{
 "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_extras 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_extras.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": [
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [y]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2610298041c0479c8253eff83c265d87",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "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 1 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>0.775</td>\n",
       "      <td>2.088</td>\n",
       "      <td>-3.117</td>\n",
       "      <td>3.85</td>\n",
       "      <td>0.092</td>\n",
       "      <td>0.065</td>\n",
       "      <td>664.0</td>\n",
       "      <td>1956.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  ess_bulk  ess_tail  \\\n",
       "y  0.775  2.088  -3.117     3.85      0.092    0.065     664.0    1956.0   \n",
       "\n",
       "   r_hat  \n",
       "y    1.0  "
      ]
     },
     "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 4 jobs)\n",
      "CompoundStep\n",
      ">BinaryGibbsMetropolis: [idx]\n",
      ">NUTS: [y]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e8acde4d31414bd7af3042776d0a2f00",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "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 1 seconds.\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>0.658</td>\n",
       "      <td>0.475</td>\n",
       "      <td>0.000</td>\n",
       "      <td>1.000</td>\n",
       "      <td>0.028</td>\n",
       "      <td>0.020</td>\n",
       "      <td>292.0</td>\n",
       "      <td>292.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y</th>\n",
       "      <td>0.633</td>\n",
       "      <td>2.144</td>\n",
       "      <td>-3.297</td>\n",
       "      <td>3.678</td>\n",
       "      <td>0.117</td>\n",
       "      <td>0.083</td>\n",
       "      <td>433.0</td>\n",
       "      <td>2054.0</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  0.658  0.475   0.000    1.000      0.028    0.020     292.0     292.0   \n",
       "y    0.633  2.144  -3.297    3.678      0.117    0.083     433.0    2054.0   \n",
       "\n",
       "     r_hat  \n",
       "idx   1.01  \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": [
      "Initializing NUTS using jitter+adapt_diag...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [y]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "7eda66992bf94a3aacfcc817be8145af",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "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 1 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>0.787</td>\n",
       "      <td>2.095</td>\n",
       "      <td>-3.176</td>\n",
       "      <td>3.843</td>\n",
       "      <td>0.085</td>\n",
       "      <td>0.06</td>\n",
       "      <td>780.0</td>\n",
