{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "bc1f69aa-913d-49fa-8e20-58f953301851",
   "metadata": {},
   "source": [
    "(model_configuration)=\n",
    "# Model Configuration\n",
    "\n",
    "This notebook provides details about the model configuration in PyMC-Marketing. This API provides a very flexible way to express the model Priors and likelihoods so that we can have enough expressiveness to build custom models."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d539a0c",
   "metadata": {},
   "source": [
    "## Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "9d6bc077-24d1-47de-8542-5497ade670e3",
   "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",
    "\n",
    "from pymc_marketing.model_config import ModelConfigError, parse_model_config\n",
    "from pymc_marketing.prior import Prior\n",
    "\n",
    "az.style.use(\"arviz-darkgrid\")\n",
    "plt.rcParams[\"figure.figsize\"] = [12, 7]\n",
    "plt.rcParams[\"figure.dpi\"] = 100\n",
    "\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "%config InlineBackend.figure_format = \"retina\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "6fa99350-cc39-4ef9-9c9a-f6e0f7091636",
   "metadata": {},
   "outputs": [],
   "source": [
    "seed = sum(map(ord, \"Create priors to reflect your marketing beliefs\"))\n",
    "rng = np.random.default_rng(seed)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5f28af2-a8a2-4046-ad65-940464862424",
   "metadata": {},
   "source": [
    "## Prior Distributions\n",
    "\n",
    "The {class}`~pymc_marketing.prior.Prior` class is our way to expression distributions and relationships between them.\n",
    "\n",
    "### Basic Usage\n",
    "\n",
    "Every prior will need a distribution name that comes from `PyMC`. View the full list in the documentation [here](https://www.pymc.io/projects/docs/en/stable/api/distributions.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "34815050-4f1b-4345-b31b-466fb357a974",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Prior(\"Normal\")"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scalar_distribution = Prior(\"Normal\")\n",
    "scalar_distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b76493fe-48a1-472e-9c8a-fbf632d89baf",
   "metadata": {},
   "source": [
    "If not, then an exception will be raised."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "06314bd5-ebce-4c41-b2c5-b99143c13192",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PyMC doesn't have a distribution of name 'UnknownDistribution'\n"
     ]
    }
   ],
   "source": [
    "try:\n",
    "    Prior(\"UnknownDistribution\")\n",
    "except Exception as e:\n",
    "    print(e)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d76c8fbd-5a22-408d-af96-c9a0ae712da5",
   "metadata": {},
   "source": [
    "Specific parameters can be passed as **keyword arguments** but are not required if the `PyMC` distribution has defaults."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d12e116e-32f4-4f15-a9ee-4d6a0472590c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Prior(\"Normal\", mu=0, sigma=3.5)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scalar_distribution = Prior(\"Normal\", mu=0, sigma=3.5)\n",
    "scalar_distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b46a0bd-d178-4afc-9f5e-3dcf19170e7e",
   "metadata": {},
   "source": [
    "There will be a check at initialization against the `PyMC` distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "38a7db8f-9cc0-4e5b-8c64-c04415b0f35a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameters {'b', 'mu'} are not a subset of the pymc distribution parameters {'mu', 'sigma', 'tau'}\n"
     ]
    }
   ],
   "source": [
    "try:\n",
    "    Prior(\"Normal\", mu=0, b=1)\n",
    "except Exception as e:\n",
    "    print(e)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4bb33ab-9045-4701-9daa-eaa3b4b6d80c",
   "metadata": {},
   "source": [
    "However, there are some limitations to that. Take this invalid parameterization below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a8dcb6f8-1357-4de4-b5d5-a30ab2c48e5b",
   "metadata": {},
   "outputs": [],
   "source": [
    "invalid_distribution = Prior(\"Normal\", mu=1, sigma=1, tau=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "660cb88e-3693-43fa-819e-866cd06aba81",
   "metadata": {},
   "source": [
    "The `create_variable` method is used to make variables from this distribution and it isn't until then that there is an error."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "5e1df586-c4d2-4ac0-9a27-cc3313a0005b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Can't pass both tau and sigma\n"
     ]
    }
   ],
   "source": [
    "with pm.Model():\n",
    "    try:\n",
    "        invalid_distribution.create_variable(\"mu\")\n",
    "    except Exception as e:\n",
    "        print(e)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9db15fc8-86ac-4a4f-94f2-54bbe7e6fc1e",
   "metadata": {},
   "source": [
    "This goes for incorrect values as well!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "bb04847a-0500-4597-9fbe-bb772607d4de",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Prior(\"Normal\", mu=1, sigma=-1)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "invalid_distribution = Prior(\"Normal\", mu=1, sigma=-1)\n",
    "invalid_distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5de45592-94fb-4bb8-976f-48edf4244a57",
   "metadata": {},
   "source": [
    "The `dims` parameter are used to express the dimensions of the distribution. This variable is not part of a model so the values are not reflected with the distribution itself."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "925e49bf-97f3-4fa8-863e-2655abc65e82",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Prior(\"Normal\", dims=\"channel\")"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vector_distribution = Prior(\"Normal\", dims=\"channel\")\n",
    "vector_distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "56f329cd-c5fc-44c2-9c27-07d33fe9697c",
   "metadata": {},
   "source": [
    "If there are dimensions, then the coords need to exist in the larger model. But they exist separately and can defined in advance.\n",
    "\n",
    "```{tip}\n",
    "Each `Prior` instance is just instructions to create a variable, so they can be used multiple times!\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "ad58dacf-9f56-47f9-b5ca-6678f27d5856",
   "metadata": {},
   "outputs": [
    {
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       "<g id=\"clust1\" class=\"cluster\">\n",
       "<title>clusterchannel (2)</title>\n",
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       "<text text-anchor=\"middle\" x=\"170\" y=\"-15.8\" font-family=\"Times,serif\" font-size=\"14.00\">channel (2)</text>\n",
       "</g>\n",
       "<!-- alpha -->\n",
       "<g id=\"node1\" class=\"node\">\n",
       "<title>alpha</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"159\" cy=\"-76.48\" rx=\"41.94\" ry=\"37.45\"/>\n",
       "<text text-anchor=\"middle\" x=\"159\" y=\"-87.78\" font-family=\"Times,serif\" font-size=\"14.00\">alpha</text>\n",
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       "<text text-anchor=\"middle\" x=\"159\" y=\"-57.78\" font-family=\"Times,serif\" font-size=\"14.00\">Normal</text>\n",
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       "<!-- beta -->\n",
