{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "241ec99a-6825-4d61-b90b-5d255a9b1764",
   "metadata": {},
   "source": [
    "(marginalizing-models)=\n",
    "# Automatic marginalization of discrete variables\n",
    "\n",
    ":::{post} Jan 20, 2024\n",
    ":tags: mixture model\n",
    ":category: intermediate, how-to\n",
    ":author: Rob Zinkov\n",
    ":::\n",
    "\n",
    "PyMC is very amendable to sampling models with discrete latent variables. But if you insist on using the NUTS sampler exclusively, you will need to get rid of your discrete variables somehow. The best way to do this is by marginalizing them out, as then you benefit from Rao-Blackwell's theorem and get a lower variance estimate of your parameters.\n",
    "\n",
    "Formally the argument goes like this, samplers can be understood as approximating the expectation $\\mathbb{E}_{p(x, z)}[f(x, z)]$ for some function $f$ with respect to a distribution $p(x, z)$. By [law of total expectation](https://en.wikipedia.org/wiki/Law_of_total_expectation) we know that\n",
    "\n",
    "$$ \\mathbb{E}_{p(x, z)}[f(x, z)] =  \\mathbb{E}_{p(z)}\\left[\\mathbb{E}_{p(x \\mid z)}\\left[f(x, z)\\right]\\right] $$\n",
    "\n",
    "Letting $g(z) = \\mathbb{E}_{p(x \\mid z)}\\left[f(x, z)\\right]$, we know by [law of total variance](https://en.wikipedia.org/wiki/Law_of_total_variance) that\n",
    "\n",
    "$$ \\mathbb{V}_{p(x, z)}[f(x, z)] = \\mathbb{V}_{p(z)}[g(z)] + \\mathbb{E}_{p(z)}\\left[\\mathbb{V}_{p(x \\mid z)}\\left[f(x, z)\\right]\\right] $$\n",
    "\n",
    "Because the expectation is over a variance it must always be positive, and thus we know\n",
    "\n",
    "$$ \\mathbb{V}_{p(x, z)}[f(x, z)] \\geq \\mathbb{V}_{p(z)}[g(z)] $$\n",
    "\n",
    "Intuitively, marginalizing variables in your model lets you use $g$ instead of $f$. This lower variance manifests most directly in lower Monte-Carlo standard error (mcse), and indirectly in a generally higher effective sample size (ESS).\n",
    "\n",
    "Unfortunately, the computation to do this is often tedious and unintuitive. Luckily, `pymc-experimental` now supports a way to do this work automatically!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e40e8a9d-7516-4ad2-af1e-09fb85f77639",
   "metadata": {},
   "outputs": [],
   "source": [
    "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.tensor as pt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "495efc5b-a0c0-45f0-a723-3278495e1ace",
   "metadata": {},
   "source": [
    ":::{include} ../extra_installs.md\n",
    ":::"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8d802429-a250-4c22-9ecd-0dcb6778d876",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pymc_experimental as pmx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d686f41b-d55c-417d-8ef4-772c421a47cf",
   "metadata": {},
   "outputs": [],
   "source": [
    "%config InlineBackend.figure_format = 'retina'  # high resolution figures\n",
    "az.style.use(\"arviz-darkgrid\")\n",
    "rng = np.random.default_rng(32)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f646c49f-41af-4004-a2c4-63d6ead8e007",
   "metadata": {},
   "source": [
    "As a motivating example, consider a gaussian mixture model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "314c7fb7-3339-4e82-abe2-1d0aebf85242",
   "metadata": {},
   "source": [
    "## Gaussian Mixture model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0eecdf9b-4527-45fe-84d5-8a776086cb0c",
   "metadata": {},
   "source": [
    "There are two ways to specify the same model. One where the choice of mixture is explicit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "2e7b84e4-1323-4508-93e6-1f00fe21f90d",
   "metadata": {},
   "outputs": [],
   "source": [
    "mu = pt.as_tensor([-2.0, 2.0])\n",
    "\n",
    "with pmx.MarginalModel() as explicit_mixture:\n",
    "    idx = pm.Bernoulli(\"idx\", 0.7)\n",
    "    y = pm.Normal(\"y\", mu=mu[idx], sigma=1.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "63c63f01-8a34-4ef1-a316-384c721a3966",
   "metadata": {},
   "outputs": [
    {
     "data": {