       "      <td>2274.0</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  0.787  2.095  -3.176    3.843      0.085     0.06     780.0    2274.0   \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_extras.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_extras.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>0.787</td>\n",
       "      <td>2.095</td>\n",
       "      <td>-3.176</td>\n",
       "      <td>3.843</td>\n",
       "      <td>0.085</td>\n",
       "      <td>0.060</td>\n",
       "      <td>780.0</td>\n",
       "      <td>2274.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>idx</th>\n",
       "      <td>0.700</td>\n",
       "      <td>0.458</td>\n",
       "      <td>0.000</td>\n",
       "      <td>1.000</td>\n",
       "      <td>0.019</td>\n",
       "      <td>0.014</td>\n",
       "      <td>576.0</td>\n",
       "      <td>576.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>lp_idx[0]</th>\n",
       "      <td>-6.214</td>\n",
       "      <td>5.195</td>\n",
       "      <td>-14.360</td>\n",
       "      <td>-0.000</td>\n",
       "      <td>0.192</td>\n",
       "      <td>0.136</td>\n",
       "      <td>780.0</td>\n",
       "      <td>2274.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>lp_idx[1]</th>\n",
       "      <td>-2.219</td>\n",
       "      <td>3.969</td>\n",
       "      <td>-10.623</td>\n",
       "      <td>-0.000</td>\n",
       "      <td>0.157</td>\n",
       "      <td>0.111</td>\n",
       "      <td>780.0</td>\n",
       "      <td>2274.0</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          0.787  2.095  -3.176    3.843      0.085    0.060     780.0   \n",
       "idx        0.700  0.458   0.000    1.000      0.019    0.014     576.0   \n",
       "lp_idx[0] -6.214  5.195 -14.360   -0.000      0.192    0.136     780.0   \n",
       "lp_idx[1] -2.219  3.969 -10.623   -0.000      0.157    0.111     780.0   \n",
       "\n",
       "           ess_tail  r_hat  \n",
       "y            2274.0   1.01  \n",
       "idx           576.0   1.01  \n",
       "lp_idx[0]    2274.0   1.01  \n",
       "lp_idx[1]    2274.0   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": [
      "/var/home/fonnesbeck/repos/pymc-examples/.pixi/envs/default/lib/python3.12/site-packages/pymc/model/core.py:1288: RuntimeWarning: invalid value encountered in cast\n",
      "  data = convert_observed_data(data).astype(rv_var.dtype)\n",
      "/var/home/fonnesbeck/repos/pymc-examples/.pixi/envs/default/lib/python3.12/site-packages/pymc/model/core.py:1302: 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": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "491dc32aa9ea4b9890293b998b737218",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "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 1 seconds.\n",
      "We recommend running at least 4 chains for robust computation of convergence diagnostics\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",