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       "<text text-anchor=\"middle\" x=\"58\" y=\"-72.78\" font-family=\"Times,serif\" font-size=\"14.00\">~</text>\n",
       "<text text-anchor=\"middle\" x=\"58\" y=\"-57.78\" font-family=\"Times,serif\" font-size=\"14.00\">Normal</text>\n",
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       "<graphviz.graphs.Digraph at 0x7c23673c4d10>"
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     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coords = {\"channel\": [\"C1\", \"C2\"]}\n",
    "with pm.Model(coords=coords) as model:\n",
    "    alpha = vector_distribution.create_variable(\"alpha\")\n",
    "    beta = vector_distribution.create_variable(\"beta\")\n",
    "\n",
    "pm.model_to_graphviz(model)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "27f9583f-b676-4ac2-85a5-d522815de5e3",
   "metadata": {},
   "source": [
    "If the coords were not specified then this would cause a PyMC error."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "76a89202-7f68-4e89-a77a-ae917b1b3573",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\"Dimensions {'channel'} are unknown to the model and cannot be used to specify a `shape`.\"\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as model:\n",
    "    try:\n",
    "        vector_distribution.create_variable(\"var\")\n",
    "    except Exception as e:\n",
    "        print(e)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1000cc0-2087-48b0-a276-f8921f5db750",
   "metadata": {},
   "source": [
    "The variables can get arbitrarily large as well by providing additional dims in a tuple."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "26101b33-78b3-47fc-996f-140660efb1c9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Prior(\"Normal\", dims=(\"channel\", \"geo\"))"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix_distribution = Prior(\"Normal\", dims=(\"channel\", \"geo\"))\n",
    "matrix_distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "d129b86f-80ac-473b-b815-9a7ef733ab5d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Prior(\"Normal\", dims=(\"channel\", \"geo\", \"store\"))"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tensor_distribution = Prior(\"Normal\", dims=(\"channel\", \"geo\", \"store\"))\n",
    "tensor_distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "15d51049-02e6-42e1-a31c-942a855347fb",
   "metadata": {},
   "source": [
    "### Hierarchical Variables\n",
    "\n",
    "Hierarchical variables can be defined by using distributions as the parameters of another distribution. The parent distributions will usually have a larger dimensionality than each of the parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "5620b88f-5137-4f4b-8ffb-f7362deaea85",
   "metadata": {},
   "outputs": [],
   "source": [
    "hierarchical_variable = Prior(\n",
    "    \"Normal\",\n",
    "    mu=Prior(\"Normal\"),\n",
    "    sigma=Prior(\"HalfNormal\"),\n",
    "    dims=\"channel\",\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "32c14b21-66b0-4948-9804-870c25876cbe",
   "metadata": {},
   "source": [
    "We can use the `to_graph` method to create visualize the variable with dummy coordinates.\n",
    "\n",
    "```{note}\n",
    "No need to worry about variable naming! The child parameters will all be automatically named based on the parent.\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "e830baac-08fd-492a-ae65-0f6aa36debf9",
   "metadata": {},
   "outputs": [
    {
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     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hierarchical_variable.to_graph()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b80a4e49-bb8c-4e4d-b533-c00ab150d886",
   "metadata": {},
   "source": [
    "```{warning}\n",
    "The validity of the parameter values will not be checked. \n",
    "```\n",
    "\n",
    "There can be negative sigma parameter in a Normal distribution whether that comes from value or another distribution!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "b82d2483-1064-4014-a0c5-498f95ab6b0d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Prior(\"Normal\", mu=1, sigma=-1)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Prior(\"Normal\", mu=1, sigma=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "3062face-a9c6-446d-8c93-91b99af18059",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Prior(\"Normal\", sigma=Prior(\"Normal\"))"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Prior(\"Normal\", sigma=Prior(\"Normal\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0d12fd8-07ef-4fcc-816f-cabd6667c1dc",
   "metadata": {},
   "source": [
    "```{tip}\n",
    "Model reparamterizations can help with model convergence depending on the model posterior!\n",
    "```\n",
    "\n",
    "For Normal distribution, the common non-centered parameterization is supported with the `centered` flag."
   ]
  },
  {
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   "execution_count": 19,
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   "source": [
    "non_centered_hierarchical_variable = Prior(\n",
    "    \"Normal\",\n",
    "    mu=Prior(\"Normal\"),\n",
    "    sigma=Prior(\"HalfNormal\"),\n",
    "    dims=\"channel\",\n",
    "    # Flag for non-centered\n",
    "    centered=False,\n",
    ")\n",
    "non_centered_hierarchical_variable.to_graph()"
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   "cell_type": "markdown",
   "id": "003ba849-188c-47ac-98c0-248f5c5a08c3",
   "metadata": {},
   "source": [
    "Other distributions can be hierarchical as well. Just use distributions for parameters of a parent distribution. For instance, the Beta distribution has two positive parameters, `alpha` and `beta` which can be reflect as HalfNormal distributions."
   ]
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   "execution_count": 20,
   "id": "04bf7a16-89a5-4ef7-865e-aab5fe576ca6",
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   "source": [
    "zero_to_one_variable = Prior(\n",
    "    \"Beta\",\n",
    "    alpha=Prior(\"HalfNormal\"),\n",
    "    beta=Prior(\"HalfNormal\"),\n",
    "    dims=\"channel\",\n",
    ")\n",
    "zero_to_one_variable.to_graph()"
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  {
   "cell_type": "markdown",
   "id": "485d6608-228c-491b-93ec-0af713508a25",
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   "source": [
    "### Transformations\n",
    "\n",
    "The `transform` variable can be used for any of the distributions to change its domain.\n",
    "\n",
    "These transformations will be taken from `pytensor.tensor` or `pm.math` in that order.\n",
    "\n",
    "Below is a non-centered hierarchical Normal distribution that is put through a sigmoid function in order to change the domain to (0, 1)."
   ]
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   "execution_count": 21,
   "id": "33529f87-e8e0-471d-8a09-3c7df6b9dcaa",
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   "source": [
    "hierarchical_zero_to_one_distribution = Prior(\n",
    "    \"Normal\",\n",
    "    mu=Prior(\"Normal\"),\n",
    "    sigma=Prior(\"HalfNormal\"),\n",
    "    dims=\"channel\",\n",
    "    centered=False,\n",
    "    transform=\"sigmoid\",\n",
    ")\n",
    "hierarchical_zero_to_one_distribution.to_graph()"
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  {
