{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Prior Simulation based calibration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from arviz_plots import plot_ecdf_pit, style\n",
    "import numpy as np\n",
    "import simuk\n",
    "style.use(\"arviz-variat\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Out-of-the-box Prior SBC\n",
    "This example demonstrates how to use the `SBC` class for prior simulation-based calibration, supporting PyMC, Bambi and Numpyro models. By default, the generative model implied by the probabilistic model is used.\n",
    "\n",
    "We perform Prior SBC on the centered eight school model, which is known to have a funnel-shaped posterior distribution. The inference algorithm struggles with this model when $\\tau$ is small, and thus we expect to see deviations from the uniform distribution in the rank statistics.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### PyMC\n",
    "\n",
    "First, define a PyMC model. In this example, we will use the centered eight schools model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pymc as pm\n",
    "\n",
    "data = np.array([28.0, 8.0, -3.0, 7.0, -1.0, 1.0, 18.0, 12.0])\n",
    "sigma = np.array([15.0, 10.0, 16.0, 11.0, 9.0, 11.0, 10.0, 18.0])\n",
    "\n",
    "with pm.Model() as centered_eight:\n",
    "    mu = pm.Normal('mu', mu=0, sigma=5)\n",
    "    tau = pm.HalfCauchy('tau', beta=5)\n",
    "    theta = pm.Normal('theta', mu=mu, sigma=tau, shape=8)\n",
    "    y_obs = pm.Normal('y', mu=theta, sigma=sigma, observed=data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pass the model to the SBC class, set the number of simulations to 100, and run the simulations. This process may take\n",
    "some time since the model runs multiple times (100 in this example)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "sbc = simuk.SBC(centered_eight,\n",
    "    num_simulations=100,\n",
    "    sample_kwargs={'draws': 100, 'tune': 100})\n",
    "\n",
    "sbc.run_simulations();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To compare the prior and posterior distributions, we will plot the results from the simulations,\n",
    "using the ArviZ function `plot_ecdf_pit`.\n",
    "If the inference algorithm was well-calibrated, we expect a uniform distribution that lies within the 94% credible interval, indicated by not having any red points.\n",
    "In our case, we see a clear deviation from the uniform distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 2880x1148.7 with 12 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_ecdf_pit(sbc.simulations,\n",
    "              visuals={\"xlabel\":False},\n",
    ");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bambi\n",
    "\n",
    "Now, we define a Bambi Model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import bambi as bmb\n",
    "import pandas as pd\n",
    "\n",
    "x = np.random.normal(0, 1, 200)\n",
    "y = 2 + np.random.normal(x, 1)\n",
