(1, 1000)),\n",
    "}\n",
    "az.plot_forest(\n",
    "    list(coeftab.values()),\n",
    "    model_names=list(coeftab.keys()),\n",
    "    var_names=[\"bA\", \"bM\"],\n",
    "    hdi_prob=0.89,\n",
    ")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 50  # number of simulated States\n",
    "age = dist.Normal().sample(random.PRNGKey(0), sample_shape=(N,))  # sim A\n",
    "mar = dist.Normal(age).sample(random.PRNGKey(1))  # sim A -> M\n",
    "div = dist.Normal(age).sample(random.PRNGKey(2))  # sim A -> D"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.13"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000/1000 [00:00<00:00, 1218.61it/s, init loss: 2288.6685, avg. loss [951-1000]: 52.6188]\n"
     ]
    }
   ],
   "source": [
    "def model(A, M=None):\n",
    "    a = numpyro.sample(\"a\", dist.Normal(0, 0.2))\n",
    "    bAM = numpyro.sample(\"bA\", dist.Normal(0, 0.5))\n",
    "    sigma = numpyro.sample(\"sigma\", dist.Exponential(1))\n",
    "    mu = numpyro.deterministic(\"mu\", a + bAM * A)\n",
    "    numpyro.sample(\"M\", dist.Normal(mu, sigma), obs=M)\n",
    "\n",
    "\n",
    "m5_4 = AutoLaplaceApproximation(model)\n",
    "svi = SVI(model, m5_4, optim.Adam(0.1), Trace_ELBO(), A=d.A.values, M=d.M.values)\n",
    "svi_result = svi.run(random.PRNGKey(0), 1000)\n",
    "p5_4 = svi_result.params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.14"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "post = m5_4.sample_posterior(random.PRNGKey(1), p5_4, sample_shape=(1000,))\n",
    "post.pop(\"mu\")\n",
    "post_pred = Predictive(m5_4.model, post)(random.PRNGKey(2), A=d.A.values)\n",
    "mu = post_pred[\"mu\"]\n",
    "mu_mean = jnp.mean(mu, 0)\n",
    "mu_resid = d.M.values - mu_mean"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# call predictive without specifying new data\n",
    "# so it uses original data\n",
    "post = m5_3.sample_posterior(random.PRNGKey(1), p5_3, sample_shape=(int(1e4),))\n",
    "post.pop(\"mu\")\n",
    "post_pred = Predictive(m5_3.model, post)(random.PRNGKey(2), M=d.M.values, A=d.A.values)\n",
    "mu = post_pred[\"mu\"]\n",
    "\n",
    "# summarize samples across cases\n",
    "mu_mean = jnp.mean(mu, 0)\n",
    "mu_PI = jnp.percentile(mu, q=jnp.array([5.5, 94.5]), axis=0)\n",
    "\n",
    "# simulate observations\n",
    "# again no new data, so uses original data\n",
    "D_sim = post_pred[\"D\"]\n",
    "D_PI = jnp.percentile(D_sim, q=jnp.array([5.5, 94.5]), axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.16"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = plt.subplot(\n",
    "    ylim=(float(mu_PI.min()), float(mu_PI.max())),\n",
    "    xlabel=\"Observed divorce\",\n",
    "    ylabel=\"Predicted divorce\",\n",
    ")\n",
    "plt.plot(d.D, mu_mean, \"o\")\n",
    "x = jnp.linspace(mu_PI.min(), mu_PI.max(), 101)\n",
    "plt.plot(x, x, \"--\")\n",
    "for i in range(d.shape[0]):\n",
    "    plt.plot([d.D[i]] * 2, mu_PI[:, i], \"b\")\n",
    "fig = plt.gcf()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.17"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x480 with 1 Axes>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "for i in range(d.shape[0]):\n",
    "    if d.Loc[i] in [\"ID\", \"UT\", \"RI\", \"ME\"]:\n",
    "        ax.annotate(\n",
    "            d.Loc[i], (d.D[i], mu_mean[i]), xytext=(-25, -5), textcoords=\"offset pixels\"\n",
    "        )\n",
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.18"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 100  # number of cases\n",
    "# x_real as Gaussian with mean 0 and stddev 1\n",
    "x_real = dist.Normal().sample(random.PRNGKey(0), (N,))\n",
    "# x_spur as Gaussian with mean=x_real\n",
    "x_spur = dist.Normal(x_real).sample(random.PRNGKey(1))\n",
    "# y as Gaussian with mean=x_real\n",
    "y = dist.Normal(x_real).sample(random.PRNGKey(2))\n",
    "# bind all together in data frame\n",
    "d = pd.DataFrame({\"y\": y, \"x_real\": x_real, \"x_spur\": x_spur})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.19"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000/1000 [00:01<00:00, 734.26it/s, init loss: 10480.9580, avg. loss [951-1000]: 112.1909]\n"
     ]
    }
   ],
   "source": [
    "WaffleDivorce = pd.read_csv(\"../data/WaffleDivorce.csv\", sep=\";\")\n",
    "d = WaffleDivorce\n",
    "d[\"A\"] = d.MedianAgeMarriage.pipe(lambda x: (x - x.mean()) / x.std())\n",
    "d[\"D\"] = d.Divorce.pipe(lambda x: (x - x.mean()) / x.std())\n",
    "d[\"M\"] = d.Marriage.pipe(lambda x: (x - x.mean()) / x.std())\n",
    "\n",
    "\n",
    "def model(A, M=None, D=None):\n",