   "cell_type": "markdown",
   "id": "ee2270a5-2c73-4464-b924-59d01133dc5d",
   "metadata": {},
   "source": [
    "### Prior Visualization\n",
    "\n",
    "For scalar distributions, make use of the `preliz` attribute of the model in order to visualize. \n",
    "\n",
    "```{tip}\n",
    "Defaults for the parameters will have to be provided or there will be an error.\n",
    "```"
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  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "68ac9293-3d2c-4797-81ed-a50171c7f384",
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      "text/plain": [
       "<Figure size 1200x700 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 582,
       "width": 1261
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "beta_distribution = Prior(\"Beta\", alpha=1, beta=4)\n",
    "\n",
    "beta_distribution.preliz.plot_pdf();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d1a6d281-9646-48e1-ab09-6e9de21e9c11",
   "metadata": {},
   "source": [
    "```{tip}\n",
    "Using the `constrain` method can help hone in on a prior. It is a wrapper around [PreliZ's `maxent` function](https://preliz.readthedocs.io/en/latest/api_reference.html#preliz.unidimensional.maxent).\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "6a02cdb4-9fe9-4eb5-97a3-91fd7abf1835",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Prior(\"Normal\", mu=4.999999933423391, sigma=0.5102139704250529)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "constrained_distribution = Prior(\"Normal\").constrain(lower=4, upper=6)\n",
    "constrained_distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "07ef8e38",
   "metadata": {},
   "source": [
    "To keep a parameter value fixed, pass it to the Prior instance. In the following example, the mean is fixed at 2. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "59d7fecc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Prior(\"Gamma\", mu=2.0, sigma=0.7030365085992409)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "constrained_distribution = Prior(\"Gamma\", mu=2).constrain(lower=1, upper=10)\n",
    "constrained_distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "007646bd-61f4-4a2d-8400-14c36e08f289",
   "metadata": {},
   "source": [
    "For more complicated distributions, consider using the `sample_prior` method in order to access the prior. Or PreliZ's functions like [predictive explorer](https://preliz.readthedocs.io/en/latest/examples/observed_space_examples.html#predictive-explorer).\n",
    "\n",
    "\n",
    "```{note}\n",
    "Any coordinates will have to be passed like in `pm.Model`.\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "8c2b4ea7-c33d-4d86-a7f8-18434bd0a298",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling: [var_raw_mu, var_raw_offset, var_raw_sigma_raw]\n"
     ]
    },
    {
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       "  --xr-disabled-color: var(--jp-layout-color3, #bdbdbd);\n",
       "  --xr-background-color: var(--jp-layout-color0, white);\n",
       "  --xr-background-color-row-even: var(--jp-layout-color1, white);\n",
       "  --xr-background-color-row-odd: var(--jp-layout-color2, #eeeeee);\n",
       "}\n",
       "\n",
       "html[theme=dark],\n",
       "body[data-theme=dark],\n",
       "body.vscode-dark {\n",
       "  --xr-font-color0: rgba(255, 255, 255, 1);\n",
       "  --xr-font-color2: rgba(255, 255, 255, 0.54);\n",
       "  --xr-font-color3: rgba(255, 255, 255, 0.38);\n",
       "  --xr-border-color: #1F1F1F;\n",
       "  --xr-disabled-color: #515151;\n",
       "  --xr-background-color: #111111;\n",
       "  --xr-background-color-row-even: #111111;\n",
       "  --xr-background-color-row-odd: #313131;\n",
       "}\n",
       "\n",
       ".xr-wrap {\n",
       "  display: block !important;\n",
       "  min-width: 300px;\n",
       "  max-width: 700px;\n",
       "}\n",
       "\n",
       ".xr-text-repr-fallback {\n",
       "  /* fallback to plain text repr when CSS is not injected (untrusted notebook) */\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-header {\n",
       "  padding-top: 6px;\n",
       "  padding-bottom: 6px;\n",
       "  margin-bottom: 4px;\n",
       "  border-bottom: solid 1px var(--xr-border-color);\n",
       "}\n",
       "\n",
       ".xr-header > div,\n",
       ".xr-header > ul {\n",
       "  display: inline;\n",
       "  margin-top: 0;\n",
       "  margin-bottom: 0;\n",
       "}\n",
       "\n",
       ".xr-obj-type,\n",
       ".xr-array-name {\n",
       "  margin-left: 2px;\n",
       "  margin-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-obj-type {\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-sections {\n",
       "  padding-left: 0 !important;\n",
       "  display: grid;\n",
       "  grid-template-columns: 150px auto auto 1fr 20px 20px;\n",
       "}\n",
       "\n",
       ".xr-section-item {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-section-item input {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-section-item input + label {\n",
       "  color: var(--xr-disabled-color);\n",
       "}\n",
       "\n",
       ".xr-section-item input:enabled + label {\n",
       "  cursor: pointer;\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-section-item input:enabled + label:hover {\n",
       "  color: var(--xr-font-color0);\n",
       "}\n",
       "\n",
       ".xr-section-summary {\n",
       "  grid-column: 1;\n",
       "  color: var(--xr-font-color2);\n",
       "  font-weight: 500;\n",
       "}\n",
       "\n",
       ".xr-section-summary > span {\n",
       "  display: inline-block;\n",
       "  padding-left: 0.5em;\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:disabled + label {\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-section-summary-in + label:before {\n",
       "  display: inline-block;\n",
       "  content: '►';\n",
       "  font-size: 11px;\n",
       "  width: 15px;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:disabled + label:before {\n",
       "  color: var(--xr-disabled-color);\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:checked + label:before {\n",
       "  content: '▼';\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:checked + label > span {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-section-summary,\n",
       ".xr-section-inline-details {\n",
       "  padding-top: 4px;\n",
       "  padding-bottom: 4px;\n",
       "}\n",
       "\n",
       ".xr-section-inline-details {\n",
       "  grid-column: 2 / -1;\n",
       "}\n",
       "\n",
       ".xr-section-details {\n",
       "  display: none;\n",
       "  grid-column: 1 / -1;\n",
       "  margin-bottom: 5px;\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:checked ~ .xr-section-details {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-array-wrap {\n",
       "  grid-column: 1 / -1;\n",
       "  display: grid;\n",
       "  grid-template-columns: 20px auto;\n",
       "}\n",
       "\n",
       ".xr-array-wrap > label {\n",
       "  grid-column: 1;\n",
       "  vertical-align: top;\n",
       "}\n",
       "\n",
       ".xr-preview {\n",
       "  color: var(--xr-font-color3);\n",
       "}\n",
       "\n",
       ".xr-array-preview,\n",
       ".xr-array-data {\n",
       "  padding: 0 5px !important;\n",
       "  grid-column: 2;\n",
       "}\n",
       "\n",
       ".xr-array-data,\n",