    "df = pd.DataFrame({\"x\": x, \"y\": y})\n",
    "bmb_model = bmb.Model(\"y ~ x\", df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pass the model to the `SBC` class, set the number of simulations to 100, and run the simulations.\n",
    "This process may take some time, as the model runs multiple times"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "sbc = simuk.SBC(bmb_model,\n",
    "    num_simulations=100,\n",
    "    sample_kwargs={'draws': 25, 'tune': 50})\n",
    "\n",
    "sbc.run_simulations();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To compare the prior and posterior distributions, we will plot the results from the simulations.\n",
    "If the inference algorithm was well-calibrated, we expect a uniform distribution that lies within the 94% credible interval, indicated by not having any red points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<arviz_plots.plot_collection.PlotCollection at 0x206de31cb90>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 3600x535.887 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_ecdf_pit(sbc.simulations)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Numpyro\n",
    "\n",
    "We define a Numpyro Model, we use the centered eight schools model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpyro\n",
    "import numpyro.distributions as dist\n",
    "from jax import random\n",
    "from numpyro.infer import NUTS\n",
    "\n",
    "y = np.array([28.0, 8.0, -3.0, 7.0, -1.0, 1.0, 18.0, 12.0])\n",
    "sigma = np.array([15.0, 10.0, 16.0, 11.0, 9.0, 11.0, 10.0, 18.0])\n",
    "\n",
    "def eight_schools_cauchy_prior(J, sigma, y=None):\n",
    "    mu = numpyro.sample(\"mu\", dist.Normal(0, 5))\n",
    "    tau = numpyro.sample(\"tau\", dist.HalfCauchy(5))\n",
    "    with numpyro.plate(\"J\", J):\n",
    "        theta = numpyro.sample(\"theta\", dist.Normal(mu, tau))\n",
    "    numpyro.sample(\"y\", dist.Normal(theta, sigma), obs=y)\n",
    "\n",
    "# We use the NUTS sampler\n",
    "nuts_kernel = NUTS(eight_schools_cauchy_prior)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pass the model to the `SBC` class, set the number of simulations to 100, and run the simulations. For numpyro model,\n",
    "we pass in the ``data_dir`` parameter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 100/100 [01:49<00:00,  1.09s/it]\n"
     ]
    }
   ],
   "source": [
    "sbc = simuk.SBC(nuts_kernel,\n",
    "    sample_kwargs={\"num_warmup\": 50, \"num_samples\": 75},\n",
    "    num_simulations=100,\n",
    "    data_dir={\"J\": 8, \"sigma\": sigma, \"y\": y},\n",
    ")\n",
    "sbc.run_simulations()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To compare the prior and posterior distributions, we will plot the results from the simulations,\n",
    "using the ArviZ function `plot_ecdf_pit`.\n",
    "If the inference algorithm was well-calibrated, we expect a uniform distribution that lies within the 94% credible interval, indicated by not having any red points.\n",