    "    # A -> M\n",
    "    aM = numpyro.sample(\"aM\", dist.Normal(0, 0.2))\n",
    "    bAM = numpyro.sample(\"bAM\", dist.Normal(0, 0.5))\n",
    "    sigma_M = numpyro.sample(\"sigma_M\", dist.Exponential(1))\n",
    "    mu_M = aM + bAM * A\n",
    "    M = numpyro.sample(\"M\", dist.Normal(mu_M, sigma_M), obs=M)\n",
    "    # A -> D <- M\n",
    "    a = numpyro.sample(\"a\", dist.Normal(0, 0.2))\n",
    "    bM = numpyro.sample(\"bM\", dist.Normal(0, 0.5))\n",
    "    bA = numpyro.sample(\"bA\", dist.Normal(0, 0.5))\n",
    "    sigma = numpyro.sample(\"sigma\", dist.Exponential(1))\n",
    "    mu = a + bM * M + bA * A\n",
    "    numpyro.sample(\"D\", dist.Normal(mu, sigma), obs=D)\n",
    "\n",
    "\n",
    "m5_3_A = AutoLaplaceApproximation(model)\n",
    "svi = SVI(\n",
    "    model,\n",
    "    m5_3_A,\n",
    "    optim.Adam(0.1),\n",
    "    Trace_ELBO(),\n",
    "    A=d.A.values,\n",
    "    M=d.M.values,\n",
    "    D=d.D.values,\n",
    ")\n",
    "svi_result = svi.run(random.PRNGKey(0), 1000)\n",
    "p5_3_A = svi_result.params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "A_seq = jnp.linspace(-2, 2, num=30)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.21"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# prep data\n",
    "sim_dat = dict(A=A_seq)\n",
    "\n",
    "# simulate M and then D, using A_seq\n",
    "post = m5_3_A.sample_posterior(random.PRNGKey(1), p5_3_A, sample_shape=(1000,))\n",
    "s = Predictive(m5_3_A.model, post)(random.PRNGKey(2), **sim_dat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.22"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sim_dat[\"A\"], jnp.mean(s[\"D\"], 0))\n",
    "plt.gca().set(ylim=(-2, 2), xlabel=\"manipulated A\", ylabel=\"counterfactual D\")\n",
    "plt.fill_between(\n",
    "    sim_dat[\"A\"],\n",
    "    *jnp.percentile(s[\"D\"], q=jnp.array([5.5, 94.5]), axis=0),\n",
    "    color=\"k\",\n",
    "    alpha=0.2\n",
    ")\n",
    "plt.title(\"Total counterfactual effect of A on D\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.23"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DeviceArray(-4.6818223, dtype=float32)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# new data frame, standardized to mean 26.1 and stddev 1.24\n",
    "sim2_dat = dict(A=(jnp.array([20, 30]) - 26.1) / 1.24)\n",
    "s2 = Predictive(m5_3_A.model, post, return_sites=[\"M\", \"D\"])(\n",
    "    random.PRNGKey(2), **sim2_dat\n",
    ")\n",
    "jnp.mean(s2[\"D\"][:, 1] - s2[\"D\"][:, 0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.24"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sim_dat = dict(M=jnp.linspace(-2, 2, num=30), A=0)\n",
    "s = Predictive(m5_3_A.model, post)(random.PRNGKey(2), **sim_dat)[\"D\"]\n",
    "\n",
    "plt.plot(sim_dat[\"M\"], jnp.mean(s, 0))\n",
    "plt.gca().set(ylim=(-2, 2), xlabel=\"manipulated A\", ylabel=\"counterfactual D\")\n",
    "plt.fill_between(\n",
    "    sim_dat[\"M\"],\n",
    "    *jnp.percentile(s, q=jnp.array([5.5, 94.5]), axis=0),\n",
    "    color=\"k\",\n",
    "    alpha=0.2\n",
    ")\n",
    "plt.title(\"Total counterfactual effect of M on D\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.25"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "A_seq = jnp.linspace(-2, 2, num=30)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.26"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "post = m5_3_A.sample_posterior(random.PRNGKey(1), p5_3_A, sample_shape=(1000,))\n",
    "post = {k: v[..., None] for k, v in post.items()}\n",
    "M_sim = dist.Normal(post[\"aM\"] + post[\"bAM\"] * A_seq).sample(random.PRNGKey(1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.27"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "D_sim = dist.Normal(post[\"a\"] + post[\"bA\"] * A_seq + post[\"bM\"] * M_sim).sample(\n",
    "    random.PRNGKey(1)\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.28"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 29 entries, 0 to 28\n",
      "Data columns (total 8 columns):\n",
      " #   Column          Non-Null Count  Dtype  \n",
      "---  ------          --------------  -----  \n",
      " 0   clade           29 non-null     object \n",
      " 1   species         29 non-null     object \n",
      " 2   kcal.per.g      29 non-null     float64\n",
      " 3   perc.fat        29 non-null     float64\n",
      " 4   perc.protein    29 non-null     float64\n",
      " 5   perc.lactose    29 non-null     float64\n",
      " 6   mass            29 non-null     float64\n",
      " 7   neocortex.perc  17 non-null     float64\n",