       ".xr-array-in:checked ~ .xr-array-preview {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-array-in:checked ~ .xr-array-data,\n",
       ".xr-array-preview {\n",
       "  display: inline-block;\n",
       "}\n",
       "\n",
       ".xr-dim-list {\n",
       "  display: inline-block !important;\n",
       "  list-style: none;\n",
       "  padding: 0 !important;\n",
       "  margin: 0;\n",
       "}\n",
       "\n",
       ".xr-dim-list li {\n",
       "  display: inline-block;\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "}\n",
       "\n",
       ".xr-dim-list:before {\n",
       "  content: '(';\n",
       "}\n",
       "\n",
       ".xr-dim-list:after {\n",
       "  content: ')';\n",
       "}\n",
       "\n",
       ".xr-dim-list li:not(:last-child):after {\n",
       "  content: ',';\n",
       "  padding-right: 5px;\n",
       "}\n",
       "\n",
       ".xr-has-index {\n",
       "  font-weight: bold;\n",
       "}\n",
       "\n",
       ".xr-var-list,\n",
       ".xr-var-item {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-var-item > div,\n",
       ".xr-var-item label,\n",
       ".xr-var-item > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-even);\n",
       "  margin-bottom: 0;\n",
       "}\n",
       "\n",
       ".xr-var-item > .xr-var-name:hover span {\n",
       "  padding-right: 5px;\n",
       "}\n",
       "\n",
       ".xr-var-list > li:nth-child(odd) > div,\n",
       ".xr-var-list > li:nth-child(odd) > label,\n",
       ".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-odd);\n",
       "}\n",
       "\n",
       ".xr-var-name {\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-var-dims {\n",
       "  grid-column: 2;\n",
       "}\n",
       "\n",
       ".xr-var-dtype {\n",
       "  grid-column: 3;\n",
       "  text-align: right;\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-var-preview {\n",
       "  grid-column: 4;\n",
       "}\n",
       "\n",
       ".xr-index-preview {\n",
       "  grid-column: 2 / 5;\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-var-name,\n",
       ".xr-var-dims,\n",
       ".xr-var-dtype,\n",
       ".xr-preview,\n",
       ".xr-attrs dt {\n",
       "  white-space: nowrap;\n",
       "  overflow: hidden;\n",
       "  text-overflow: ellipsis;\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-var-name:hover,\n",
       ".xr-var-dims:hover,\n",
       ".xr-var-dtype:hover,\n",
       ".xr-attrs dt:hover {\n",
       "  overflow: visible;\n",
       "  width: auto;\n",
       "  z-index: 1;\n",
       "}\n",
       "\n",
       ".xr-var-attrs,\n",
       ".xr-var-data,\n",
       ".xr-index-data {\n",
       "  display: none;\n",
       "  background-color: var(--xr-background-color) !important;\n",
       "  padding-bottom: 5px !important;\n",
       "}\n",
       "\n",
       ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
       ".xr-var-data-in:checked ~ .xr-var-data,\n",
       ".xr-index-data-in:checked ~ .xr-index-data {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       ".xr-var-data > table {\n",
       "  float: right;\n",
       "}\n",
       "\n",
       ".xr-var-name span,\n",
       ".xr-var-data,\n",
       ".xr-index-name div,\n",
       ".xr-index-data,\n",
       ".xr-attrs {\n",
       "  padding-left: 25px !important;\n",
       "}\n",
       "\n",
       ".xr-attrs,\n",
       ".xr-var-attrs,\n",
       ".xr-var-data,\n",
       ".xr-index-data {\n",
       "  grid-column: 1 / -1;\n",
       "}\n",
       "\n",
       "dl.xr-attrs {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  display: grid;\n",
       "  grid-template-columns: 125px auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt,\n",
       ".xr-attrs dd {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  float: left;\n",
       "  padding-right: 10px;\n",
       "  width: auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt {\n",
       "  font-weight: normal;\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-attrs dt:hover span {\n",
       "  display: inline-block;\n",
       "  background: var(--xr-background-color);\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-attrs dd {\n",
       "  grid-column: 2;\n",
       "  white-space: pre-wrap;\n",
       "  word-break: break-all;\n",
       "}\n",
       "\n",
       ".xr-icon-database,\n",
       ".xr-icon-file-text2,\n",
       ".xr-no-icon {\n",
       "  display: inline-block;\n",
       "  vertical-align: middle;\n",
       "  width: 1em;\n",
       "  height: 1.5em !important;\n",
       "  stroke-width: 0;\n",
       "  stroke: currentColor;\n",
       "  fill: currentColor;\n",
       "}\n",
       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
       "Dimensions:            (chain: 1, draw: 1000, channel: 2)\n",
       "Coordinates:\n",
       "  * chain              (chain) int64 0\n",
       "  * draw               (draw) int64 0 1 2 3 4 5 6 ... 994 995 996 997 998 999\n",
       "  * channel            (channel) &lt;U2 &#x27;C1&#x27; &#x27;C2&#x27;\n",
       "Data variables:\n",
       "    var                (chain, draw, channel) float64 0.336 0.3785 ... 0.7889\n",
       "    var_raw            (chain, draw, channel) float64 -0.6811 -0.496 ... 1.318\n",
       "    var_raw_mu         (chain, draw) float64 -0.527 1.038 1.526 ... 0.8435 1.136\n",
       "    var_raw_offset     (chain, draw, channel) float64 -0.4456 0.08964 ... 0.5605\n",
       "    var_raw_sigma      (chain, draw) float64 0.3459 0.4046 ... 0.4709 0.3259\n",
       "    var_raw_sigma_raw  (chain, draw) float64 -1.062 -0.905 ... -0.7531 -1.121\n",
       "Attributes:\n",
       "    created_at:                 2024-09-09T13:18:06.084229+00:00\n",
       "    arviz_version:              0.20.0.dev0\n",
       "    inference_library:          pymc\n",
       "    inference_library_version:  5.15.1</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-c4321557-0692-4713-91d2-a82f572d4b5f' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-c4321557-0692-4713-91d2-a82f572d4b5f' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>chain</span>: 1</li><li><span class='xr-has-index'>draw</span>: 1000</li><li><span class='xr-has-index'>channel</span>: 2</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-7f80c294-74f7-48ba-a259-661be653dc36' class='xr-section-summary-in' type='checkbox'  checked><label for='section-7f80c294-74f7-48ba-a259-661be653dc36' class='xr-section-summary' >Coordinates: <span>(3)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>chain</span></div><div class='xr-var-dims'>(chain)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0</div><input id='attrs-e654e7dc-efda-4c63-a58a-bc687e35ff91' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-e654e7dc-efda-4c63-a58a-bc687e35ff91' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-053e309c-5968-4283-892a-cfbacc42813c' class='xr-var-data-in' type='checkbox'><label for='data-053e309c-5968-4283-892a-cfbacc42813c' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>draw</span></div><div class='xr-var-dims'>(draw)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 5 ... 995 996 997 998 999</div><input id='attrs-71b4e337-b745-4245-85f0-942a50e4931c' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-71b4e337-b745-4245-85f0-942a50e4931c' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-eee7b188-e0d0-4dd9-94ad-8510f31a2176' class='xr-var-data-in' type='checkbox'><label for='data-eee7b188-e0d0-4dd9-94ad-8510f31a2176' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([  0,   1,   2, ..., 997, 998, 999])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>channel</span></div><div class='xr-var-dims'>(channel)</div><div class='xr-var-dtype'>&lt;U2</div><div class='xr-var-preview xr-preview'>&#x27;C1&#x27; &#x27;C2&#x27;</div><input id='attrs-4fa4e9f7-e696-4742-8cc7-fe3be18a3bae' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-4fa4e9f7-e696-4742-8cc7-fe3be18a3bae' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-041bf963-2e18-4055-9ce6-d1bc4c527fb2' class='xr-var-data-in' type='checkbox'><label for='data-041bf963-2e18-4055-9ce6-d1bc4c527fb2' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([&#x27;C1&#x27;, &#x27;C2&#x27;], dtype=&#x27;&lt;U2&#x27;)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-4052e4b5-6db8-4d01-a494-17f9bd1008ae' class='xr-section-summary-in' type='checkbox'  checked><label for='section-4052e4b5-6db8-4d01-a494-17f9bd1008ae' class='xr-section-summary' >Data variables: <span>(6)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>var</span></div><div class='xr-var-dims'>(chain, draw, channel)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.336 0.3785 ... 0.7969 0.7889</div><input id='attrs-c8e93b98-4337-47b1-863a-552b401f8b01' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-c8e93b98-4337-47b1-863a-552b401f8b01' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-bbe74957-a3a7-432b-89ca-fa92617acd55' class='xr-var-data-in' type='checkbox'><label for='data-bbe74957-a3a7-432b-89ca-fa92617acd55' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[[0.33602329, 0.37849269],\n",
       "        [0.77569514, 0.73908473],\n",
       "        [0.76582254, 0.830907  ],\n",
       "        ...,\n",
       "        [0.34984391, 0.20997451],\n",
       "        [0.76820991, 0.83378516],\n",
       "        [0.79693798, 0.78891027]]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>var_raw</span></div><div class='xr-var-dims'>(chain, draw, channel)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>-0.6811 -0.496 ... 1.367 1.318</div><input id='attrs-5370cf37-33bd-4011-aab8-8908c5f44149' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-5370cf37-33bd-4011-aab8-8908c5f44149' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-759e8c35-00b5-4313-8c35-3e3cbe0ad48d' class='xr-var-data-in' type='checkbox'><label for='data-759e8c35-00b5-4313-8c35-3e3cbe0ad48d' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[[-0.68106661, -0.4959509 ],\n",
       "        [ 1.24075349,  1.04121686],\n",
       "        [ 1.18487128,  1.59206903],\n",
       "        ...,\n",
       "        [-0.61972537, -1.32507905],\n",
       "        [ 1.19823081,  1.61269463],\n",
       "        [ 1.3672654 ,  1.31836926]]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>var_raw_mu</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>-0.527 1.038 1.526 ... 0.8435 1.136</div><input id='attrs-025bc452-a2ca-434a-8b1a-f60076494797' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-025bc452-a2ca-434a-8b1a-f60076494797' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-92cddb8e-aba8-4510-8620-4929778575c6' class='xr-var-data-in' type='checkbox'><label for='data-92cddb8e-aba8-4510-8620-4929778575c6' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[-5.26954020e-01,  1.03767721e+00,  1.52587004e+00,\n",
       "         1.31068152e+00,  2.38224064e-01, -9.15606854e-02,\n",
       "         1.34951389e+00, -1.28258253e+00,  1.65655525e+00,\n",
       "        -3.69474700e-01,  2.45313844e-01, -7.42131395e-02,\n",
       "         2.10335513e-01, -4.49634310e-01,  2.55078082e-01,\n",
       "        -8.72162018e-01,  3.48025423e-01,  2.29318608e+00,\n",
       "        -1.68946300e+00, -3.92775115e-01, -3.18843383e-01,\n",
       "        -7.92344104e-01,  4.37500323e-02, -7.26653530e-01,\n",
       "        -9.27155387e-01,  7.97692019e-01,  1.09571799e+00,\n",
       "         9.48849140e-01,  5.89356297e-01,  4.04912350e-01,\n",
       "        -5.01304558e-01, -1.88485215e+00,  1.20567194e-01,\n",
       "         2.59191443e-01, -2.44623777e-01, -7.28007904e-01,\n",
       "         7.28888960e-01,  8.75447580e-02, -8.12717589e-01,\n",
       "         5.02074969e-01, -2.26275396e-01,  6.49160142e-01,\n",
       "        -1.84085099e-01, -7.70015581e-01,  5.93401536e-01,\n",
       "        -1.19508453e+00, -8.56052517e-01, -9.70530981e-01,\n",
       "         2.28074070e-01, -7.30808639e-02,  9.84480195e-02,\n",
       "        -9.13223839e-02, -1.53039339e+00,  8.43763623e-01,\n",
       "        -9.41755664e-02,  1.31282115e+00, -1.67932770e+00,\n",
       "        -8.46758061e-01,  1.39041501e+00,  1.51236040e+00,\n",
       "...\n",
       "        -4.77991747e-01,  1.59201606e+00, -6.13379387e-01,\n",
       "         1.85420782e-01,  1.32743241e+00,  1.70211801e+00,\n",
       "         1.70203576e+00,  9.36442585e-01, -3.21146251e-01,\n",
       "        -3.42323993e-01, -7.41320338e-01,  6.75565903e-01,\n",
       "        -1.12019751e+00, -3.60841658e-01, -5.29801545e-01,\n",
       "         7.41338966e-01, -3.71720152e-01,  1.15065274e+00,\n",
       "         1.31670532e+00, -4.93084043e-01, -1.37370237e+00,\n",
       "        -4.49154124e-01,  1.05585110e+00,  9.81957330e-01,\n",
       "        -6.57397398e-01,  3.07251821e-01,  9.56065529e-01,\n",
       "        -1.23530916e+00,  1.26430981e-01, -5.71052076e-02,\n",
       "         4.38158102e-01,  9.63558688e-01, -5.80362251e-02,\n",
       "        -1.47962972e-01,  1.56350465e+00,  1.16690793e+00,\n",
       "        -1.02200156e-02,  1.66389532e-01, -1.46612606e+00,\n",
       "         1.01043724e+00, -7.89777902e-01, -1.85367748e+00,\n",
       "         1.52355588e-01,  4.10928830e-01,  6.20254863e-02,\n",
       "         7.09396366e-01, -2.52423119e+00,  8.46411547e-01,\n",
       "        -5.70259561e-01, -3.78882987e-02, -4.05355418e-01,\n",
       "        -4.18985025e-01, -8.99948818e-01, -7.89309916e-01,\n",
       "         6.37104941e-01, -1.08363957e+00,  8.43525055e-01,\n",
       "         1.13569421e+00]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>var_raw_offset</span></div><div class='xr-var-dims'>(chain, draw, channel)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>-0.4456 0.08964 ... 0.7106 0.5605</div><input id='attrs-95f69d9c-e0e4-4a62-8ff8-d18ab673c558' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-95f69d9c-e0e4-4a62-8ff8-d18ab673c558' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-2da5a995-6a38-4318-88bd-02f943a4f12e' class='xr-var-data-in' type='checkbox'><label for='data-2da5a995-6a38-4318-88bd-02f943a4f12e' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[[-0.44557269,  0.0896367 ],\n",
       "        [ 0.50196999,  0.0087494 ],\n",
       "        [-0.82466893,  0.16009515],\n",
       "        ...,\n",
       "        [ 1.63353663, -0.85015768],\n",
       "        [ 0.75327689,  1.63346   ],\n",
       "        [ 0.71055462,  0.56052136]]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>var_raw_sigma</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.3459 0.4046 ... 0.4709 0.3259</div><input id='attrs-bbb72235-a0b3-46a5-9086-17cdd6b90dff' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-bbb72235-a0b3-46a5-9086-17cdd6b90dff' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-fff9f6ed-cb08-48a2-9134-3f0cf63cfe22' class='xr-var-data-in' type='checkbox'><label for='data-fff9f6ed-cb08-48a2-9134-3f0cf63cfe22' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[0.34587531, 0.40455861, 0.41349777, 0.40205709, 0.28275283,\n",