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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.hist(pm.draw(y, draws=2000, random_seed=rng), bins=30, rwidth=0.9);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e1b1cab-56ce-4ddd-95d3-6454c8d0aae0",
   "metadata": {},
   "source": [
    "The other way is where we use the built-in {class}`NormalMixture <pymc.NormalMixture>` distribution. Here the mixture assignment is not an explicit variable in our model. There is nothing unique about the first model other than we initialize it with {class}`pmx.MarginalModel <pymc_experimental.MarginalModel>` instead of {class}`pm.Model <pymc.model.core.Model>`. This different class is what will allow us to marginalize out variables later."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "27852bef-f23b-4151-bc41-1af26f934e61",
   "metadata": {},
   "outputs": [],
   "source": [
    "with pm.Model() as prebuilt_mixture:\n",
    "    y = pm.NormalMixture(\"y\", w=[0.3, 0.7], mu=[-2, 2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "e318f820-9a2c-4b7d-bdfd-34cb1a9eecff",
   "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.hist(pm.draw(y, draws=2000, random_seed=rng), bins=30, rwidth=0.9);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "363b907c-8146-4694-a821-7a2ebacbcab6",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 2 jobs)\n",
      "NUTS: [y]\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='12000' class='' max='12000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
       "      100.00% [12000/12000 00:09&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 2_000 draw iterations (4_000 + 8_000 draws total) took 10 seconds.\n",
      "The rhat statistic is larger than 1.01 for some parameters. This indicates problems during sampling. See https://arxiv.org/abs/1903.08008 for details\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_3%</th>\n",
       "      <th>hdi_97%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>y</th>\n",
       "      <td>0.863</td>\n",
       "      <td>2.08</td>\n",
       "      <td>-3.138</td>\n",
       "      <td>3.832</td>\n",
       "      <td>0.095</td>\n",
       "      <td>0.067</td>\n",
       "      <td>555.0</td>\n",
       "      <td>1829.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    mean    sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  ess_bulk  ess_tail  r_hat\n",
       "y  0.863  2.08  -3.138    3.832      0.095    0.067     555.0    1829.0   1.01"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "with prebuilt_mixture:\n",
    "    idata = pm.sample(draws=2000, chains=4, random_seed=rng)\n",
    "\n",
    "az.summary(idata)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "e6d9a596-af22-4074-bc96-85a91cd35a64",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Multiprocess sampling (4 chains in 2 jobs)\n",
      "CompoundStep\n",
      ">BinaryGibbsMetropolis: [idx]\n",
      ">NUTS: [y]\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       "    /* Turns off some styling */\n",
       "    progress {\n",
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       "        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",
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       "    .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='12000' class='' max='12000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
       "      100.00% [12000/12000 00:09&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 2_000 draw iterations (4_000 + 8_000 draws total) took 10 seconds.\n",
      "The rhat statistic is larger than 1.01 for some parameters. This indicates problems during sampling. See https://arxiv.org/abs/1903.08008 for details\n",
      "The effective sample size per chain is smaller than 100 for some parameters.  A higher number is needed for reliable rhat and ess computation. See https://arxiv.org/abs/1903.08008 for details\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_3%</th>\n",
       "      <th>hdi_97%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>idx</th>\n",
       "      <td>0.718</td>\n",
       "      <td>0.450</td>\n",
       "      <td>0.000</td>\n",
       "      <td>1.000</td>\n",
       "      <td>0.028</td>\n",
       "      <td>0.020</td>\n",
       "      <td>252.0</td>\n",
       "      <td>252.0</td>\n",