      "/var/home/fonnesbeck/repos/pymc-examples/.pixi/envs/default/lib/python3.12/site-packages/pymc_extras/model/marginal/marginal_model.py:174: 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": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "4229ae740a274482859d304f079434f0",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "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 4 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",
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       "\n",
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       "    }\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>3.100</td>\n",
       "      <td>0.289</td>\n",
       "      <td>2.547</td>\n",
       "      <td>3.620</td>\n",
       "      <td>0.008</td>\n",
       "      <td>0.005</td>\n",
       "      <td>1437.0</td>\n",
       "      <td>1294.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>late_rate</th>\n",
       "      <td>0.940</td>\n",
       "      <td>0.115</td>\n",
       "      <td>0.713</td>\n",
       "      <td>1.143</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.002</td>\n",
       "      <td>1294.0</td>\n",
       "      <td>1148.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>switchpoint</th>\n",
       "      <td>1889.406</td>\n",
       "      <td>2.387</td>\n",
       "      <td>1885.000</td>\n",
       "      <td>1893.000</td>\n",
       "      <td>0.214</td>\n",
       "      <td>0.151</td>\n",
       "      <td>127.0</td>\n",
       "      <td>334.0</td>\n",
       "      <td>1.02</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 mean     sd    hdi_3%   hdi_97%  mcse_mean  mcse_sd  \\\n",
       "early_rate      3.100  0.289     2.547     3.620      0.008    0.005   \n",
       "late_rate       0.940  0.115     0.713     1.143      0.003    0.002   \n",
       "switchpoint  1889.406  2.387  1885.000  1893.000      0.214    0.151   \n",
       "\n",
       "             ess_bulk  ess_tail  r_hat  \n",
       "early_rate     1437.0    1294.0   1.00  \n",
       "late_rate      1294.0    1148.0   1.00  \n",
       "switchpoint     127.0     334.0   1.02  "
      ]
     },
     "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",
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       "    }\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>3.098</td>\n",
       "      <td>0.291</td>\n",
       "      <td>2.539</td>\n",
       "      <td>3.603</td>\n",
       "      <td>0.007</td>\n",
       "      <td>0.005</td>\n",
       "      <td>1796.0</td>\n",
       "      <td>1532.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>late_rate</th>\n",
       "      <td>0.930</td>\n",
       "      <td>0.121</td>\n",
       "      <td>0.704</td>\n",
       "      <td>1.152</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.002</td>\n",
       "      <td>1578.0</td>\n",
       "      <td>1433.0</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  3.098  0.291   2.539    3.603      0.007    0.005    1796.0   \n",