       "        0.30305144, 0.46011074, 0.41796206, 0.3544711 , 0.31693253,\n",
       "        0.29979704, 0.31525412, 0.42897328, 0.47088888, 0.36723093,\n",
       "        0.42472   , 0.34267684, 0.39302212, 0.39660436, 0.41424468,\n",
       "        0.30955489, 0.37931752, 0.41059179, 0.4542857 , 0.35728653,\n",
       "        0.34379435, 0.38017607, 0.3290264 , 0.37750758, 0.37564665,\n",
       "        0.41679089, 0.35525572, 0.44007033, 0.34757496, 0.30712211,\n",
       "        0.35804494, 0.35082023, 0.35158368, 0.41351848, 0.47035027,\n",
       "        0.4661122 , 0.33156189, 0.41736224, 0.4548133 , 0.40541666,\n",
       "        0.32603096, 0.3058259 , 0.31515486, 0.30167727, 0.35307321,\n",
       "        0.3275891 , 0.43215209, 0.2895675 , 0.33100919, 0.37254446,\n",
       "        0.33642296, 0.3400955 , 0.29781471, 0.37944252, 0.34799543,\n",
       "        0.42162445, 0.62146485, 0.26973369, 0.43075118, 0.39810285,\n",
       "        0.37339062, 0.32639161, 0.44694868, 0.36090846, 0.32164243,\n",
       "        0.38855953, 0.33683003, 0.35233947, 0.39817017, 0.2971075 ,\n",
       "        0.33511508, 0.35976958, 0.34854387, 0.49728517, 0.27402162,\n",
       "        0.28343149, 0.43108207, 0.38080588, 0.23780503, 0.3157372 ,\n",
       "        0.41421356, 0.30091698, 0.28919233, 0.55416363, 0.34232608,\n",
       "        0.40985235, 0.29898663, 0.37501661, 0.41741698, 0.32122689,\n",
       "        0.37060189, 0.2995365 , 0.32886084, 0.41886281, 0.33570565,\n",
       "...\n",
       "        0.35919838, 0.37337755, 0.32262721, 0.29906758, 0.31844148,\n",
       "        0.361801  , 0.3082266 , 0.31952556, 0.32455638, 0.35755068,\n",
       "        0.32386692, 0.38083621, 0.41529478, 0.51291148, 0.35660524,\n",
       "        0.46481498, 0.40430028, 0.36051399, 0.32263062, 0.42372492,\n",
       "        0.39860553, 0.39146735, 0.33794562, 0.42017499, 0.32263948,\n",
       "        0.28492654, 0.28064267, 0.31805633, 0.36645983, 0.38469294,\n",
       "        0.40867267, 0.37410926, 0.47295881, 0.40298759, 0.39493888,\n",
       "        0.3123832 , 0.34073121, 0.35042727, 0.3013781 , 0.40657372,\n",
       "        0.34078565, 0.41177494, 0.35007591, 0.31511175, 0.33420508,\n",
       "        0.34283203, 0.46052291, 0.36419496, 0.3200748 , 0.36616992,\n",
       "        0.44673809, 0.44406181, 0.3275173 , 0.38436764, 0.31824063,\n",
       "        0.36083445, 0.33738634, 0.3457741 , 0.28849061, 0.42897949,\n",
       "        0.38286717, 0.38796753, 0.29721937, 0.31633777, 0.36132535,\n",
       "        0.38149242, 0.38787993, 0.3603407 , 0.41874603, 0.40448488,\n",
       "        0.49863775, 0.39901021, 0.48077947, 0.45862753, 0.40027408,\n",
       "        0.39010497, 0.41978124, 0.37033936, 0.27249946, 0.32907154,\n",
       "        0.40047   , 0.34095389, 0.37480443, 0.36796608, 0.41320493,\n",
       "        0.27467298, 0.33711484, 0.27390103, 0.37258801, 0.2958531 ,\n",
       "        0.3304755 , 0.37476435, 0.32620143, 0.40221695, 0.32138661,\n",
       "        0.35845468, 0.25492278, 0.28399376, 0.47088363, 0.32590202]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>var_raw_sigma_raw</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>-1.062 -0.905 ... -0.7531 -1.121</div><input id='attrs-59923919-759c-4d3f-ba9e-7cd041faf357' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-59923919-759c-4d3f-ba9e-7cd041faf357' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-b98fbc1d-3606-4530-a517-4c8165f968a3' class='xr-var-data-in' type='checkbox'><label for='data-b98fbc1d-3606-4530-a517-4c8165f968a3' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[-1.06167695, -0.90495865, -0.88310316, -0.91116118, -1.26318216,\n",
       "        -1.19385272, -0.77628808, -0.87236461, -1.03712847, -1.14906636,\n",
       "        -1.20464957, -1.15437623, -0.84636065, -0.75313315, -1.0017644 ,\n",
       "        -0.85632516, -1.07096743, -0.93388939, -0.92481608, -0.88129846,\n",
       "        -1.17261986, -0.96938164, -0.89015576, -0.78902898, -1.02921721,\n",
       "        -1.06771162, -0.96712079, -1.1116173 , -0.97416462, -0.97910634,\n",
       "        -0.87517065, -1.0349174 , -0.82082071, -1.05677494, -1.18050985,\n",
       "        -1.02709677, -1.04748136, -1.04530752, -0.88305307, -0.7542776 ,\n",
       "        -0.7633289 , -1.1039408 , -0.87380075, -0.78786828, -0.90283995,\n",
       "        -1.12076293, -1.18473931, -1.15469114, -1.19839749, -1.04107986,\n",
       "        -1.1159952 , -0.83897769, -1.23936686, -1.10560914, -0.98739889,\n",
       "        -1.0893861 , -1.07852882, -1.21128376, -0.96905215, -1.05556592,\n",
       "        -0.86364029, -0.47567593, -1.31032013, -0.84222466, -0.92104489,\n",
       "        -0.98513016, -1.11965737, -0.80531151, -1.01913094, -1.13431482,\n",
       "        -0.94530889, -1.08817683, -1.04316015, -0.92087579, -1.21366125,\n",
       "        -1.09328128, -1.02229151, -1.05399118, -0.69859163, -1.29454827,\n",
       "        -1.26078483, -0.84145678, -0.96546554, -1.43630414, -1.15284506,\n",
       "        -0.8813736 , -1.20092086, -1.24066332, -0.59029528, -1.07199155,\n",
       "        -0.89195831, -1.20735644, -0.98078495, -0.87366961, -1.13560758,\n",
       "        -0.99262686, -1.205519  , -1.11212061, -0.87021184, -1.09152053,\n",
       "...\n",
       "        -1.02388046, -0.98516518, -1.13125779, -1.20708573, -1.14431655,\n",
       "        -1.01666095, -1.17692004, -1.140918  , -1.12529602, -1.02847815,\n",
       "        -1.12742259, -0.96538588, -0.87876669, -0.667652  , -1.03112588,\n",
       "        -0.76611584, -0.90559742, -1.02022452, -1.13124719, -0.85867081,\n",
       "        -0.91978299, -0.93785317, -1.08487029, -0.867084  , -1.13121974,\n",
       "        -1.25552387, -1.27067306, -1.14552676, -1.00386637, -0.95530981,\n",
       "        -0.89484076, -0.9832074 , -0.74874698, -0.90884952, -0.92902427,\n",
       "        -1.16352464, -1.07666136, -1.04860209, -1.19938966, -0.89999001,\n",
       "        -1.07650159, -0.88727833, -1.04960527, -1.15482793, -1.09600046,\n",
       "        -1.07051465, -0.77539268, -1.01006596, -1.13920057, -1.00465779,\n",
       "        -0.80578279, -0.81179151, -1.1162144 , -0.95615578, -1.1449475 ,\n",
       "        -1.01933602, -1.08652658, -1.06196961, -1.24309274, -0.84634617,\n",
       "        -0.96006716, -0.94683363, -1.2132848 , -1.15094474, -1.01797648,\n",
       "        -0.9636643 , -0.94705945, -1.02070532, -0.87049068, -0.90514093,\n",
       "        -0.69587541, -0.91876828, -0.7323466 , -0.77951688, -0.91560577,\n",
       "        -0.94133943, -0.86802156, -0.99333551, -1.30011866, -1.11148011,\n",
       "        -0.91511642, -1.07600803, -0.9813509 , -0.99976451, -0.88381161,\n",
       "        -1.29217405, -1.08733165, -1.29498843, -0.98728201, -1.21789223,\n",
       "        -1.10722275, -0.98145785, -1.1202402 , -0.91076365, -1.1351105 ,\n",