      "dtypes: float64(6), object(2)\n",
      "memory usage: 1.9+ KB\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>clade</th>\n",
       "      <th>species</th>\n",
       "      <th>kcal.per.g</th>\n",
       "      <th>perc.fat</th>\n",
       "      <th>perc.protein</th>\n",
       "      <th>perc.lactose</th>\n",
       "      <th>mass</th>\n",
       "      <th>neocortex.perc</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Strepsirrhine</td>\n",
       "      <td>Eulemur fulvus</td>\n",
       "      <td>0.49</td>\n",
       "      <td>16.60</td>\n",
       "      <td>15.42</td>\n",
       "      <td>67.98</td>\n",
       "      <td>1.95</td>\n",
       "      <td>55.16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Strepsirrhine</td>\n",
       "      <td>E macaco</td>\n",
       "      <td>0.51</td>\n",
       "      <td>19.27</td>\n",
       "      <td>16.91</td>\n",
       "      <td>63.82</td>\n",
       "      <td>2.09</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Strepsirrhine</td>\n",
       "      <td>E mongoz</td>\n",
       "      <td>0.46</td>\n",
       "      <td>14.11</td>\n",
       "      <td>16.85</td>\n",
       "      <td>69.04</td>\n",
       "      <td>2.51</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Strepsirrhine</td>\n",
       "      <td>E rubriventer</td>\n",
       "      <td>0.48</td>\n",
       "      <td>14.91</td>\n",
       "      <td>13.18</td>\n",
       "      <td>71.91</td>\n",
       "      <td>1.62</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Strepsirrhine</td>\n",
       "      <td>Lemur catta</td>\n",
       "      <td>0.60</td>\n",
       "      <td>27.28</td>\n",
       "      <td>19.50</td>\n",
       "      <td>53.22</td>\n",
       "      <td>2.19</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           clade         species  kcal.per.g  perc.fat  perc.protein  \\\n",
       "0  Strepsirrhine  Eulemur fulvus        0.49     16.60         15.42   \n",
       "1  Strepsirrhine        E macaco        0.51     19.27         16.91   \n",
       "2  Strepsirrhine        E mongoz        0.46     14.11         16.85   \n",
       "3  Strepsirrhine   E rubriventer        0.48     14.91         13.18   \n",
       "4  Strepsirrhine     Lemur catta        0.60     27.28         19.50   \n",
       "\n",
       "   perc.lactose  mass  neocortex.perc  \n",
       "0         67.98  1.95           55.16  \n",
       "1         63.82  2.09             NaN  \n",
       "2         69.04  2.51             NaN  \n",
       "3         71.91  1.62             NaN  \n",
       "4         53.22  2.19             NaN  "
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "milk = pd.read_csv(\"../data/milk.csv\", sep=\";\")\n",
    "d = milk\n",
    "d.info()\n",
    "d.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.29"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "d[\"K\"] = d[\"kcal.per.g\"].pipe(lambda x: (x - x.mean()) / x.std())\n",
    "d[\"N\"] = d[\"neocortex.perc\"].pipe(lambda x: (x - x.mean()) / x.std())\n",
    "d[\"M\"] = d.mass.map(math.log).pipe(lambda x: (x - x.mean()) / x.std())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.30"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Normal distribution got invalid loc parameter.\n"
     ]
    }
   ],
   "source": [
    "def model(N, K):\n",
    "    a = numpyro.sample(\"a\", dist.Normal(0, 1))\n",
    "    bN = numpyro.sample(\"bN\", dist.Normal(0, 1))\n",
    "    sigma = numpyro.sample(\"sigma\", dist.Exponential(1))\n",
    "    mu = a + bN * N\n",
    "    numpyro.sample(\"K\", dist.Normal(mu, sigma), obs=K)\n",
    "\n",
    "\n",
    "with numpyro.validation_enabled():\n",
    "    try:\n",
    "        m5_5_draft = AutoLaplaceApproximation(model)\n",
    "        svi = SVI(\n",
    "            model, m5_5_draft, optim.Adam(1), Trace_ELBO(), N=d.N.values, K=d.K.values\n",
    "        )\n",
    "        svi_result = svi.run(random.PRNGKey(0), 1000)\n",
    "        p5_5_draft = svi_result.params\n",
    "    except ValueError as e:\n",
    "        print(str(e))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.31"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0     55.16\n",
       "1       NaN\n",
       "2       NaN\n",
       "3       NaN\n",
       "4       NaN\n",
       "5     64.54\n",
       "6     64.54\n",
       "7     67.64\n",
       "8       NaN\n",
       "9     68.85\n",
       "10    58.85\n",
       "11    61.69\n",
       "12    60.32\n",
       "13      NaN\n",
       "14      NaN\n",
       "15    69.97\n",
       "16      NaN\n",
       "17    70.41\n",
       "18      NaN\n",