       "late_rate   0.930  0.121   0.704    1.152      0.003    0.002    1578.0   \n",
       "\n",
       "            ess_tail  r_hat  \n",
       "early_rate    1532.0    1.0  \n",
       "late_rate     1433.0    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": [
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       "</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>3.098</td>\n",
       "      <td>0.291</td>\n",
       "      <td>2.539</td>\n",
       "      <td>3.603</td>\n",
       "      <td>0.007</td>\n",
       "      <td>0.005</td>\n",
       "      <td>1796.0</td>\n",
       "      <td>1532.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>late_rate</th>\n",
       "      <td>0.930</td>\n",
       "      <td>0.121</td>\n",
       "      <td>0.704</td>\n",
       "      <td>1.152</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.002</td>\n",
       "      <td>1578.0</td>\n",
       "      <td>1433.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>switchpoint</th>\n",
       "      <td>1889.692</td>\n",
       "      <td>2.444</td>\n",
       "      <td>1885.000</td>\n",
       "      <td>1893.000</td>\n",
       "      <td>0.076</td>\n",
       "      <td>0.054</td>\n",
       "      <td>965.0</td>\n",
       "      <td>1637.0</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",
       "early_rate      3.098  0.291     2.539     3.603      0.007    0.005   \n",
       "late_rate       0.930  0.121     0.704     1.152      0.003    0.002   \n",
       "switchpoint  1889.692  2.444  1885.000  1893.000      0.076    0.054   \n",
       "\n",
       "             ess_bulk  ess_tail  r_hat  \n",
       "early_rate     1796.0    1532.0    1.0  \n",
       "late_rate      1578.0    1433.0    1.0  \n",
       "switchpoint     965.0    1637.0    1.0  "
      ]
     },
     "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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Prm3fvj2/wJcwp2QsKSlJr7zyitEeO3aswsPDLa2LkmX3jOV+WnqNGjX05Zdf6oUXXvB6TDk5OVq2bJl27dqlTz/9NE+BCMXH7hmTLk7/MGfOHL366qtavHixLly4oLVr12rt2rUFrhMcHKx77rlHo0eP9umhOvBdSWbs2muv1e7du4326tWrde+993o9pp9++inPspSUlDzLck/5IFl/qNIlVapU8bg9FB8756wwGPeXPqdkjHG//7J7xhj3+z+7Z0xyxrifK7fhsxtvvFHLly/Xgw8+aJqkPj+9evXShx9+aPnLunTxF8mhQ4dq+fLlXuc2DgoK0hNPPKFp06YVe2F7yZIlplsTQ0JCNH78+GLdB/LnhIxNmTJFiYmJki5+OerXr5/ldVHy7Jyxs2fPGq/Pnz+viRMnGu0+ffroiy++0MaNG7Vt2zYtW7ZMI0eOND18JDY2Vk8++aTpykkUPztn7JIqVaropZde0ty5c9WkSROPfWvVqqUpU6Zo7NixfjHALQ9KKmPueZo9e7bXByQlJSVp3rx5eZbnV3h2/3Ll6x137v0pbpcsu+bMV4z7y44TMsa437/ZOWOM++3Bzhm7xO7jforb8Nnq1avVr18/ffLJJ16fHL1ixQp169ZNr7zyimkyfE+ys7P1ySefqG/fvvn+4pRbZmampk+fri5dumjBggWW34M327ZtM/3DIUnPPvus11vFUTzsnrHffvtNX331laSLv2i6Zwllz84Zyz0wSU1NVVZWllwul1577TVNnTpVbdu2VbVq1VSxYkU1bdpUTz75pObPn296CveWLVvyHfSg+Ng5Y5ecO3dO48eP17333qt9+/Z57JuQkKCnn35affr00caNGy3vA4VXUhm76aab1KxZM6N95MgRPffccwV+MU5PT9fTTz+thISEfP+fu4yMDFPb14etuT9QyduXPBSNXXPmC8b9ZcvuGWPc7//snDHG/fZg54xdYvdxP9OSwCczZ87UO++8Y7Rr1KihoUOHqnPnzqpbt64CAwN16tQp/fHHH5o9e7b++usvZWZmas6cOdq2bZs++eSTPLeT5paRkaEnnnhCq1evNpY1a9ZM999/v9q1a6fIyEhlZmbqyJEjWr16tebMmaPExESdPn1a48eP1969e4s838+BAwc0YsQI0x//gAEDNHjw4CJtF9bYPWPnz583XekzYsQI/dd//VfRTgqKld0zFhISkucBIYMHD1b//v0LXOfKK6/U5MmT9dhjjxnLPv30Uw0ePNiYIw7Fx+4Zk6Tjx49ryJAhpofidOrUSXfddZdatmypsLAwpaamau/evfr222/1r3/9S5mZmdq3b5+GDBmiN998U7179y78SYRHJZkxl8ulF198Uffdd5/x5Wn58uU6ePCgRowYoXbt2iksLEynT5/Wb7/9pvfee8+YE7RKlSqmK7Pzm3LEvTidmZnp03t3L477yxVDTmTnnFnFuL9s2T1jjPv9n90zxrjf/9k9Y5Izxv2unJycnDI9ApSaLl26GE+Uj4qK0o8//ujT+suXL9fo0aONdnR0tGbNmqWIiIh8+2dkZGjcuHHGL9nSxVtnpk6dWuA+JkyYoPnz5xvt/v37a/LkyQVe1RMfH6/hw4dr165dxrKXXnrJ9LRXX8TFxemee+4xzpN08VaQd999V4GB/BbkDRm7+ITkTz75RJLUsGFDLV26NM8X+dyuuOIK43Vhzll5Q8akDh06GA8HlKTAwED9+OOPlubS69evn2netq+++krR0dFe1ytPyNjFYxo4cKD27NljLHvxxRd11113FXhM27Zt00MPPWQ8uCgoKEhLliwxXW2Ci+yQMUn617/+pfHjx3u9AumSOnXq6IEHHtCUKVOMZc8995yGDh1q6hcbG2v6AtS1a1fNnDnT0j4kafLkyaaH/s2aNUs333yz5fXLi/KeMysY9xcNGWPcX9LIGOP+kkbGnDPu52cbWJKZmWl6SEZISIhmzpxZ4B+tdPHKnMmTJ5v+EV+2bJl27NiRb/89e/aYbpe+9Iujp9tVIyIiNGPGDNP8i9OmTSvU7YmJiYl68MEHTQPctm3b6p133mGAWwqckLGdO3dqzpw5RvvFF1/0OMBF6XJCxqS8D1Nr3ry55YfEuM/bdulp3SgeTsnYwoULTQPce+65x+MAV5JatWqlSZMmGe3MzEyvA3X4rjQydsnAgQP14Ycfql69el6Pq23btpo7d65cLpdpeVhYWJ6+7lcO+fowQPf+RblqF/lzQs68YdxftpyQMcb9/s0JGZMY9/szp2TMKeN+ituwZO3atYqPjzfaffr0sfRQqqCgID344IOmZV9//XW+fb/66ivlvpHggQcesDQPY1RUlPr06WO0T58+rZ9//tnrerklJydr2LBhxi0cknTVVVfp/fff9/lBRygcJ2TsjTfeMH5N7d+/v9q3b+912yg9TsiYdPGX+NyaNm3qdfuXuP+afvLkScvrwjunZGzJkiWm9vDhw71uX7r4gJz69esb7TVr1uj06dOW1oU1pZGx3Dp27KgVK1bojTfe0K233qr69eurSpUqCgkJUf369dWzZ0/NnDlTn332maKionT06FHT+vnNWVyrVi1T8TAuLs7rceTm3t/9MxFF54ScecK4v+w5IWOM+/2bEzImMe73Z07JmFPG/fwsDUu2bt1qal9//fWW13Xv++eff1raR7t27Xzax+LFi432jh071L17d0vrpqWl6ZFHHtHOnTuNZY0aNdJHH32kqlWrWj4GFI0TMpb7w/ybb77R0qVLLW9fko4dO6bmzZsb7aioKK1atcqnbaBgTsiYdHFgsn79eqPtyxVr7n3PnDljeV1454SMZWRkmG5hrVevnqWBunRxXsA2bdro8OHDkqScnBzt3LlTHTt2tHyM8Kw0MuYuKChIffv2Vd++fb32zX3lUVBQkK688sp8t1e3bl0dPHhQ0sVidU5OTp4rjApy4sQJ43WlSpUUFRVlaT1Y54ScFYRxv39wQsYY9/s3J2RMYtzvz5yQMSeN+7lyG5YkJiaa2p5utXBXq1YtU7ugX3Pc9+G+XnHsw11mZqZGjRqlDRs2GMuioqI0e/Zs1ahRw/L+UXROy1h2drYuXLjg9T933v4/Cs8pGXO/YsP94WqeuPfl9tni5YSMnT592vTZ48v2pbzvmSu3i1dpZKywzp8/r5iYGKMdHR1d4GdM7quH0tLStH//fkv7SE5O1qFDh4x2w4YNLRfFYZ1TcuaOcb//cFrGGPf7H6dkjHG//3JCxpw07qe4DUvcb9FLS0uzvK5730qVKuXbz/2PzZd5s63uI7fs7Gz97//+r9asWWMsi4iI0OzZsy3PY4Xi48SMwb84JWNt27Y1tX25xdD9dn6+zBcvJ2TM/T34+gyL8+fPe90HCq80MlZYq1atMuUl9zQ47q677jpTe/PmzZb2sX37dmVnZxvtNm3a+HiUsMIpOcuNcb9/cWLG4F+ckjHG/f7LCRlz0rifaUlgifsHYWxsrLp27Wpp3X379pnaNWvWzLef+/LY2Fi1atWqWPeR24QJE7R8+XKjHR4erk8//dQ0bxBKjxMyZmWuLHc8Nb30OCFj0sX58xo0aGBcvbh161ZlZ2erQgXvv1dv2bLF1M59OyyKzgkZCwsLU1BQkDIzMyVJBw8eVFZWluUHrOWew7agfaDwSiNjhTV37lzjdXBwsPr161dg365du+r111832t99950GDRrkdR8rV67Msx0UP6fkLDfG/f7FCRlj3O/fnJAxiXG/P3NCxpw07ufKbVjSsmVLU3vFihWW1122bJmpfc0111jax7fffmtp+zk5OXn6FrSPS15//XUtXLjQaFerVk0ff/