    "In our case, we see a clear deviation from the uniform distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
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q2ZbD+PHjs/6sv/76oV7ERODUT8qDDz6YXGrwwAMPTM6i3HXXXZMJ5ViROQa+9SS+hn/84x/7bsd+ZrPzzjsnya1RrMbb/7HFiJPbd999d97bj2fbxTNUU9WrUxWvB7v55psHtJmtKnzcadpjjz36bt90000Z142J1an/u3333XdA5eZcnnvuufDd7343qbgc3xeTJ09O3iNf+9rXVpvg//a3v933vooJyrXWfzzjCRSDTwzpLy47+OCD8xrPYrZfztezkuLBoZSrrrqqJn0AoLGIgatHDCwGzocYuHBiYAAyEeu2TqxbqH/7t3/r+/v5558vS5vrrLPOanPQmZjvNd+bL7EuQPMTs1ZPo8WsxXr00UfDL3/5y+TvQw45JOy5555FtSNmFbPmS8wK0FqaPrl61KhRA26/9tprBT1+8Bl5qWqxlXTPPfck1YP7Vwx+//vfn1StJoRzzz03qYxx2WWXhWeeeSaptrto0aLw0EMPhR/+8IdJ0mmmhOBaiH2MlXX7VxbJpf86f/nLX0rafqwsHC+3nTo5YIcddsi6/tChQ8OUKVOybj8mP99///1p+1vqc4qXBkoZfFmibH71q18lSdUXXHBB+Mc//pG8L2Ll+Tj+8azc9773vX3JG3FnMlUde9KkSWGjjTYKtfbXv/61Zu+RSr6elRT7kEq+/9Of/pTs6ANAsxIDF0YMLAbORQwMAPVDrFtZ/YsopCoXlurJJ58ccDtbRULzveZ782W+F4B6JmatP/HY8H/+538meTVrr712OP3004tuS8wqZs2XmBWgtTR9cvWmm2464PaLL75Y0OP7J8VGG2+8caikhx9+OJxwwglJUmhKTBaOly8hhIsvvjj8+Mc/TiaBN9lkk/Ce97wnOcuy/6UNFyxYEI4//vjwwAMP1MWQ9Z9ojpe+yacq+Hbbbdf391NPPVW27W+99daho6Oj5O3Hy+qkJuLj5Hz/9YttM4pt9q+yHc+QzUdMqv/Od77TV/E6/t8fdthh4YADDghjxoxJ7ovL4gkKsbp1TCROfRb0P7OwVmK19fi+TSl0POfPnx8WL15c9PYr9XpW2ujRo8Nb3vKW5O/XX389qWgPAM1IDFw4MbAYOBcxMADUB7Fu5T3++OMDqkWWKhbyOPvss/tux0Id48aNS7uu+d5VzPfmx3wvAPVKzFqfYvG11PHhL37xi2Hs2LFFtSNmXUXMmh8xK0BryZ1l2eDiF1sMolIVqF9++eWwdOnSMGLEiLweP/gyeVtssUWolJig+IlPfCJJtEzZe++9w1lnndVXnbXVfe973wvDhg0L3/jGN8Khhx46YFlMmP385z8f5s6dm1Qt/tKXvhR+//vfJ+sPFqsZx52gcpo8efJqfUodtM+ngkd//dcrNXG1mO1vsMEGWbff/754Cch0YzxY/20vXLgw+Z8cvIMT200lCcezSzNNyvd31113hfPPP7/v9mc+85lw0kkn9VVkiduKleBjZej4vx8vCzR8+PC+9bMlV//3f/93KKf4nGJfsr1G+b5Og9eJY9f/JINCVOr1rIZ4wkDqAFH8DIj/hwDQbMTAhRMDi4FzEQMDQH0Q61ZWLDDR/6pzxV4mPSZUx+IQ8aqbF154YXjkkUf6rpT4la98JePjzPeuYr43f+Z7AahHYtb6EwuqxaJ80a677hre9773Fd2WmHUVMWv+xKwAraPpk6ujWNl05syZfWedxbPXYoCVj5isN7itSnjhhRfCxz/+8b4k8GiXXXZJLi/T2dlZkW02ou7u7vCDH/wgvOtd71ptWUyqjImz06ZNS5JoY0LFFVdcET70oQ+ttm6s9HvppZeWtW8xoTtdcnVMPO2fuJqPddddt+/v+Fzi5PXQoUOL6lcx248VtlNiReByP6dUG4OTcR977LGCT2Q477zzQm9vb/L32972tnDyySevltAcd3gPOuigZCxvvvnmvv+pzTffPOv/dLnfIxtttFHa5OrXXnut7+9Ro0YNSP7OJJ4gMnLkyLBkyZKMr1O+KvV6VsOWW27Z93fqoA4ANBsxcOHEwGLgSrxHxMAAUH5i3cqKV/uLl0tPJUvsu+++eT82Vq5LPTadzTbbLJxzzjlhm222ybiO+V7zvYUy3wtAPRKz1p8zzjgjOfYfj/vHq8CnCq8VQ8wqZi2UmBWgdbREOeTB1RhidYV8zJs3L6mCnBITMfOt/FuIV155JXzsYx9LqkikTJo0Kfz0pz/NK8mylcSk+HSJ1f1fo4985CN9ty+//PJQazHpOiXf13PweqkE2mptv3/l4nTbLsdz6t9Gukrx+VyiMv5/9v9/Pv7449OuF9uKVeCjWGElnswQHXDAAaEeFDOeg9dNN56V3H4+r2c19K9uPvhKAwDQLMTAhRMDi4Er8R4RAwNA+Yl1K+fKK68MN9xwQ9/tL3zhC0UX8OgvXmXzuOOOC9dee23WxOrIfK/53kKZ7wWgHolZ60sssHf33Xf35Qf0T3QthphVzFooMStA62iJytWxGsMPf/jDvttXX311OPHEE3M+7qqrrlqtnXJ74403wic+8YnwzDPP9N0Xg79f/OIXSQVbBkpXGXqwWLn6/PPPT/5+9NFHk4q+o0ePHrDO7rvvPuAMxErq6urq+zvfKuSDJ7n7t1Ht7afbdjme07Jly1Zb5+WXXx5QcbqQyvKxanK2ivRvf/vbw4033jjgvv333z9r+/X8Hhk8punGs5Lbz+f1rIYxY8akff8AQDMRAxdODLyKGLhy75FIDAwApRPrVsbs2bPDf/3Xf/XdjgVL3vve9xbUxtFHH51cCTSKVQFjcZgHHnggKcbx85//PEncjhUDY8yZifle872FMt8LQD0Ss9aPGF/Gq1anrqRywgknlKXNFDkKuclRELMCtJKWqFw9ceLEsPXWW/fdfvLJJ8Ptt9+e9THxIOn06dMH3Pee97ynrP2K2/jUpz4VHnnkkb77JkyYEC688MIkUZTVTZkyJeewxCA6FfT29vYOGN9a6F8FOl4yKB/Lly/P2Ea1t59u2+V4Tumqw8VJ+mzLB4v/yyk77LBDUjUlk1gNvr8NNtgg7LjjjqEeFDOeg8e0lCr3lXo9q6H/dvu/fwCgmYiBCycGXkUMXLn3SCQGBoDSiXXL77nnnkuKy6ROJovHRv77v/+74Ha+8pWvhK9+9avJz3e+853wq1/9Ktx5553h1FNPTRIq5syZkxzfiBWyMzHfa763UOZ7AahHYtb6EePaWFwv9Xc5rswiZhWzFkrMCtA6WiK5Ojr55JMH3P7GN77RF3Sl8/3vfz/MnTt3QIXb7bbbLuP6M2bMSJK4Uz/HHnts1v7Eg7ef+cxnwr333tt33/rrr59MUPa/hARhtYTYQtd79dVXazqMa6yxRsGVzQavN3LkyKpuv38Vt3TbLsdz6t9Gsfr/D2+44YZZ133LW94yoCJdrqrV1VTMeA5et5TxrJfXsxjxBAoAaHZi4MKJgVcRA5f3PSIGBoDyE+uW10svvRQ+/vGPhwULFiS3N9544/DLX/4yrLnmmmVpP8ZQxx13XPif//mf5HasbB0rZMeE7nIw32u+13wvAPVIzFofbr755uTqKdHhhx+eXK28FsSsYlYxK0DraJnk6gMOOCDstNNOfbfjZN8xxxwTHnvssQHrvfHGG0ni9cUXXzygotUpp5xS1v6cdtpp4Y477hhwZtM3v/nN0NbWFp5//vm8fxYtWhRayYgRIwpeL16msJb6XzrmlVdeKfjSM/G5lHLGZTHbT02+R6NHjy77cxrcRrrXLZ8Eh/5nkeZ6b8Qx3GqrrfpuT506NdSL/pc6XLx48YDk9mzPvf97O93rlK9KvZ7V0H+s8v18AIBGIwYunBh4FTFwed8jYmAAKD+xbvm89tprSWJ1rCgdrbfeeslVMmNRl3KLc6t77LFH3/zcb37zm7Trme8131so870A1CMxa+3FY+Nf//rX+46tf+lLXypb22JWMWuhxKwAraMjtIiYtHzOOeeEI444IqneED3++OPh0EMPTS6VHCs4LFy4MDzwwAOrJePGpOf+SZnlcM011wy4HRNJjz/++KIqcscK2K0iBs2jRo3Ka71slZefeeaZAQn05TB58uTk/TTY5ptv3vf3Cy+8kFdb/dfbYostSupXMdt/8cUXs26//30xESEGj/0vq51O/23HRIaxY8eutk6c8O9/MKCQHZ3Bl+hOJ3W5746OjrDLLrvkXL+Yy2VmE5/3Zz/72ayvURSr5ud63Qe/lqW8Tyr1elZD/8r0/d8/ANBMxMCFEwP/ixg4PTEwANQHsW55xIINn/zkJ8MTTzzRN18XE6vjcY9K2XPPPcPdd9+d/P33v/897Trme1cx35s/870A1CMxa+3FY9ipPJ+Y+/OpT30q47qD8wZiTk2qmN0+++wTTjrppAHLxayriFnzJ2YFaB0tk1wdjRs3LrkEXkxufPrpp/su1/Dggw8mP4PF5MJYYfqQQw6pQW/JlPSbT6J7/+Tg/lWBU+bPnx8uvfTSsg7ym2++mTa5essttxxQETr+5EoCffjhh8uWXN1/+/GEghUrViTJxaVsPyartLe3J5d9jP9DjzzySJgyZUpJbUYbbbRR39/z5s0Luay11lp5V5uLBxZSBxfiGMT3wIYbbpj1MeV+j8Tnly65Ol6WM74nUhXD43jmet37j2f8bMvnpINMKvV6VkN8HdO9fwCgmYiBCycGXkUMnJkYGADqg1i3PPPSxx13XN8xjjhPGI+DlLtgzGD9r6QXC9ekY77XfG+hzPcCUI/ErPUlJrb2T27NJR77znZcW8wqZi2UmBWgdbSHFrP11luHK6+8MplsXGedddKu09nZGd75zneGyy+/PBx99NFV7yOZ3XfffTmHJ1alTk3mxrMWt9tuu5oO6WabbRbGjx/fd3vmzJk5H9N/nbe+9a0lbX+nnXbqOxMzTrSnO5Fg8Jmc/cc53fbjiQexUne6/mbyt7/9LWub0TbbbNP3d+oEiGze8pa3DEgcz+baa68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      "text/plain": [
       "<Figure size 2880x1148.7 with 12 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_ecdf_pit(sbc.simulations,\n",
    "              visuals={\"xlabel\":False},\n",
    ");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Custom simulator SBC"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### PyMC\n",
    "\n",
    "In certain scenarios, you might want to pass a custom function to the `SBC` class to generate the data. For instance, if you aim to evaluate the effect of model misspecification by generating data from a different model than the one used for model fitting.\n",
    "\n",