       "19    73.40\n",
       "20      NaN\n",
       "21    67.53\n",
       "22      NaN\n",
       "23    71.26\n",
       "24    72.60\n",
       "25      NaN\n",
       "26    70.24\n",
       "27    76.30\n",
       "28    75.49\n",
       "Name: neocortex.perc, dtype: float64"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d[\"neocortex.perc\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.32"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "dcc = d.iloc[d[[\"K\", \"N\", \"M\"]].dropna(how=\"any\", axis=0).index]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.33"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000/1000 [00:00<00:00, 1444.83it/s, init loss: 411.1621, avg. loss [951-1000]: 26.8758]\n"
     ]
    }
   ],
   "source": [
    "def model(N, K=None):\n",
    "    a = numpyro.sample(\"a\", dist.Normal(0, 1))\n",
    "    bN = numpyro.sample(\"bN\", dist.Normal(0, 1))\n",
    "    sigma = numpyro.sample(\"sigma\", dist.Exponential(1))\n",
    "    mu = numpyro.deterministic(\"mu\", a + bN * N)\n",
    "    numpyro.sample(\"K\", dist.Normal(mu, sigma), obs=K)\n",
    "\n",
    "\n",
    "m5_5_draft = AutoLaplaceApproximation(model)\n",
    "svi = SVI(\n",
    "    model, m5_5_draft, optim.Adam(0.1), Trace_ELBO(), N=dcc.N.values, K=dcc.K.values\n",
    ")\n",
    "svi_result = svi.run(random.PRNGKey(0), 1000)\n",
    "p5_5_draft = svi_result.params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.34"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xseq = jnp.array([-2, 2])\n",
    "prior_pred = Predictive(model, num_samples=1000)(random.PRNGKey(1), N=xseq)\n",
    "mu = prior_pred[\"mu\"]\n",
    "plt.subplot(xlim=xseq, ylim=xseq)\n",
    "for i in range(50):\n",
    "    plt.plot(xseq, mu[i], \"k\", alpha=0.3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.35"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000/1000 [00:00<00:00, 1399.46it/s, init loss: 414.1050, avg. loss [951-1000]: 24.6918]\n"
     ]
    }
   ],
   "source": [
    "def model(N, K=None):\n",
    "    a = numpyro.sample(\"a\", dist.Normal(0, 0.2))\n",
    "    bN = numpyro.sample(\"bN\", dist.Normal(0, 0.5))\n",
    "    sigma = numpyro.sample(\"sigma\", dist.Exponential(1))\n",
    "    mu = numpyro.deterministic(\"mu\", a + bN * N)\n",
    "    numpyro.sample(\"K\", dist.Normal(mu, sigma), obs=K)\n",
    "\n",
    "\n",
    "m5_5 = AutoLaplaceApproximation(model)\n",
    "svi = SVI(model, m5_5, optim.Adam(1), Trace_ELBO(), N=dcc.N.values, K=dcc.K.values)\n",
    "svi_result = svi.run(random.PRNGKey(0), 1000)\n",
    "p5_5 = svi_result.params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.36"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                mean       std    median      5.5%     94.5%     n_eff     r_hat\n",
      "         a      0.05      0.16      0.05     -0.21      0.29    931.50      1.00\n",
      "        bN      0.13      0.23      0.13     -0.21      0.53   1111.88      1.00\n",
      "     mu[0]     -0.22      0.51     -0.22     -0.99      0.60    911.65      1.00\n",
      "     mu[1]     -0.02      0.20     -0.01     -0.36      0.27    906.66      1.00\n",
      "     mu[2]     -0.02      0.20     -0.01     -0.36      0.27    906.66      1.00\n",
      "     mu[3]      0.05      0.16      0.05     -0.21      0.29    931.28      1.00\n",
      "     mu[4]      0.08      0.17      0.08     -0.18      0.36    940.50      1.00\n",
      "     mu[5]     -0.14      0.38     -0.13     -0.74      0.45    889.84      1.00\n",
      "     mu[6]     -0.08      0.28     -0.07     -0.52      0.36    874.50      1.00\n",
      "     mu[7]     -0.11      0.33     -0.10     -0.65      0.37    884.63      1.00\n",
      "     mu[8]      0.10      0.18      0.10     -0.18      0.41    964.72      1.00\n",
      "     mu[9]      0.11      0.19      0.11     -0.17      0.43    975.68      1.00\n",
      "    mu[10]      0.17      0.28      0.17     -0.25      0.63   1037.05      1.00\n",
      "    mu[11]      0.05      0.16      0.05     -0.21      0.29    931.71      1.00\n",
      "    mu[12]      0.13      0.21      0.13     -0.18      0.49    996.35      1.00\n",
      "    mu[13]      0.16      0.25      0.15     -0.21      0.58   1024.00      1.00\n",
      "    mu[14]      0.11      0.19      0.10     -0.17      0.43    971.43      1.00\n",
      "    mu[15]      0.24      0.37      0.23     -0.39      0.80   1067.60      1.00\n",
      "    mu[16]      0.22      0.35      0.21     -0.37      0.74   1061.13      1.00\n",
      "     sigma      1.05      0.18      1.03      0.78      1.35    944.03      1.00\n",