yxTw9oQPFyWsbgf5yUsd69exuv4+PjTVeiFSQpKck0l2NQUBBXPRYzJ2TM5XLp6quvNtqpqalavXq1pX2cPHnSdLt/SEiIoqOjLa0La0ojY4XxzTffmL5EDxo0SOHh4QX2b9iwoWnux19//dU03Uh+zpw5YypO1qpVK88VbSgeTsnZJYz7/Y/TMgb/46SMMe73T07ImJPG/RS3YUnbtm0VGhpqtGNiYvTPf/7T63pbtmwxDSYl6ZZbbsm3b5cuXUzt+fPnW5pYf/bs2dq7d6/RDg8PV+vWrQvs/8EHH+jjjz822pUqVdIHH3xg+qNG6XNSxuCfnJSxoUOHqlq1akZ7ypQpSk5O9riPyZMnKzU11WgPGDCAh2cVM6dkzH0fb7zxhs6ePetx+zk5OZo4caJpfscOHTqoYsWKXo8N1pVGxny1efNmTZgwwWjXrl1bY8aM8breo48+arzOzs7WxIkTlZOTU2D/V199VefOnTPaw4cPt3xlEXzjpJwx7vdPTsoY/JOTMsa43z85JWNOGfdT3IYlISEheuihh0zLJk+erBkzZuQ7t1BOTo6WLl2qYcOGGbc4SBf/aAsaTF5zzTW68cYbjXZ6eroefPBBrVy5Mt8vO6mpqXrrrbf02muvmZaPGDGiwIclLFiwQNOmTTPawcHBmjlzZp65H1H6nJIx+C8nZSw8PNxUGDp06JDuv/9+HTx4ME/f5ORkPffcc1q6dKmxLDQ01LQ+iodTMnbPPfeYrvA4ePCgBg8erF27duXb/+TJkxo5cmSe26sfe+yxfPuj8EojY9LF22WHDx+u1atXm9bLLS0tTR9++KEeeOAB4wt0hQoV9NJLL1n6At2jRw+1aNHCaP/222965plnlJKSYuqXkZGhKVOmaMmSJcayqKgo3X333V73gcJxSs4Y9/svp2QM/stJGWPc75+ckjGnjPtdOZ4ukYDtHDt2TN27d8/3/7k/gTkgICDffrNnz9b111+fZ3lGRoYeeughrV+/3rQ8PDxcHTp0UN26dRUQEKBTp05p3bp1OnbsmKnfZZddpgULFnh8aMuxY8d05513Kj4+3rS8fv36uv7661W7dm1lZWXp0KFDWrdunc6cOWPq17FjR33wwQcFXsnTpUuXPMdV0HnwZNWqVYqKivJ5PScgY54z5ivm3suLjFnLWE5OjkaPHm26BS4oKEjt2rXTFVdcoaCgIB05ckS//PKL6df3gIAAzZw5U507d/a4fScjY94ztmbNGo0cOVJZWVmm5S1btlSrVq0UFham1NRU7dmzR+vXr88z2B41alSZD3LLkt0ztnfvXv33f/+3pItTOLRq1UqNGjVSaGiozp49q6NHj2rdunWmq8JcLpcmTJjgU9H5+PHjGjhwoP7++29jWVhYmLp06aLIyEglJCRozZo1pqxXrlxZ8+bNM01rUl6RM88Y9xcdGStejPvzImPWMO4vPDLmnRPG/RS3Hebo0aNFfrjOZ599pnbt2uX7/86dO6fnnnvONH+TFdHR0Xr77bfVsGFDr31jY2P11FNPmW6ftqJ3796aPHmyqlSpUmCf/Aa5hfHDDz+obt26Rd6OHZExzxnzFYPcvMiY9Yylp6fr+eefzzNvW0GqVq2qadOmqVOnTj4dl9OQMWsZ+/777/WPf/xDSUlJlrcfGBioUaNGacSIET4dl9PYPWO5v0hZER4erpdfflndunXz6Xgk6c8//9SoUaMsjc+qV6+uqVOnmu5eKM/ImWeM+4uOjBUvxv15kTHrGPcXDhmzxu7jfqYlgU+qVaumd999VzNmzFC7du3kcrk89m/SpInGjx+vhQsXWvqyLkmNGzfW4sWL9cILL6hRo0Ye+1aoUEE33HCD3n//fb311lvFWnRE2SBjKGlOylhISIimTp2qd955x3R7v7vKlSvrnnvu0fLly8v9ALc0OCVj3bp1M26fdH8ivLuQkBD1799fixcv9osBrtOVdMZq1aql2267TZdffrnHfjVq1NDw4cO1cuXKQheDrr76an399de67777FBYWlm+fSpUqqX///lq6dCmF7VLkpJzBP5ExlDQnZYxxv39ySsbsPu7nym0Uyblz57R9+3YdPXpUZ8+eVXZ2tqpWrarIyEi1aNHC4+0VVsXFxWnHjh06deqUkpOTVaFCBYWGhqpevXpq2bIlc6E5HBlDSXNSxg4dOqSYmBidOnVK6enpql69uho0aKDWrVsrKCioWPYB3zkhYzk5OYqNjdWuXbt0+vRppaSkqGLFigoNDVWTJk0UHR3NswjKUElm7MiRI9q9e7eOHz+ulJQUBQYGqmbNmmrWrJmuuuoqVahQfNfKZGRkaOPGjTp27JgSExMVFhamyy67TG3atOHHZT/glJzBf5ExlDQnZYxxv39yQsbsOO6nuA0AAAAAAAAAsB1+ngQAAAAAAAAA2A7FbQAAAAAAAACA7VDcBgAAAAAAAADYDsVtAAAAAAAAAIDtUNwGAAAAAAAAANgOxW0AAAAAAAAAgO1Q3AYAAAAAAAAA2A7FbQAAAAAAAACA7VDcBgAAAAAAAADYDsVtAAAAAAAAAIDtUNwGAAAAAAAAANgOxW0AAAAAAAAAgO1Q3AYAAAAAAAAA2A7FbQAAAAAAAACA7VDcBgAAAAAAAADYDsVtAAAAAAAAAIDtUNwGAAAAAAAAANgOxW0AAAAAAAAAgO1Q3AYAAAAAAAAA2A7FbQAAAAAAAACA7VDcBgAAAAAAAADYDsVtAAAAAAAAAIDtUNwGAAAAAAAAANgOxW0AAAAAAAAAgO1Q3AYAAAAAAAAA2A7FbQAAAAAAAACA7fw/sBJohW6E5jsAAAAASUVORK5CYII=",