    "Next, we determine the impact of occasional large deviations (outliers) by drawing from a Laplace distribution instead of a normal distribution (which we use to fit the model)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def simulator(theta, seed, **kwargs):\n",
    "    rng = np.random.default_rng(seed)\n",
    "    # Here we use a Laplace distribution, but it could also be some mechanistic simulator\n",
    "    scale = sigma / np.sqrt(2)\n",
    "    return {\"y\": rng.laplace(theta, scale)}\n",
    "\n",
    "sbc = simuk.SBC(centered_eight,\n",
    "    num_simulations=100,\n",
    "    simulator=simulator,\n",
    "    sample_kwargs={'draws': 25, 'tune': 50})\n",
    "\n",
    "sbc.run_simulations();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bambi\n",
    "\n",
    "In certain scenarios, you might want to pass a custom function to the `SBC` class to generate the data. For instance, if you aim to evaluate the effect of model misspecification by generating data from a different model than the one used for model fitting.\n",
    "\n",
    "Next, we determine the impact of occasional large deviations (outliers) by drawing from a Laplace distribution instead of a normal distribution (which we use to fit the model)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def simulator(mu, seed, sigma, **kwargs):\n",
    "    rng = np.random.default_rng(seed)\n",
    "    # Here we use a Laplace distribution, but it could also be some mechanistic simulator\n",
    "    scale = sigma / np.sqrt(2)\n",
    "    return {\"y\": rng.laplace(mu, scale)}\n",
    "\n",
    "sbc = simuk.SBC(bmb_model,\n",
    "    num_simulations=100,\n",
    "    simulator=simulator,\n",
    "    sample_kwargs={'draws': 25, 'tune': 50})\n",
    "\n",
    "sbc.run_simulations();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Numpyro\n",
    "\n",
    "In certain scenarios, you might want to pass a custom function to the `SBC` class to generate the data. For instance, if you aim to evaluate the effect of model misspecification by generating data from a different model than the one used for model fitting.\n",
    "\n",
    "Next, we determine the impact of occasional large deviations (outliers) by drawing from a Laplace distribution instead of a normal distribution (which we use to fit the model)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def simulator(theta, seed, **kwargs):\n",
    "    rng = np.random.default_rng(seed)\n",
    "    # Here we use a Laplace distribution, but it could also be some mechanistic simulator\n",
    "    scale = sigma / np.sqrt(2)\n",
    "    return {\"y\": rng.laplace(theta, scale)}\n",
    "\n",
    "sbc = simuk.SBC(nuts_kernel,\n",
    "    sample_kwargs={\"num_warmup\": 50, \"num_samples\": 75},\n",
    "    num_simulations=100,\n",
    "    simulator=simulator,\n",
    "    data_dir={\"J\": 8, \"sigma\": sigma, \"y\": y}\n",
    ")\n",
    "\n",
    "sbc.run_simulations();"
   ]
  }
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