      "\n"
     ]
    }
   ],
   "source": [
    "post = m5_5.sample_posterior(random.PRNGKey(1), p5_5, sample_shape=(1000,))\n",
    "print_summary(post, 0.89, False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.37"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xseq = jnp.linspace(start=dcc.N.min() - 0.15, stop=dcc.N.max() + 0.15, num=30)\n",
    "post = m5_5.sample_posterior(random.PRNGKey(1), p5_5, sample_shape=(1000,))\n",
    "post.pop(\"mu\")\n",
    "post_pred = Predictive(m5_5.model, post)(random.PRNGKey(2), N=xseq)\n",
    "mu = post_pred[\"mu\"]\n",
    "mu_mean = jnp.mean(mu, 0)\n",
    "mu_PI = jnp.percentile(mu, q=jnp.array([5.5, 94.5]), axis=0)\n",
    "az.plot_pair(dcc[[\"N\", \"K\"]].to_dict(orient=\"list\"))\n",
    "plt.plot(xseq, mu_mean, \"k\")\n",
    "plt.fill_between(xseq, mu_PI[0], mu_PI[1], color=\"k\", alpha=0.2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.38"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000/1000 [00:00<00:00, 1457.13it/s, init loss: 756.0300, avg. loss [951-1000]: 23.9327]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                mean       std    median      5.5%     94.5%     n_eff     r_hat\n",
      "         a      0.06      0.16      0.06     -0.20      0.29    931.50      1.00\n",
      "        bM     -0.28      0.20     -0.28     -0.61      0.03   1088.44      1.00\n",
      "     mu[0]      0.18      0.18      0.19     -0.11      0.47    944.38      1.00\n",
      "     mu[1]      0.02      0.16      0.02     -0.24      0.26    932.90      1.00\n",
      "     mu[2]      0.02      0.16      0.02     -0.24      0.26    933.51      1.00\n",
      "     mu[3]      0.14      0.17      0.15     -0.11      0.42    958.01      1.00\n",
      "     mu[4]      0.36      0.27      0.36     -0.07      0.78    872.95      1.00\n",
      "     mu[5]      0.65      0.45      0.65     -0.03      1.39    898.89      1.00\n",
      "     mu[6]      0.42      0.31      0.43     -0.07      0.89    878.58      1.00\n",
      "     mu[7]      0.49      0.35      0.50     -0.09      1.00    885.51      1.00\n",
      "     mu[8]      0.22      0.20      0.23     -0.12      0.51    906.05      1.00\n",
      "     mu[9]      0.10      0.16      0.10     -0.17      0.33    940.69      1.00\n",
      "    mu[10]     -0.12      0.20     -0.13     -0.40      0.21    989.01      1.00\n",
      "    mu[11]      0.02      0.16      0.02     -0.24      0.26    933.51      1.00\n",
      "    mu[12]     -0.30      0.29     -0.30     -0.75      0.18   1050.56      1.00\n",
      "    mu[13]     -0.43      0.38     -0.44     -1.07      0.12   1073.41      1.00\n",
      "    mu[14]     -0.32      0.31     -0.33     -0.81      0.16   1055.58      1.00\n",
      "    mu[15]     -0.29      0.28     -0.29     -0.74      0.16   1047.84      1.00\n",
      "    mu[16]     -0.37      0.34     -0.38     -0.95      0.12   1064.72      1.00\n",
      "     sigma      0.99      0.17      0.98      0.72      1.26    957.10      1.00\n",
      "\n"
     ]
    }
   ],
   "source": [
    "def model(M, K=None):\n",
    "    a = numpyro.sample(\"a\", dist.Normal(0, 0.2))\n",
    "    bM = numpyro.sample(\"bM\", dist.Normal(0, 0.5))\n",
    "    sigma = numpyro.sample(\"sigma\", dist.Exponential(1))\n",
    "    mu = numpyro.deterministic(\"mu\", a + bM * M)\n",
    "    numpyro.sample(\"K\", dist.Normal(mu, sigma), obs=K)\n",
    "\n",
    "\n",
    "m5_6 = AutoLaplaceApproximation(model)\n",
    "svi = SVI(model, m5_6, optim.Adam(1), Trace_ELBO(), M=dcc.M.values, K=dcc.K.values)\n",
    "svi_result = svi.run(random.PRNGKey(0), 1000)\n",
    "p5_6 = svi_result.params\n",
    "post = m5_6.sample_posterior(random.PRNGKey(1), p5_6, sample_shape=(1000,))\n",
    "print_summary(post, 0.89, False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.39"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000/1000 [00:00<00:00, 1324.26it/s, init loss: 136.3944, avg. loss [951-1000]: 21.6292]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                mean       std    median      5.5%     94.5%     n_eff     r_hat\n",
      "         a      0.06      0.13      0.06     -0.15      0.26   1049.96      1.00\n",
      "        bM     -0.68      0.23     -0.68     -1.06     -0.32    837.54      1.00\n",
      "        bN      0.65      0.25      0.66      0.25      1.06    885.39      1.00\n",
      "     mu[0]     -0.99      0.47     -1.00     -1.72     -0.22    953.05      1.00\n",
      "     mu[1]     -0.36      0.20     -0.35     -0.64     -0.03   1076.34      1.00\n",