       "      <td>1.02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y</th>\n",
       "      <td>0.875</td>\n",
       "      <td>2.068</td>\n",
       "      <td>-3.191</td>\n",
       "      <td>3.766</td>\n",
       "      <td>0.122</td>\n",
       "      <td>0.087</td>\n",
       "      <td>379.0</td>\n",
       "      <td>1397.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  ess_bulk  ess_tail  \\\n",
       "idx  0.718  0.450   0.000    1.000      0.028    0.020     252.0     252.0   \n",
       "y    0.875  2.068  -3.191    3.766      0.122    0.087     379.0    1397.0   \n",
       "\n",
       "     r_hat  \n",
       "idx   1.02  \n",
       "y     1.01  "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "with explicit_mixture:\n",
    "    idata = pm.sample(draws=2000, chains=4, random_seed=rng)\n",
    "\n",
    "az.summary(idata)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "043b1591-ff13-4dde-880a-aee4572a0b19",
   "metadata": {},
   "source": [
    "We can immediately see that the marginalized model has a higher ESS. Let's now marginalize out the choice and see what it changes in our model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "e9a84902-73af-4485-a40b-72200411a500",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 2 jobs)\n",
      "NUTS: [y]\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"
      ],
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       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "    <div>\n",
       "      <progress value='12000' class='' max='12000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
       "      100.00% [12000/12000 00:09&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 2_000 draw iterations (4_000 + 8_000 draws total) took 10 seconds.\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_3%</th>\n",
       "      <th>hdi_97%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>y</th>\n",
       "      <td>0.731</td>\n",
       "      <td>2.102</td>\n",
       "      <td>-3.202</td>\n",
       "      <td>3.811</td>\n",
       "      <td>0.099</td>\n",
       "      <td>0.07</td>\n",
       "      <td>567.0</td>\n",
       "      <td>2251.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  ess_bulk  ess_tail  \\\n",
       "y  0.731  2.102  -3.202    3.811      0.099     0.07     567.0    2251.0   \n",
       "\n",
       "   r_hat  \n",
       "y   1.01  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "explicit_mixture.marginalize([\"idx\"])\n",
    "with explicit_mixture:\n",
    "    idata = pm.sample(draws=2000, chains=4, random_seed=rng)\n",
    "\n",
    "az.summary(idata)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4034eb4d-83f9-4543-992f-0f68bf47fb68",
   "metadata": {},
   "source": [
    "As we can see, the `idx` variable is gone now. We also were able to use the NUTS sampler, and the ESS has improved.\n",
    "\n",
    "But {class}`MarginalModel <pymc_experimental.MarginalModel>` has a distinct advantage. It still knows about the discrete variables that were marginalized out, and we can obtain estimates for the posterior of `idx` given the other variables. We do this using the {meth}`recover_marginals <pymc_experimental.MarginalModel.recover_marginals>` method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "a6c4457a-0af5-4ba8-89c9-e2c8267f0336",
   "metadata": {},
   "outputs": [],
   "source": [
    "explicit_mixture.recover_marginals(idata, random_seed=rng);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "627f23bf-c871-4b81-bbf7-14f411604eb3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_3%</th>\n",
       "      <th>hdi_97%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>y</th>\n",
       "      <td>0.731</td>\n",
       "      <td>2.102</td>\n",
       "      <td>-3.202</td>\n",
       "      <td>3.811</td>\n",
       "      <td>0.099</td>\n",
       "      <td>0.070</td>\n",
       "      <td>567.0</td>\n",
       "      <td>2251.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>idx</th>\n",
       "      <td>0.683</td>\n",
       "      <td>0.465</td>\n",
       "      <td>0.000</td>\n",
       "      <td>1.000</td>\n",
       "      <td>0.023</td>\n",