       "        -1.02595305, -1.3667946 , -1.25880303, -0.75314429, -1.12115849]])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-5b2cd31f-b092-457c-9e06-62ab15b0ba7c' class='xr-section-summary-in' type='checkbox'  ><label for='section-5b2cd31f-b092-457c-9e06-62ab15b0ba7c' class='xr-section-summary' >Indexes: <span>(3)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-index-name'><div>chain</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-8c2f2a5d-8d45-428a-a86e-38013b001830' class='xr-index-data-in' type='checkbox'/><label for='index-8c2f2a5d-8d45-428a-a86e-38013b001830' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Index([0], dtype=&#x27;int64&#x27;, name=&#x27;chain&#x27;))</pre></div></li><li class='xr-var-item'><div class='xr-index-name'><div>draw</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-310a5c69-0136-4fe2-93a0-0ef85b42444a' class='xr-index-data-in' type='checkbox'/><label for='index-310a5c69-0136-4fe2-93a0-0ef85b42444a' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,\n",
       "       ...\n",
       "       990, 991, 992, 993, 994, 995, 996, 997, 998, 999],\n",
       "      dtype=&#x27;int64&#x27;, name=&#x27;draw&#x27;, length=1000))</pre></div></li><li class='xr-var-item'><div class='xr-index-name'><div>channel</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-c418f207-f7c4-465e-9e8d-9a56941304e4' class='xr-index-data-in' type='checkbox'/><label for='index-c418f207-f7c4-465e-9e8d-9a56941304e4' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Index([&#x27;C1&#x27;, &#x27;C2&#x27;], dtype=&#x27;object&#x27;, name=&#x27;channel&#x27;))</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-8a0c84ed-9a85-4659-8373-0fd9ffef8624' class='xr-section-summary-in' type='checkbox'  checked><label for='section-8a0c84ed-9a85-4659-8373-0fd9ffef8624' class='xr-section-summary' >Attributes: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>created_at :</span></dt><dd>2024-09-09T13:18:06.084229+00:00</dd><dt><span>arviz_version :</span></dt><dd>0.20.0.dev0</dd><dt><span>inference_library :</span></dt><dd>pymc</dd><dt><span>inference_library_version :</span></dt><dd>5.15.1</dd></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.Dataset>\n",
       "Dimensions:            (chain: 1, draw: 1000, channel: 2)\n",
       "Coordinates:\n",
       "  * chain              (chain) int64 0\n",
       "  * draw               (draw) int64 0 1 2 3 4 5 6 ... 994 995 996 997 998 999\n",
       "  * channel            (channel) <U2 'C1' 'C2'\n",
       "Data variables:\n",
       "    var                (chain, draw, channel) float64 0.336 0.3785 ... 0.7889\n",
       "    var_raw            (chain, draw, channel) float64 -0.6811 -0.496 ... 1.318\n",
       "    var_raw_mu         (chain, draw) float64 -0.527 1.038 1.526 ... 0.8435 1.136\n",
       "    var_raw_offset     (chain, draw, channel) float64 -0.4456 0.08964 ... 0.5605\n",
       "    var_raw_sigma      (chain, draw) float64 0.3459 0.4046 ... 0.4709 0.3259\n",
       "    var_raw_sigma_raw  (chain, draw) float64 -1.062 -0.905 ... -0.7531 -1.121\n",
       "Attributes:\n",
       "    created_at:                 2024-09-09T13:18:06.084229+00:00\n",
       "    arviz_version:              0.20.0.dev0\n",
       "    inference_library:          pymc\n",
       "    inference_library_version:  5.15.1"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "complicated_distribution = Prior(\n",
    "    \"Normal\",\n",
    "    mu=Prior(\"Normal\", sigma=1),\n",
    "    sigma=Prior(\"Normal\", mu=-1, sigma=0.15, transform=\"exp\"),\n",
    "    centered=False,\n",
    "    dims=\"channel\",\n",
    "    transform=\"sigmoid\",\n",
    ")\n",
    "\n",
    "coords = {\n",
    "    \"channel\": [\"C1\", \"C2\"],\n",
    "}\n",
    "prior = complicated_distribution.sample_prior(\n",
    "    coords=coords, samples=1_000, random_seed=rng\n",
    ")\n",
    "prior"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "876f6d5e-9131-4077-b7cd-a8e0000d2dea",
   "metadata": {},
   "source": [
    "The prior variables can be visualized in whatever way works best. Here is a KDE of the variables to see the marginal distributions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "e7bd00b8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x900 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 911,
       "width": 1011
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(\n",
    "    nrows=2, ncols=1, figsize=(10, 9), sharex=True, sharey=True, layout=\"constrained\"\n",
    ")\n",
    "\n",
    "az.plot_posterior(prior, var_names=[\"var\"], grid=(2, 1), ax=axes)\n",
    "fig.suptitle(\"Prior Distribution\", fontsize=18, fontweight=\"bold\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22c8037e-4168-443b-b1b5-150d73dd4129",
   "metadata": {},
   "source": [
    "Use any workflow to make sense of the prior distribution! For instance, the joint distribution which shows these two channels are correlated due to the hierarchical generation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "c9911821-e9c3-4607-b53e-78c086c6a89c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1200x700 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 711,
       "width": 1211
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_correlation(df: pd.DataFrame, x: str = \"C1\", y: str = \"C2\") -> plt.Axes:\n",
    "    corr = df.loc[:, [x, y]].corr().iloc[0, 1]\n",
    "    title = f\"Joint distribution between {x} and {y} ({corr = :.3f})\"\n",
    "    return df.plot.scatter(x=x, y=y, title=title)\n",
    "\n",
    "\n",
    "ax = prior[\"var\"].to_series().unstack().pipe(plot_correlation)\n",
    "padding = 0.025\n",
    "bounds = (0 - padding, 1 + padding)\n",
    "ax.set(xlim=bounds, ylim=bounds);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "90a9d504-6118-4fb9-a21b-7e01d8e5b5e8",
   "metadata": {},
   "source": [
    "### Automatic Broadcasting\n",
    "\n",
    "The broadcasting of the dims will be handled automatically.\n",
    "\n",
    "For instance, the `mu` of the variable needs to be transposed in order to work with `(\"channel\", \"geo\")` dims.\n",
    "\n",
    "With all this functionality, we can see that the prior distributions can become quite expressive!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "078a2501-0e82-4551-b01a-042450e36ddb",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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   ],
   "source": [
    "def create_2d_variable(mu_dims, sigma_dims) -> Prior:\n",
    "    mu = Prior(\n",
    "        \"Normal\",\n",
    "        mu=Prior(\"Normal\"),\n",
    "        sigma=Prior(\"HalfNormal\"),\n",
    "        dims=mu_dims,\n",
    "    )\n",
    "    sigma = Prior(\n",
    "        \"Normal\",\n",
    "        mu=Prior(\"Normal\"),\n",
    "        sigma=Prior(\"HalfNormal\"),\n",
    "        centered=False,\n",
    "        dims=sigma_dims,\n",
    "        transform=\"exp\",\n",
    "    )\n",
    "    return Prior(\n",
    "        \"Normal\",\n",
    "        mu=mu,\n",
    "        sigma=sigma,\n",
    "        dims=(\"channel\", \"geo\"),\n",
    "    )\n",
    "\n",
    "\n",
    "variable_2d = create_2d_variable(mu_dims=\"channel\", sigma_dims=\"geo\")\n",
    "variable_2d.to_graph()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e018082e-23fb-48ab-ac69-e506a8fe9d9b",
   "metadata": {},
   "source": [
    "And the user can spend more time thinking about just the assumptions of the variables rather than logic to ensure the dimensions work."