      "     mu[2]     -0.37      0.20     -0.36     -0.65     -0.03   1068.21      1.00\n",
      "     mu[3]      0.28      0.16      0.28      0.03      0.52    967.73      1.00\n",
      "     mu[4]      0.94      0.33      0.94      0.43      1.44    876.35      1.00\n",
      "     mu[5]      0.53      0.39      0.53     -0.10      1.11   1015.67      1.00\n",
      "     mu[6]      0.30      0.26      0.30     -0.10      0.73   1041.23      1.00\n",
      "     mu[7]      0.30      0.30      0.30     -0.16      0.76   1039.12      1.00\n",
      "     mu[8]      0.73      0.27      0.73      0.35      1.17    867.10      1.00\n",
      "     mu[9]      0.48      0.21      0.49      0.16      0.80    872.50      1.00\n",
      "    mu[10]      0.27      0.23      0.28     -0.06      0.66    895.61      1.00\n",
      "    mu[11]     -0.04      0.14     -0.04     -0.25      0.17    992.18      1.00\n",
      "    mu[12]     -0.39      0.25     -0.39     -0.81     -0.00    864.74      1.00\n",
      "    mu[13]     -0.56      0.32     -0.57     -1.03      0.01    871.33      1.00\n",
      "    mu[14]     -0.55      0.27     -0.55     -0.98     -0.10    858.97      1.00\n",
      "    mu[15]      0.20      0.30      0.20     -0.29      0.66    916.65      1.00\n",
      "    mu[16]     -0.10      0.30     -0.10     -0.59      0.37    895.92      1.00\n",
      "     sigma      0.77      0.14      0.77      0.55      0.97   1029.58      1.00\n",
      "\n"
     ]
    }
   ],
   "source": [
    "def model(N, M, K=None):\n",
    "    a = numpyro.sample(\"a\", dist.Normal(0, 0.2))\n",
    "    bN = numpyro.sample(\"bN\", dist.Normal(0, 0.5))\n",
    "    bM = numpyro.sample(\"bM\", dist.Normal(0, 0.5))\n",
    "    sigma = numpyro.sample(\"sigma\", dist.Exponential(1))\n",
    "    mu = numpyro.deterministic(\"mu\", a + bN * N + bM * M)\n",
    "    numpyro.sample(\"K\", dist.Normal(mu, sigma), obs=K)\n",
    "\n",
    "\n",
    "m5_7 = AutoLaplaceApproximation(model)\n",
    "svi = SVI(\n",
    "    model,\n",
    "    m5_7,\n",
    "    optim.Adam(1),\n",
    "    Trace_ELBO(),\n",
    "    N=dcc.N.values,\n",
    "    M=dcc.M.values,\n",
    "    K=dcc.K.values,\n",
    ")\n",
    "svi_result = svi.run(random.PRNGKey(0), 1000)\n",
    "p5_7 = svi_result.params\n",
    "post = m5_7.sample_posterior(random.PRNGKey(1), p5_7, sample_shape=(1000,))\n",
    "print_summary(post, 0.89, False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.40"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x940 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "coeftab = {\n",
    "    \"m5.5\": m5_5.sample_posterior(random.PRNGKey(1), p5_5, sample_shape=(1, 1000)),\n",
    "    \"m5.6\": m5_6.sample_posterior(random.PRNGKey(2), p5_6, sample_shape=(1, 1000)),\n",
    "    \"m5.7\": m5_7.sample_posterior(random.PRNGKey(3), p5_7, sample_shape=(1, 1000)),\n",
    "}\n",
    "az.plot_forest(\n",
    "    list(coeftab.values()),\n",
    "    model_names=list(coeftab.keys()),\n",
    "    var_names=[\"bM\", \"bN\"],\n",
    "    hdi_prob=0.89,\n",
    ")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.41"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xseq = jnp.linspace(start=dcc.N.min() - 0.15, stop=dcc.N.max() + 0.15, num=30)\n",
    "post = m5_7.sample_posterior(random.PRNGKey(1), p5_7, sample_shape=(1000,))\n",
    "post.pop(\"mu\")\n",
    "post_pred = Predictive(m5_7.model, post)(random.PRNGKey(2), M=0, N=xseq)\n",
    "mu = post_pred[\"mu\"]\n",
    "mu_mean = jnp.mean(mu, 0)\n",
    "mu_PI = jnp.percentile(mu, q=jnp.array([5.5, 94.5]), axis=0)\n",
    "plt.subplot(xlim=(dcc.M.min(), dcc.M.max()), ylim=(dcc.K.min(), dcc.K.max()))\n",
    "plt.plot(xseq, mu_mean, \"k\")\n",
    "plt.fill_between(xseq, mu_PI[0], mu_PI[1], color=\"k\", alpha=0.2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.42"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "# M -> K <- N\n",
    "# M -> N\n",
    "n = 100\n",
    "M = dist.Normal().sample(random.PRNGKey(0), (n,))\n",
    "N = dist.Normal(M).sample(random.PRNGKey(1))\n",
    "K = dist.Normal(N - M).sample(random.PRNGKey(2))\n",
    "d_sim = pd.DataFrame({\"K\": K, \"N\": N, \"M\": M})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.43"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "# M -> K <- N\n",
    "# N -> M\n",
    "n = 100\n",
    "N = dist.Normal().sample(random.PRNGKey(0), (n,))\n",
    "M = dist.Normal(N).sample(random.PRNGKey(1))\n",
    "K = dist.Normal(N - M).sample(random.PRNGKey(2))\n",
    "d_sim2 = pd.DataFrame({\"K\": K, \"N\": N, \"M\": M})\n",
    "\n",
    "# M -> K <- N\n",
    "# M <- U -> N\n",
    "n = 100\n",