       "      <td>0.016</td>\n",
       "      <td>420.0</td>\n",
       "      <td>420.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>lp_idx[0]</th>\n",
       "      <td>-6.064</td>\n",
       "      <td>5.242</td>\n",
       "      <td>-14.296</td>\n",
       "      <td>-0.000</td>\n",
       "      <td>0.227</td>\n",
       "      <td>0.160</td>\n",
       "      <td>567.0</td>\n",
       "      <td>2251.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>lp_idx[1]</th>\n",
       "      <td>-2.294</td>\n",
       "      <td>3.931</td>\n",
       "      <td>-10.548</td>\n",
       "      <td>-0.000</td>\n",
       "      <td>0.173</td>\n",
       "      <td>0.122</td>\n",
       "      <td>567.0</td>\n",
       "      <td>2251.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  ess_bulk  \\\n",
       "y          0.731  2.102  -3.202    3.811      0.099    0.070     567.0   \n",
       "idx        0.683  0.465   0.000    1.000      0.023    0.016     420.0   \n",
       "lp_idx[0] -6.064  5.242 -14.296   -0.000      0.227    0.160     567.0   \n",
       "lp_idx[1] -2.294  3.931 -10.548   -0.000      0.173    0.122     567.0   \n",
       "\n",
       "           ess_tail  r_hat  \n",
       "y            2251.0   1.01  \n",
       "idx           420.0   1.01  \n",
       "lp_idx[0]    2251.0   1.01  \n",
       "lp_idx[1]    2251.0   1.01  "
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d687f4b-ef2a-4512-8e81-0c0b1bc0d0bc",
   "metadata": {},
   "source": [
    "This `idx` variable lets us recover the mixture assignment variable after running the NUTS sampler! We can split out the samples of `y` by reading off the mixture label from the associated `idx` for each sample."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "70d23a58-3ebd-4b67-80f5-42dd495dfc81",
   "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": [
    "# fmt: off\n",
    "post = idata.posterior\n",
    "plt.hist(\n",
    "    post.where(post.idx == 0).y.values.reshape(-1),\n",
    "    bins=30,\n",
    "    rwidth=0.9,\n",
    "    alpha=0.75,\n",
    "    label='idx = 0',\n",
    ")\n",
    "plt.hist(\n",
    "    post.where(post.idx == 1).y.values.reshape(-1),\n",
    "    bins=30,\n",
    "    rwidth=0.9,\n",
    "    alpha=0.75,\n",
    "    label='idx = 1'\n",
    ")\n",
    "# fmt: on\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7fe000d6-9e6a-4ae7-9cae-3d0eed952410",
   "metadata": {},
   "source": [
    "One important thing to notice is that this discrete variable has a lower ESS, and particularly so for the tail. This means `idx` might not be estimated well particularly for the tails. If this is important, I recommend using the `lp_idx` instead, which is the log-probability of `idx` given sample values on each iteration. The benefits of working with `lp_idx` will explored further in the next example."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b458c9e-3b2d-4ba3-a657-5d7db1c046c5",
   "metadata": {},
   "source": [
    "## Coal mining model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e8dd6e73-6d3b-4ee0-9bff-eb0a581399af",
   "metadata": {},
   "source": [
    "The same methods work for the {ref}`Coal mining <pymc:pymc_overview#case-study-2-coal-mining-disasters>` switchpoint model as well. The coal mining dataset records the number of coal mining disasters in the UK between 1851 and 1962. The time series dataset captures a time when mining safety regulations are being introduced, we try to estimate when this occurred using a discrete `switchpoint` variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "9086c01b-5da7-4744-96ba-8d0b52e088c4",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/zv/upstream/pymc/pymc/model/core.py:1307: RuntimeWarning: invalid value encountered in cast\n",
      "  data = convert_observed_data(data).astype(rv_var.dtype)\n",
      "/home/zv/upstream/pymc/pymc/model/core.py:1321: ImputationWarning: Data in disasters contains missing values and will be automatically imputed from the sampling distribution.\n",
      "  warnings.warn(impute_message, ImputationWarning)\n"
     ]
    }
   ],
   "source": [
    "# fmt: off\n",
    "disaster_data = pd.Series(\n",
    "    [4, 5, 4, 0, 1, 4, 3, 4, 0, 6, 3, 3, 4, 0, 2, 6,\n",