      "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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jcSSyhIpXXlmi9lD6KG4D8HpFn4BcuXJly/vZryHsyvLly03tvn37Wt7XioSEBFO7U6dOlvYr+s2xo3EAT5R1luxvBgsJCbF8jKJ9Xc2OI0uoaDt27DC1W7RoYWm/yMhI1a9f32h/++23+vvvvx323b59u+nLovbt21ta97Bjx46mtYRdvc/JEipaeWSppOyLAIXLLThCllDRKjJLM2bM0OHDhyWdL6BZWS7BGbKEilZeWaL2UPoobgPwekVvYUtPT7f8hODC25Gk899EOlsXPi8vzzS7LTY2ttSfDrxlyxZT2+qFMi4uTgEBAU7HATxR1lmyv93U1Uy3os6ePau0tDSjfemllzrtS5ZQ0Yq+VyW5fPipvaJ9s7OztX37dof9tm7dampbfZ9XrlxZTZo0Mdq7du3SmTNnHPYlS6ho5ZGlkipcO7WQq5l7ZAkVraKytGPHDs2bN0/S+evPmDFjLO/rCFlCRSuPLFF7KBsUtwF4vZtvvtn4OTc3V59//rnbfQ4fPmx6gEK7du2czgbdvXu36aETLVu2vICzdeyPP/4wfq5cubIaNGhgab8qVaqYCn379+8vNjsWsKqss1SjRg3TrdxJSUmWCtwbNmxQXl6e0Y6Pj3falyyhotnPxAkODra8r/3s63379jnsZ7+9aK7cKVrclsyZcbadLKEilEeWSsJms2nPnj2mbdHR0U77kyVUtIrIUn5+vl588UXjQeWPP/6424e2ukOWUNHKI0vUHsoGxW0AXq9fv36mZRGmTJli3P7mSHZ2tp5//nmjWBYcHKzHHnvMaX/7b1UL1xfOzc3Vp59+qqFDh+r2229XixYt1KZNG3Xt2lVjxozRt99+a+n8c3NzdeTIEaMdHR3tctkFe5dcconx87lz50yzaAFPlHWWJGnw4MHGz3l5eXrhhRdczhDfv3+/XnnlFaNdv359de3a1WFfsgRvYL+WqLOZ0Y7Y93X2h499QbpOnTqWj1H0fe5oLIkswTuUR5ZKIjEx0fTFbMOGDRUZGemwL1mCN6iILH3wwQf67bffJElXXHGFHnnkEcvHdIQswRuUR5aoPZQNitsAvF7dunU1YcIE48F0J0+eVI8ePfTOO+9o3759ysnJUX5+vo4ePaply5apW7duxi3dAQEBmjhxossH5+3du9fUrlevnnbt2qX77rtPI0aM0MaNG3Xw4EFlZ2fr1KlT2rVrlxYtWqRHH31UDzzwQLHZPfZSU1NNs1I9KVJIxW+HOnbsmEf7A4XKOkuSdMcdd5geavfjjz/qnnvu0cqVK3Xs2DHl5+crJydHe/bs0axZs9SjRw9jLdPq1atr5syZTtcWJkvwBrVr1za17a8hzthstmJ9//zzT4d9i663HRgYqFq1alk+P/sZpo7e52QJ3qA8slQSb775pql9xx13OO1LluANyjtLhw4dMnLi5+ensWPHmp73UBJkCd6gPLJE7aFsUNwG4BM6d+6s999/37jdLSMjQ6+//rruuusuNW/eXE2bNlV8fLxefPFFHTp0SJLUqFEjzZs3z+ks0EIZGRmmdmpqqnr16qWdO3e6Pa9ff/1VDz74oH788UenfYrediR59qBL6fztQa7GAzxRllkqNHr0aI0cOVJhYWGSzs8cfeGFF9SuXTs1bdpUzZs3V5cuXTRjxgxjXdP4+HitWLFCDRs2dDouWYI3uPbaa03tr776ytJ+W7Zs0V9//WXa5uw9WHR7SEiIRzNurLzPyRK8QXlkyVPLli0zfaaLiIhw+aAvsgRvUN5Zeumll4y78nr06FEqyyqQJXiD8sgStYeyQXEbgM+46aabtG7dOg0YMMD0oANH7rzzTr377ru6/vrr3Y5rfwvR2LFjjYLb1VdfrTfffFPff/+9kpOT9eWXX2rcuHGmb0AzMzM1fPhwp9/O2j+UyNmsVGfs+/vKBQbeq6yyVMjPz08PP/yw1q1b53L9bEkKCgrSE088oddff73Ycgr2yBK8QevWrVW5cmWjnZCQ4HYWjSTNnj272DYrxW1P3+f260M6OgZZgjcojyx5Ys+ePZo4caJp2/PPP69q1ao53YcswRuUZ5Y+/vhj/fDDD5LO33H33HPPeXi2jpEleIPyyBK1h7JBcRuAz/jqq6/UrVs3ffDBB8bDS5z59NNPdeutt2rSpEnFHgxhz/4f7MJvXR944AEtWbJEt912m2rUqKHg4GBdcskl6tmzp9asWaOrr77a2Cc9PV2TJk1yOH5OTo6p7elte/aFClfrFwNWlFWWChUUFOiDDz5Q165d9eWXX7rsm5ubq5kzZ6pDhw5asmSJy75kCd4gIiJCPXr0MNp5eXkaMWKEUlNTne4zc+ZMbdq0qdh2Z+/Bolkri/c5WYI3KI8sWZWWlqahQ4fq7NmzxrZOnTrp3nvvdbkfWYI3KK8snTp1yvSclBdeeEERERElO2k7ZAneoDyyRO2hbFDcBuAT3nrrLQ0ePNh4MFZkZKSefvpprVmzRj///LOSkpK0ceNGTZw4UVdeeaWk80WzefPmqV+/fsW+wSzK0beZTZo00ejRo53eCl61alVNnz7ddNvOxo0bdeDAgWJ97S8Qubm5bl9vUfYXqKLfJgOeKsssSeffr48//rimTJmi9PR0SecfxjVx4kRt3LhRycnJ+vnnn7V69Wo99dRTxkO60tLS9NJLL2n8+PFOxyZL8BZPPPGEaRbN3r171a1bNy1YsEBHjx5Vfn6+MjMz9f3332vgwIHG2qT2t3ratwsVvS6VxfucLMFblHWWrDh79qwee+wxHTx40NjWuHFjp4WDosgSvEV5ZGnChAnGZ7sbbrhB3bt3L7XzJ0vwFuX5Ga8QtYcLR3EbgNdbt26dpk+fbrSbNGmiNWvWaPDgwWrUqJGqVKmiSpUqKSYmRvfdd59WrFhh+rD1yy+/6KWXXnI6vqN1qAYNGqTAwECX51WnTh3TN7sFBQUO1+Wyv7BZnf3qrL+n62YBhco6S5I0ceJEUw66d++uFStW6L777lNMTIyCg4NVpUoVNW7cWI899pjWrFmjJk2aGP0XLFigpUuXOhybLMFbVK9eXW+++aaqV69ubEtNTdX48eMVHx+vpk2b6rrrrlP//v31zTffSDo/c2bcuHGmccLDwx2OX/S96en73P6PEkfvc7IEb1HWWXInNzdXTzzxhH755RdjW7169fTee+8Zz41whSzBW5R1lr766iutW7dO0vni2dixY0v1/MkSvEV5fsYrRO3hwlHcBuDVcnNzTTNnKlWqpLfeeku1atVyuk9wcLAmTJigRo0aGdvWrl2r5ORkh/3tLwD+/v5q166dpfPr0KGDqf3zzz8X62N/QXA389WefX9fucDAu5RHlnbt2mVaWqRx48aaMGGCy9vhatWqpVmzZplmMbz++usOP4iRJXiTZs2aadmyZZbWo7/kkks0Z84cXXHFFabtztbyLfrePHv2rAoKCiyfl5X3OVmCNynLLLlSUFCg//3f/9W3335rbKtVq5Y+/PBD1a5d29IYZAnepKyylJWVpTFjxhjtQYMGqUGDBhd8vkWRJXiTsrwuUXsoGxS3AXi17777TidPnjTaXbp0cfvQOen8t6cDBgwwbVu9erXDvtHR0aZ23bp1Ld/e2rBhQ1P7+PHjxfrUrFnT9E3ssWPHLI3trL/9+QJWlEeWVq1aJZvNZrT79+9vaZ23unXrqkuXLkY7LS3NmAlRFFmCt4mJidGCBQs0b9489e7dWw0bNlRERISCgoIUHR2t1q1ba/z48Vq7dq1atWqlI0eOmPaPjY11OG5UVJTxc15ensu1Hu3ZP2DI0fucLMHblFWWXBkzZowxE1U6X4h4//33demll1oegyzB25RFlubNm2dcW+rXr6/BgweX+nmTJXibsrouUXsoG67nvQNABSt6m6h0fn03q+z7bt++3WE/+wtP1apVLR/Dvm/hOnRFBQUFqV69esaaWMeOHZPNZnO6ppa9ooWKkJAQ1a1b1/L5AYXKI0v2x2jVqpVHx/j444+NdnJysm677TZTH7IEb3XjjTfqxhtvdNsvKSnJ1G7evLnDfrGxsdqyZYvRPnr0qOWZpPbFbUd/XJEleKvSzpIzr7zyiulOo9DQUL377rtq3LixR+OQJXir0sxSWlqa8fPBgwd1zTXXuB3X/oHlt99+u6n9+eefm97vZAneqiw+4xVF7aF0MHMbgFc7ffq0qe1qCQV7NWvWNLWLfjArqvCheYU8eeiC/dqmjh4QIZkvYufOnTMe5udOZmam6QFH9evXt3xhAooqjyzZH8N+v9I4BlmCLyt6+2hgYKCuuuoqh/3sb/f+7bffLB/Dvq+zW8fJEnyZ1Sw5Mnv2bM2ZM8doBwcH66233rJUsHOELMGXeZolm82m/Px8t//Zs/990Tv9CpEl+DKrWaL2UDYobgPwavb/YJ87d87yvvZ9Q0JCHPaLjY1VjRo1jLaj23ucsb9tJzIy0mG/6667ztR2tD6WI0lJSaa1Vlu2bGn53ICiyiNL9k/n9uQBJlaPQZbgq/78809t3brVaLdv397pA+vs3+fbtm2zdIxz585p586dRrtRo0ZOH2hEluCrPMmSvYULF2ratGlGOzAwUNOmTVPr1q1LfD5kCb7qQrJUFsgSfJUnWaL2UDYobgPwavb/YO/bt8/yvnv37jW1i15EivL39zc9nCEjI8PycewLDk2aNHHYr2PHjqb2hg0bLI2/fv16l+MAVpVHluy3l8UxyBJ81aJFi0x/MNx///1O+zZr1sy07vZXX31l6cuijRs3mmYAuXqfkyX4Kk+yVNTq1as1fvx4o+3v768pU6Zc8HuYLMFXWc3Sv/71L+3atcuj/+yXtEtISDD9vl69esWOQ5bgqzy5LlF7KBsUtwF4tbi4OFP7008/tbzv2rVrTW1Xt5t27tzZ1F6+fLmlY9j3u+mmmxz2q1+/vmkdx02bNplu+XEkIyPD9KCjmjVrWnpiM+BIeWTJ/hiffPKJpfFtNluxvs6OQZbgiw4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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 Dec 14 2024\n",
      "\n",
      "Python implementation: CPython\n",
      "Python version       : 3.12.5\n",
      "IPython version      : 8.27.0\n",
      "\n",
      "pytensor: 2.26.4\n",
      "xarray  : 2024.7.0\n",
      "\n",
      "pytensor   : 2.26.4\n",
      "arviz      : 0.19.0\n",
      "numpy      : 1.26.4\n",
      "pandas     : 2.2.2\n",
      "matplotlib : 3.9.2\n",
      "pymc_extras: 0.2.0\n",
      "pymc       : 5.19.1\n",
      "\n",
      "Watermark: 2.5.0\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": "default",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.5"
  },
  "myst": {
   "substitutions": {
    "extra_dependencies": "pymc-experimental"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}