    "N = dist.Normal().sample(random.PRNGKey(3), (n,))\n",
    "M = dist.Normal(M).sample(random.PRNGKey(4))\n",
    "K = dist.Normal(N - M).sample(random.PRNGKey(5))\n",
    "d_sim3 = pd.DataFrame({\"K\": K, \"N\": N, \"M\": M})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.44"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "dag5_7 = nx.DiGraph()\n",
    "dag5_7.add_edges_from([(\"M\", \"K\"), (\"N\", \"K\"), (\"M\", \"N\")])\n",
    "coordinates = {\"M\": (0, 0.5), \"K\": (1, 1), \"N\": (2, 0.5)}\n",
    "MElist = []\n",
    "for i in range(2):\n",
    "    for j in range(2):\n",
    "        for k in range(2):\n",
    "            new_dag = nx.DiGraph()\n",
    "            new_dag.add_edges_from(\n",
    "                [edge[::-1] if flip else edge for edge, flip in zip(dag5_7.edges, (i, j, k))]\n",
    "            )\n",
    "            if not list(nx.simple_cycles(new_dag)):\n",
    "                MElist.append(new_dag)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.45"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 544 entries, 0 to 543\n",
      "Data columns (total 4 columns):\n",
      " #   Column  Non-Null Count  Dtype  \n",
      "---  ------  --------------  -----  \n",
      " 0   height  544 non-null    float64\n",
      " 1   weight  544 non-null    float64\n",
      " 2   age     544 non-null    float64\n",
      " 3   male    544 non-null    int64  \n",
      "dtypes: float64(3), int64(1)\n",
      "memory usage: 17.1 KB\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>height</th>\n",
       "      <th>weight</th>\n",
       "      <th>age</th>\n",
       "      <th>male</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>151.765</td>\n",
       "      <td>47.825606</td>\n",
       "      <td>63.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>139.700</td>\n",
       "      <td>36.485807</td>\n",
       "      <td>63.0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>136.525</td>\n",
       "      <td>31.864838</td>\n",
       "      <td>65.0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>156.845</td>\n",
       "      <td>53.041915</td>\n",
       "      <td>41.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>145.415</td>\n",
       "      <td>41.276872</td>\n",
       "      <td>51.0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    height     weight   age  male\n",
       "0  151.765  47.825606  63.0     1\n",
       "1  139.700  36.485807  63.0     0\n",
       "2  136.525  31.864838  65.0     0\n",
       "3  156.845  53.041915  41.0     1\n",
       "4  145.415  41.276872  51.0     0"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Howell1 = pd.read_csv(\"../data/Howell1.csv\", sep=\";\")\n",
    "d = Howell1\n",
    "d.info()\n",
    "d.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.46"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                 mean       std    median      5.5%     94.5%     n_eff     r_hat\n",
      "  mu_female    178.21     20.22    178.24    147.19    211.84   9943.61      1.00\n",
      "    mu_male    178.10     22.36    178.51    142.35    213.41  10190.57      1.00\n",
      "\n"
     ]
    }
   ],
   "source": [
    "mu_female = dist.Normal(178, 20).sample(random.PRNGKey(0), (int(1e4),))\n",
    "diff = dist.Normal(0, 10).sample(random.PRNGKey(1), (int(1e4),))\n",
    "mu_male = dist.Normal(178, 20).sample(random.PRNGKey(2), (int(1e4),)) + diff\n",
    "print_summary({\"mu_female\": mu_female, \"mu_male\": mu_male}, 0.89, False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.47"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0      1\n",
       "1      0\n",
       "2      0\n",
       "3      1\n",
       "4      0\n",
       "      ..\n",
       "539    1\n",
       "540    1\n",
       "541    0\n",
       "542    1\n",
       "543    1\n",
       "Name: sex, Length: 544, dtype: int32"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d[\"sex\"] = jnp.where(d.male.values == 1, 1, 0)\n",
    "d.sex"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.48"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 2000/2000 [00:01<00:00, 1815.39it/s, init loss: 5607.9023, avg. loss [1901-2000]: 2558.3149]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                mean       std    median      5.5%     94.5%     n_eff     r_hat\n",
      "      a[0]    135.02      1.63    135.07    132.32    137.46    931.50      1.00\n",
      "      a[1]    142.56      1.73    142.54    140.02    145.51   1111.51      1.00\n",
      "     sigma     27.32      0.84     27.32     26.03     28.71    951.62      1.00\n",
      "\n"