    "    3, 3, 5, 4, 5, 3, 1, 4, 4, 1, 5, 5, 3, 4, 2, 5,\n",
    "    2, 2, 3, 4, 2, 1, 3, np.nan, 2, 1, 1, 1, 1, 3, 0, 0,\n",
    "    1, 0, 1, 1, 0, 0, 3, 1, 0, 3, 2, 2, 0, 1, 1, 1,\n",
    "    0, 1, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 1, 1, 0, 2,\n",
    "    3, 3, 1, np.nan, 2, 1, 1, 1, 1, 2, 4, 2, 0, 0, 1, 4,\n",
    "    0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1]\n",
    ")\n",
    "\n",
    "# fmt: on\n",
    "years = np.arange(1851, 1962)\n",
    "\n",
    "with pmx.MarginalModel() as disaster_model:\n",
    "    switchpoint = pm.DiscreteUniform(\"switchpoint\", lower=years.min(), upper=years.max())\n",
    "    early_rate = pm.Exponential(\"early_rate\", 1.0, initval=3)\n",
    "    late_rate = pm.Exponential(\"late_rate\", 1.0, initval=1)\n",
    "    rate = pm.math.switch(switchpoint >= years, early_rate, late_rate)\n",
    "    disasters = pm.Poisson(\"disasters\", rate, observed=disaster_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20d95bc6-ac70-427f-9bf4-c5b42cdf09fe",
   "metadata": {},
   "source": [
    "We will sample the model both before and after we marginalize out the `switchpoint` variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "77b71716-a585-49b8-b31a-43e54211a385",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "CompoundStep\n",
      ">CompoundStep\n",
      ">>Metropolis: [switchpoint]\n",
      ">>Metropolis: [disasters_unobserved]\n",
      ">NUTS: [early_rate, late_rate]\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",
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       "    .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
       "        background: #F44336;\n",
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       "</style>\n"
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       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "    <div>\n",
       "      <progress value='4000' class='' max='4000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
       "      100.00% [4000/4000 00:07&lt;00:00 Sampling 2 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 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 8 seconds.\n",
      "We recommend running at least 4 chains for robust computation of convergence diagnostics\n",
      "/home/zv/upstream/pymc-experimental/pymc_experimental/model/marginal_model.py:169: UserWarning: There are multiple dependent variables in a FiniteDiscreteMarginalRV. Their joint logp terms will be assigned to the first RV: disasters_unobserved\n",
      "  warnings.warn(\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "CompoundStep\n",
      ">NUTS: [early_rate, late_rate]\n",
      ">Metropolis: [disasters_unobserved]\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='4000' class='' max='4000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
       "      100.00% [4000/4000 03:11&lt;00:00 Sampling 2 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 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 191 seconds.\n",
      "We recommend running at least 4 chains for robust computation of convergence diagnostics\n"
     ]
    }
   ],
   "source": [
    "with disaster_model:\n",
    "    before_marg = pm.sample(chains=2, random_seed=rng)\n",
    "\n",
    "disaster_model.marginalize([\"switchpoint\"])\n",
    "\n",
    "with disaster_model:\n",
    "    after_marg = pm.sample(chains=2, random_seed=rng)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "55b108e7-c49a-40f1-afd7-c3890587a917",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_3%</th>\n",
       "      <th>hdi_97%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>switchpoint</th>\n",
       "      <td>1890.224</td>\n",
       "      <td>2.657</td>\n",
       "      <td>1886.000</td>\n",
       "      <td>1896.000</td>\n",
       "      <td>0.192</td>\n",
       "      <td>0.136</td>\n",
       "      <td>201.0</td>\n",
       "      <td>171.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>early_rate</th>\n",
       "      <td>3.085</td>\n",
       "      <td>0.279</td>\n",
       "      <td>2.598</td>\n",
       "      <td>3.636</td>\n",
       "      <td>0.007</td>\n",