   ]
  },
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   "cell_type": "code",
   "execution_count": 29,
   "id": "e0bdf8b8-34b7-4918-8106-2203b7db6152",
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   ],
   "source": [
    "different_assumptions_2d = create_2d_variable(mu_dims=\"channel\", sigma_dims=\"channel\")\n",
    "\n",
    "different_assumptions_2d.to_graph()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e01638c-5e10-4796-a76b-7fd3b1b1ac3c",
   "metadata": {},
   "source": [
    "### Serialization\n",
    "\n",
    "The `to_dict` and `from_dict` methods can be helpful for storage of the distributions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "f34d2031-90f1-4c06-a0ab-2f3133cdb9c1",
   "metadata": {},
   "outputs": [
    {
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       "{'dist': 'Normal',\n",
       " 'kwargs': {'mu': {'dist': 'Normal',\n",
       "   'kwargs': {'mu': {'dist': 'Normal'}, 'sigma': {'dist': 'HalfNormal'}},\n",
       "   'dims': ('channel',)},\n",
       "  'sigma': {'dist': 'Normal',\n",
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       " 'dims': ('channel', 'geo')}"
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     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "variable_2d_dict = variable_2d.to_dict()\n",
    "variable_2d_dict"
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  },
  {
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     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Prior.from_dict(variable_2d_dict).to_graph()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "41abb828-e67b-4995-b20c-a83b965493c3",
   "metadata": {},
   "source": [
    "## Use in PyMC-Marketing\n",
    "\n",
    "Distributions will be expressed in this manner throughout the package including but not limited to: \n",
    "\n",
    "- MMM components\n",
    "    - [media transformations](https://www.pymc-marketing.io/en/stable/notebooks/mmm/mmm_components.html#media-transformations)\n",
    " \n",
    "### Backwards compatibility\n",
    "\n",
    "The `from_dict` method will create a `Prior` instance from the previous format.\n",
    "\n",
    "For instance, take this previous configuration: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "29e66da3-4fba-4f85-8379-f0d237d45123",
   "metadata": {},
   "outputs": [],
   "source": [
    "old_model_config = {\n",
    "    \"alpha\": {\n",
    "        \"dist\": \"Normal\",\n",
    "        \"kwargs\": {\n",
    "            \"mu\": 0,\n",
    "            \"sigma\": 1,\n",
    "        },\n",
    "    },\n",
    "    \"beta\": {\n",
    "        \"dist\": \"Laplace\",\n",
    "        \"kwargs\": {\n",
    "            \"mu\": 1,\n",
    "            \"b\": 0.5,\n",
    "        },\n",
    "    },\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d63987c0-2525-4b12-8415-cd62dd66265f",
   "metadata": {},
   "source": [
    "This can be parsed with the `Prior.from_dict` constructor for each key. Much more consise too!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "92413026-9d9a-4424-b236-09f54b254545",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'alpha': Prior(\"Normal\", mu=0, sigma=1),\n",
       " 'beta': Prior(\"Laplace\", mu=1, b=0.5)}"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_model_config = {\n",
    "    name: Prior.from_dict(key) for name, key in old_model_config.items()\n",
    "}\n",
    "\n",
    "new_model_config"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "1636ae9b-452c-4772-8b60-085c9b044154",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'dist': 'Normal', 'kwargs': {'mu': 0, 'sigma': 1}}"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_model_config[\"alpha\"].to_dict()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "01370c37-2e03-46bc-98c5-fcd8bae1b8e7",
   "metadata": {},
   "source": [
    "The `parse_model_config` function will do just this and is used internally. It also provides some deprecation warnings."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "54e8e716-b2c9-4019-8620-2616f9783576",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'alpha': Prior(\"Normal\", mu=0, sigma=1),\n",
       " 'beta': Prior(\"Laplace\", mu=1, b=0.5)}"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "parse_model_config(old_model_config)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9839e1c3-5026-405e-a019-09a20eaac6a1",
   "metadata": {},
   "source": [
    "As well as the ability to catch some errors while parsing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "00f9e291-3b8f-4457-8451-4b1fb0d0acbb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3 errors occurred while parsing model configuration. Errors: Parameter alpha: PyMC doesn't have a distribution of name 'InvalidDistribution', Parameter beta: Parameters must be one of the following types: (int, float, np.array, Prior, pt.TensorVariable). Incorrect parameters: {'mu': <class 'str'>, 'sigma': <class 'str'>}, Parameter gamma: Parameters {'mu'} are not a subset of the pymc distribution parameters {'sigma', 'tau'}\n"
     ]
    }
   ],
   "source": [
    "invalid_model_config = {\n",
    "    \"alpha\": {\n",
    "        \"dist\": \"InvalidDistribution\",\n",
    "    },\n",
    "    \"beta\": {\n",
    "        \"dist\": \"Normal\",\n",
    "        \"kwargs\": {\"mu\": \"one\", \"sigma\": \"two\"},\n",
    "    },\n",
    "    \"gamma\": {\n",
    "        \"dist\": \"HalfNormal\",\n",
    "        \"kwargs\": {\"mu\": 1},\n",
    "    },\n",
    "}\n",
    "\n",
    "try:\n",
    "    parse_model_config(invalid_model_config)\n",
    "except ModelConfigError as e:\n",
    "    print(e)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "edad3ab9",
   "metadata": {},
   "source": [
    "## Appendix: Validation\n",
    "\n",
    "Behind the scenes, the `Prior` class uses th `validate_call` from [`Pydantic`](https://docs.pydantic.dev/latest/concepts/validators/) to ensure that the parameters are valid.`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "2d9eeb00",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 validation error for __init__\n",
      "distribution\n",
      "  Missing required argument [type=missing_argument, input_value=ArgsKwargs(<unprintable tuple object>), input_type=ArgsKwargs]\n",
      "    For further information visit https://errors.pydantic.dev/2.9/v/missing_argument\n"
     ]
    }
   ],
   "source": [
    "try:\n",
    "    Prior()\n",
    "except Exception as e:\n",
    "    print(e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "b6f909da",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 validation error for __init__\n",
      "1\n",
      "  Input should be a valid string [type=string_type, input_value=1, input_type=int]\n",
      "    For further information visit https://errors.pydantic.dev/2.9/v/string_type\n"
     ]
    }
   ],
   "source": [
    "try:\n",
    "    Prior(1)\n",
    "except Exception as e:\n",
    "    print(e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "818f52e3-7d53-4b62-afd0-4331b1849509",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Last updated: Mon Sep 09 2024\n",
      "\n",
      "Python implementation: CPython\n",
      "Python version       : 3.11.5\n",
      "IPython version      : 8.16.1\n",
      "\n",
      "pymc_marketing: 0.8.0\n",
      "pytensor      : 2.22.1\n",
      "\n",
      "pandas    : 2.1.2\n",
      "matplotlib: 3.8.4\n",
      "arviz     : 0.20.0.dev0\n",
      "numpy     : 1.24.4\n",
      "pymc      : 5.15.1\n",
      "\n",
      "Watermark: 2.4.3\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -n -u -v -iv -w -p pymc_marketing,pytensor"
   ]
  }
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