     ]
    }
   ],
   "source": [
    "def model(sex, height):\n",
    "    a = numpyro.sample(\"a\", dist.Normal(178, 20).expand([len(set(sex))]))\n",
    "    sigma = numpyro.sample(\"sigma\", dist.Uniform(0, 50))\n",
    "    mu = a[sex]\n",
    "    numpyro.sample(\"height\", dist.Normal(mu, sigma), obs=height)\n",
    "\n",
    "\n",
    "m5_8 = AutoLaplaceApproximation(model)\n",
    "svi = SVI(\n",
    "    model, m5_8, optim.Adam(1), Trace_ELBO(), sex=d.sex.values, height=d.height.values\n",
    ")\n",
    "svi_result = svi.run(random.PRNGKey(0), 2000)\n",
    "p5_8 = svi_result.params\n",
    "post = m5_8.sample_posterior(random.PRNGKey(1), p5_8, sample_shape=(1000,))\n",
    "print_summary(post, 0.89, False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.49"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                mean       std    median      5.5%     94.5%     n_eff     r_hat\n",
      "      a[0]    135.02      1.63    135.07    132.32    137.46    931.50      1.00\n",
      "      a[1]    142.56      1.73    142.54    140.02    145.51   1111.51      1.00\n",
      "   diff_fm     -7.54      2.38     -7.47    -11.77     -4.32    876.56      1.00\n",
      "     sigma     27.32      0.84     27.32     26.03     28.71    951.62      1.00\n",
      "\n"
     ]
    }
   ],
   "source": [
    "post = m5_8.sample_posterior(random.PRNGKey(1), p5_8, sample_shape=(1000,))\n",
    "post[\"diff_fm\"] = post[\"a\"][:, 0] - post[\"a\"][:, 1]\n",
    "print_summary(post, 0.89, False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.50"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['Strepsirrhine', 'New World Monkey', 'Old World Monkey', 'Ape'],\n",
       "      dtype=object)"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "milk = pd.read_csv(\"../data/milk.csv\", sep=\";\")\n",
    "d = milk\n",
    "d.clade.unique()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.51"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "d[\"clade_id\"] = d.clade.astype(\"category\").cat.codes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.52"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000/1000 [00:00<00:00, 1407.72it/s, init loss: 94.6847, avg. loss [951-1000]: 35.5646]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x440 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d[\"K\"] = d[\"kcal.per.g\"].pipe(lambda x: (x - x.mean()) / x.std())\n",
    "\n",
    "\n",
    "def model(clade_id, K):\n",
    "    a = numpyro.sample(\"a\", dist.Normal(0, 0.5).expand([len(set(clade_id))]))\n",
    "    sigma = numpyro.sample(\"sigma\", dist.Exponential(1))\n",
    "    mu = a[clade_id]\n",
    "    numpyro.sample(\"height\", dist.Normal(mu, sigma), obs=K)\n",
    "\n",
    "\n",
    "m5_9 = AutoLaplaceApproximation(model)\n",
    "svi = SVI(\n",
    "    model, m5_9, optim.Adam(1), Trace_ELBO(), clade_id=d.clade_id.values, K=d.K.values\n",
    ")\n",
    "svi_result = svi.run(random.PRNGKey(0), 1000)\n",
    "p5_9 = svi_result.params\n",
    "post = m5_9.sample_posterior(random.PRNGKey(1), p5_9, sample_shape=(1000,))\n",
    "labels = [\"a[\" + str(i) + \"]:\" + s for i, s in enumerate(sorted(d.clade.unique()))]\n",
    "az.plot_forest({\"a\": post[\"a\"][None, ...]}, hdi_prob=0.89)\n",
    "plt.gca().set(yticklabels=labels[::-1], xlabel=\"expected kcal (std)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.53"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "key = random.PRNGKey(63)\n",
    "d[\"house\"] = random.choice(key, jnp.repeat(jnp.arange(4), 8), d.shape[:1], False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 5.54"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000/1000 [00:00<00:00, 1231.03it/s, init loss: 491.4240, avg. loss [951-1000]: 35.8243]\n"
     ]
    }
   ],
   "source": [
    "def model(clade_id, house, K):\n",
    "    a = numpyro.sample(\"a\", dist.Normal(0, 0.5).expand([len(set(clade_id))]))\n",
    "    h = numpyro.sample(\"h\", dist.Normal(0, 0.5).expand([len(set(house))]))\n",
    "    sigma = numpyro.sample(\"sigma\", dist.Exponential(1))\n",
    "    mu = a[clade_id] + h[house]\n",
    "    numpyro.sample(\"height\", dist.Normal(mu, sigma), obs=K)\n",
    "\n",
    "\n",
    "m5_10 = AutoLaplaceApproximation(model)\n",
    "svi = SVI(\n",
    "    model,\n",
    "    m5_10,\n",
    "    optim.Adam(1),\n",
    "    Trace_ELBO(),\n",
    "    clade_id=d.clade_id.values,\n",
    "    house=d.house.values,\n",
    "    K=d.K.values,\n",
    ")\n",
    "svi_result = svi.run(random.PRNGKey(0), 1000)\n",
    "p5_10 = svi_result.params"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}