       "      <td>0.005</td>\n",
       "      <td>1493.0</td>\n",
       "      <td>1255.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>late_rate</th>\n",
       "      <td>0.927</td>\n",
       "      <td>0.114</td>\n",
       "      <td>0.715</td>\n",
       "      <td>1.143</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.002</td>\n",
       "      <td>1136.0</td>\n",
       "      <td>1317.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 mean     sd    hdi_3%   hdi_97%  mcse_mean  mcse_sd  \\\n",
       "switchpoint  1890.224  2.657  1886.000  1896.000      0.192    0.136   \n",
       "early_rate      3.085  0.279     2.598     3.636      0.007    0.005   \n",
       "late_rate       0.927  0.114     0.715     1.143      0.003    0.002   \n",
       "\n",
       "             ess_bulk  ess_tail  r_hat  \n",
       "switchpoint     201.0     171.0    1.0  \n",
       "early_rate     1493.0    1255.0    1.0  \n",
       "late_rate      1136.0    1317.0    1.0  "
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(before_marg, var_names=[\"~disasters\"], filter_vars=\"like\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "fb62001a-3b80-4923-96e2-064d411ff523",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_3%</th>\n",
       "      <th>hdi_97%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>early_rate</th>\n",
       "      <td>3.077</td>\n",
       "      <td>0.289</td>\n",
       "      <td>2.529</td>\n",
       "      <td>3.606</td>\n",
       "      <td>0.007</td>\n",
       "      <td>0.005</td>\n",
       "      <td>1734.0</td>\n",
       "      <td>1150.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>late_rate</th>\n",
       "      <td>0.932</td>\n",
       "      <td>0.113</td>\n",
       "      <td>0.725</td>\n",
       "      <td>1.150</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.002</td>\n",
       "      <td>1871.0</td>\n",
       "      <td>1403.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  ess_bulk  \\\n",
       "early_rate  3.077  0.289   2.529    3.606      0.007    0.005    1734.0   \n",
       "late_rate   0.932  0.113   0.725    1.150      0.003    0.002    1871.0   \n",
       "\n",
       "            ess_tail  r_hat  \n",
       "early_rate    1150.0    1.0  \n",
       "late_rate     1403.0    1.0  "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(after_marg, var_names=[\"~disasters\"], filter_vars=\"like\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66532abc-38a6-4796-ab4d-9252159663fc",
   "metadata": {},
   "source": [
    "As before, the ESS improved massively"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e058dba7-9b6b-4002-8360-2fae6fe71306",
   "metadata": {},
   "source": [
    "Finally, let us recover the `switchpoint` variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "19459eaa-a781-4baf-8360-77dad3c15217",
   "metadata": {},
   "outputs": [],
   "source": [
    "disaster_model.recover_marginals(after_marg);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "b306de49-12b1-44f1-90e7-2d2320567afb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_3%</th>\n",
       "      <th>hdi_97%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>early_rate</th>\n",
       "      <td>3.077</td>\n",
       "      <td>0.289</td>\n",
       "      <td>2.529</td>\n",
       "      <td>3.606</td>\n",
       "      <td>0.007</td>\n",
       "      <td>0.005</td>\n",
       "      <td>1734.0</td>\n",
       "      <td>1150.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>late_rate</th>\n",
       "      <td>0.932</td>\n",
       "      <td>0.113</td>\n",
       "      <td>0.725</td>\n",
       "      <td>1.150</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.002</td>\n",
       "      <td>1871.0</td>\n",
       "      <td>1403.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>switchpoint</th>\n",
       "      <td>1889.764</td>\n",
       "      <td>2.458</td>\n",
       "      <td>1886.000</td>\n",
       "      <td>1894.000</td>\n",
       "      <td>0.070</td>\n",
       "      <td>0.050</td>\n",
       "      <td>1190.0</td>\n",
       "      <td>1883.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 mean     sd    hdi_3%   hdi_97%  mcse_mean  mcse_sd  \\\n",
       "early_rate      3.077  0.289     2.529     3.606      0.007    0.005   \n",
       "late_rate       0.932  0.113     0.725     1.150      0.003    0.002   \n",
       "switchpoint  1889.764  2.458  1886.000  1894.000      0.070    0.050   \n",
       "\n",
       "             ess_bulk  ess_tail  r_hat  \n",
       "early_rate     1734.0    1150.0   1.00  \n",
       "late_rate      1871.0    1403.0   1.00  \n",
       "switchpoint    1190.0    1883.0   1.01  "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(after_marg, var_names=[\"~disasters\", \"~lp\"], filter_vars=\"like\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1fc7e742-67b4-4152-8ec5-4bd8c4f7c640",
   "metadata": {},
   "source": [
    "While `recover_marginals` is able to sample the discrete variables that were marginalized out. The probabilities associated with each draw often offer a cleaner estimate of the discrete variable. Particularly for lower probability values. This is best illustrated by comparing the histogram of the sampled values with the plot of the log-probabilities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "798d9cbf-5eda-4625-8c9b-84995318bb15",
   "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": [
    "post = after_marg.posterior.switchpoint.values.reshape(-1)\n",
    "bins = np.arange(post.min(), post.max())\n",
    "plt.hist(post, bins, rwidth=0.9);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "3338722f-a0c6-4277-b458-8ff8dcb59434",
   "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": [
    "lp_switchpoint = after_marg.posterior.lp_switchpoint.mean(dim=[\"chain\", \"draw\"])\n",
    "x_max = years[lp_switchpoint.argmax()]\n",
    "\n",
    "plt.scatter(years, lp_switchpoint)\n",
    "plt.axvline(x=x_max, c=\"orange\")\n",
    "plt.xlabel(r\"$\\mathrm{year}$\")\n",
    "plt.ylabel(r\"$\\log p(\\mathrm{switchpoint}=\\mathrm{year})$\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad3cc13c-f2e7-4789-aac2-3e3e9dfe58cc",
   "metadata": {},
   "source": [
    "By plotting a histogram of sampled values instead of working with the log-probabilities directly, we are left with noisier and more incomplete exploration of the underlying discrete distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c675ae7f-2c91-4ead-90c2-ab0bd78a02ed",
   "metadata": {},
   "source": [
    "## Authors\n",
    "* Authored by [Rob Zinkov](https://zinkov.com) in January, 2024"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7073a737-5f30-44bc-ac6c-bc85b8955391",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    ":::{bibliography}\n",
    ":filter: docname in docnames \n",
    ":::\n",
    "\n",
    "* [STAN manual section on marginalization](https://mc-stan.org/docs/stan-users-guide/latent-discrete.html)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f14213a-651e-4271-9a2d-71954e84605c",
   "metadata": {},
   "source": [
    "## Watermark"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "57fd6d30-cfd8-4fc4-85df-1f4361ed7015",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Last updated: Sat Feb 10 2024\n",
      "\n",
      "Python implementation: CPython\n",
      "Python version       : 3.11.6\n",
      "IPython version      : 8.20.0\n",
      "\n",
      "pytensor: 2.18.6\n",
      "xarray  : 2023.11.0\n",
      "\n",
      "pymc             : 5.11\n",
      "numpy            : 1.26.3\n",
      "pytensor         : 2.18.6\n",
      "pymc_experimental: 0.0.15\n",
      "arviz            : 0.17.0\n",
      "pandas           : 2.1.4\n",
      "matplotlib       : 3.8.2\n",
      "\n",
      "Watermark: 2.4.3\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -n -u -v -iv -w -p pytensor,xarray"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "47987baa-2f8d-4efd-9c43-12f76e2659e2",
   "metadata": {},
   "source": [
    ":::{include} ../page_footer.md\n",
    ":::"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "pymc-dev",
   "language": "python",
   "name": "pymc-dev"
  },
  "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"
  },
  "myst": {
   "substitutions": {
    "extra_dependencies": "pymc-experimental"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}