{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Posterior Simulation-Based Calibration\n", "\n", "**Posterior SBC** (Säilynoja et al., 2025) validates the inference algorithm\n", "*conditional on observed data*, rather than averaging over the prior.\n", "\n", "```{admonition} When to use Posterior SBC\n", ":class: tip\n", "\n", "Use **Prior SBC** when you want to check that your inference pipeline works\n", "for a wide range of datasets generated under the prior.\n", "\n", "Use **Posterior SBC** when you already have observed data and want to verify\n", "that the inference algorithm is trustworthy *for that specific dataset*.\n", "Posterior SBC focuses on the region of the parameter space that matters\n", "for the observed data, making it more sensitive to local calibration issues.\n", "```" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import pymc as pm\n", "from arviz_plots import plot_ecdf_pit, style\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import simuk\n", "\n", "random_seed = 42\n", "rng = np.random.default_rng(random_seed)\n", "style.use(\"arviz-variat\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## How Posterior SBC works\n", "\n", "Given a model $\\pi(\\theta, y) = \\pi(\\theta)\\,\\pi(y \\mid \\theta)$ and\n", "observed data $y_{\\text{obs}}$, Posterior SBC proceeds as follows:\n", "\n", "1. **Fit the model** to $y_{\\text{obs}}$ to obtain posterior draws\n", " $\\theta'_i \\sim \\pi(\\theta \\mid y_{\\text{obs}})$.\n", "2. **Generate replicated data** from the posterior predictive:\n", " $y_i \\sim \\pi(y \\mid \\theta'_i)$.\n", "3. **Augment** the observations: $y_{\\text{aug}} = (y_{\\text{obs}}, y_i)$.\n", "4. **Re-fit the model** on the augmented data to get\n", " $\\theta''_{i,1}, \\ldots, \\theta''_{i,S} \\sim \\pi(\\theta \\mid y_i, y_{\\text{obs}})$.\n", "5. **Compute the rank statistics** of $f(\\theta'_i)$ among $f(\\theta''_{i,1}), \\ldots, f(\\theta''_{i,S})$. Where $f$ is an optional test quantity applied to the parameters before computing ranks.\n", "\n", "By the self-consistency of Bayesian updating, $\\theta'_i$ is also a draw\n", "from the augmented posterior $\\pi(\\theta \\mid y_i, y_{\\text{obs}})$.\n", "Therefore the rank statistics should be **uniformly distributed** if the inference\n", "is calibrated." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Out-of-the-box Posterior SBC\n", "\n", "We shall illustrate Posterior SBC using the same eight schools model as the one used in the Prior SBC example. This model is known to have a funnel-shaped posterior (Neal's Funnel) when $\\tau$ is small, which is challenging for many inference algorithms. We use Posterior SBC to focus on the parameter space relevant to the observed data (i.e. the posterior), we wish to see it avoid the funnel neck and show that locally the posterior is well-calibrated. \n", "\n", "### Define the model\n", "\n", "```{admonition} Model requirements for Posterior SBC\n", ":class: warning\n", "\n", "Posterior SBC augments the observed data (concatenating original + replicated),\n", "which changes its size. For this to work, store observed data in ``pm.Data``\n", "containers, and specify size using the ``dims`` parameter instead of setting a static shape. \n", "If your model uses ``dims`` and ``coords``, you are also responsible for resizing them to the correct size corresponding to the new augmented dataset via the ``update_data`` callback.\n", "Similarly, if your model has covariates, store them in ``pm.Data`` so they\n", "can be resized in the same callback.\n", "```\n", "\n", "We define the eight schools model as before, but with the observed data stored in `pm.Data` containers and sized using `dims` to properly handle the augmented dataset. Here we also add `sigma` and `theta_idx` to the data containers so they can be resized in the `update_data` callback." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "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", "coords={\n", " \"obs\": np.arange(8),\n", " \"school\": np.arange(8),\n", " }\n", "school_idx = np.arange(8)\n", "\n", "with pm.Model(coords=coords) as centered_eight:\n", " school_idx = pm.Data(\"school_idx\", school_idx, dims=\"obs_id\")\n", " sigma = pm.Data(\"sigma\", sigma, dims=\"obs\")\n", " data = pm.Data(\"data\", data, dims=\"obs\")\n", " \n", " mu = pm.Normal(name='mu', mu=0, sigma=5)\n", " tau = pm.HalfCauchy('tau', beta=5)\n", " theta = pm.Normal('theta', mu=mu, sigma=tau, dims=\"school\")\n", " y_obs = pm.Normal('y', mu=theta[school_idx], sigma=sigma, observed=data, dims=\"obs\")\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Fit the original posterior\n", "\n", "First, we need the posterior samples from the observed data. These will\n", "serve as the reference distribution for Posterior SBC." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "with centered_eight: \n", " trace = pm.sample(1000, tune=1000, random_seed=random_seed, progressbar=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Using `update_data` with covariates and `dims`\n", "\n", "When your model uses `dims`/`coords` or has covariates stored in `pm.Data`,\n", "you must provide an `update_data` callback that resizes everything to\n", "match the augmented observations. The callback is called **before** the model\n", "is re-conditioned, and runs inside the model context." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "def update_data(model, augmented_data, simulation_idx):\n", " with model:\n", " pm.set_data(\n", " new_data={\n", " \"sigma\": np.concatenate(\n", " [model[\"sigma\"].get_value(), model[\"sigma\"].get_value()]\n", " ),\n", " \"school_idx\": np.concatenate(\n", " [model[\"school_idx\"].get_value(), model[\"school_idx\"].get_value()]\n", " ),\n", " },\n", " coords={\"obs\": np.arange(16)},\n", " )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Custom test quantities with `transform`\n", "\n", "You can define a scalar test quantity applied to both the reference draw\n", "and the posterior draws before computing the rank statistic. The function\n", "receives `(param_name, param_value)` and should return a comparable value." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "def transform(param_name, param_value):\n", " return param_value**3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Run Posterior SBC\n", "\n", "Pass `method=\"posterior\"` and provide the `trace`. In each iteration, Posterior SBC\n", "generates replicated data from the posterior predictive, augments it\n", "with the original observations, and re-fits the model." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "sbc = simuk.SBC(\n", " centered_eight,\n", " method=\"posterior\",\n", " trace=trace,\n", " transform=transform,\n", " update_data=update_data,\n", " num_simulations=50,\n", " seed=random_seed,\n", " sample_kwargs={\"draws\": 100, \"tune\": 100},\n", " progress_bar=False,\n", ")\n", "\n", "sbc.run_simulations();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Visualize the results\n", "\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. In our case, we wish to see that the funnel neck in the eight schools model is avoided and the inference algorithm is well-calibrated locally for the observed data." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_ecdf_pit(sbc.simulations,\n", " group=\"posterior_sbc\",\n", " visuals={\"xlabel\": False},\n", ");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Intentionally Skewing the Augmented Posterior Using Custom augmentation with `augment_observed`\n", "\n", "We intentionally skew the augmented posterior by keeping only 1 of the original observations and concatenating them with the replicated data. This creates a mismatch between the reference draw (which is based on the full observed data) and the augmented posterior (which is based on a subset of the observed data), leading to skewed rank statistics." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "def augment_observed(model, observed_data, replicated_data, simulation_idx):\n", " \"\"\"Keep only the last 25 original observations + replicated.\"\"\"\n", " data = {\"y\": np.concatenate([observed_data[\"y\"].values[-1:], replicated_data[\"y\"]])}\n", " return data\n", "\n", "\n", "def update_data(model, augmented_data, simulation_idx):\n", " with model:\n", " pm.set_data(\n", " new_data={\n", " \"sigma\": np.concatenate(\n", " [model[\"sigma\"].get_value()[-1:], model[\"sigma\"].get_value()]\n", " ),\n", " \"school_idx\": np.concatenate(\n", " [model[\"school_idx\"].get_value()[-1:], model[\"school_idx\"].get_value()]\n", " ),\n", " },\n", " coords={\"obs\": np.arange(8 + 1)},\n", " )\n", "\n", "skewed_sbc = simuk.SBC(\n", " centered_eight,\n", " method=\"posterior\",\n", " trace=trace,\n", " augment_observed=augment_observed,\n", " update_data=update_data,\n", " num_simulations=50,\n", " sample_kwargs={\"chains\": 4, \"draws\": 50, \"tune\": 50},\n", " progress_bar=False,\n", ")\n", "\n", "skewed_sbc.run_simulations()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Visualize the skewed results and and Replot the Original Simulations using `compute_rank_statistics`\n", "\n", "The results indicate a clear deviation from uniformity, with the ECDF lines falling outside the credible interval, as indicated by the red points. This suggests that the self-consistency property of Bayesian updating does not hold." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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xytBU4sV2rIKdb3Gbn//855Of4+dtnM0AACiNaot1YzWY73znO83xVjpx+sqJEyc2L8dr1nTEumLdTIh1AaD4qi2mjWJBhjgDXpPTTz89L9UMxbRi2kyIaQEgN9UYl2ajZeG1WKG7vcKITcSl4tJMiEsBqlfNJFfHRMqYoNfyBnWshNt2BFysUhqn/Tj00EObH4sj1WLydT7FKtW77bZbuPXWW8OVV16ZVHKIo+/aW2/ChAnhuuuuS6ZDabJw4cKc2hR/v/i7Z/rVu3fvUAtiwN701eS5555LzoX4PsURmZtvvnnYb7/9kpGTMYgut8ED9913X/NybGc6n/3sZ5Pk1ihW42352lzEi444JU+m+48j95qqxMdRpk0jU4v5edA0AnWnnXbKKnn77bffTm4YxIrL8bwYN25cco7EKvdtL7zOPPPM5vMqJiiX2j333NP8c6wMne7vOz63xx57NC/HaZbyuf94jsTPt1SGDx+eVLHJ5/5zET9/mxRiFgMAKAaxbuXHup/5zGeaf+4orhTrinUzJdYFoJKIacszpo19dh988EHyc7zXsvPOO4d8ENOKaTMlpgWg2MSl5RmXZqPt7PGxTamIS8WlmRKXAlSnmkmujtWfWzrttNPCgAEDUq7//e9/v1Uyc+wkfPHFF/PWnjhlSvxab731Mlp/1VVXDWeccUarx+JUe7EyBIU5X+KIxb///e/hzTffTKrtzps3Lzz//PPhvPPOS5JOi50QnE5sY8tK5rEaekdarvPYY491av9x4ELTuRhHkG6yySZp1+/Ro0cYP3583vafrfvvv7/557ZTHKXzl7/8JUmqvvTSS8Nrr72WnBeLFi1Kjn8c4fulL32pOYE4Jrw3VcceM2ZMq8+TUnn88cdLdo7EZPYpU6aUbP+5im1oSr7/97//nQxGAIBKJ9atvFi35aC0pqoyqYh1xbqZEusCUMnEtOUR07YsRhD7RvNFTCumzZSYFoBSE5dWXl/r66+/vkLRr1TEpeLSTIlLAapTTSRXv/zyy+GVV15pXl5nnXXCjjvumPY1sWpry6mXo5tvvjlvbcol0XKbbbZJqkm3HEGXz4RvGl1xxRXht7/9bZK0sMYaa4Q999wzGTE5duzY5kM0e/bscPTRR4epU6eWxWFreQEwZMiQJBm/IxtttFHzz9OmTcvb/tdff/3QrVu3ou4/G/F9bTkaNlbxzkRMqj/rrLOaK17H6S332WefsOuuu4ZBgwYlj8XnJk2alFS3jonE77777gqjFEslVluP5217xz+Vluu8//77YcGCBTnv/4033mhOBIrJQdnuv5jnSEtxEE7TIJiPP/44qWgPAJVMrFuZsW7L69lhw4alXE+su+LxT0WsK9YFoHKJacsnpp08eXLzz5tttlny/V//+lf41re+FT73uc+FjTfeOLmvEe+1XHTRRRlNIy+mXfH4Z/Ie6b/VfwtA8YlLK6+vNSZ2n3POOc3LMXF76NCh7a4rLl3x+GfyHolLxaUA1aTjSKUKtBxNFu21114ZvS5WWjj33HObl++7777wwx/+MJRSnFpvxowZzcuzZs0qaXuq0a9+9avQs2fP8LOf/SzsvfferZ6LCbPf/e53k6m4Y9XieD7885//TNZvK1YzjhdU+TRu3LgV2tSUuJrJyMqWWq7X2YuQXPa/2mqr5W3/2Yj7akoSHjhwYMqLpZYeeeSRcPHFFzcvf/vb3w7HH398cwXBOAXRCSeckFSGXrhwYfjzn/8cevXq1bx+uuTqn/70pyGf4u8U25LuPcr0fWq7Tjx2LQcZZKPlexynWmrvbybd/uMxjjdfBg8eHIotXtg3JTTFz4D4dwgAlUqsW3mxbuzEj9ccTWJySipi3UZi3cyJdQGoRGLa8ohp33rrraTPruX6Mak6zgLa0ocffph8xSqFsd80zioai1akIqbN/H3Sf9tITAtAqYhLK6OvNSZUxyJkTz31VLjsssuaCxjGytmnnHJKyteJSzN/n8SljcSlANWnJpKrH3744VbLTRUUMgnSYoXpmEjbFOi98847GQd5hdC1a9dWy/X19SVrS7WKx/Q3v/lN+MIXvrDCczGpMnYA77vvvkkSbTwnrrvuunDwwQevsG4ckXfVVVfltW0xobu95OqWndgxcTUTq6yySvPP8XeJFxVxWp1c5LL/WGG7SawIXMxK9i2r2GciVlVpaGhIft5uu+2SmwRtE5rjxfPuu++eHMt77rkndO/ePXlu7bXXbq583J58nyPxM6u95Oo5c+Y0/9yvX79Wyd/pKvj37ds3qZLf2feps+do0zZKkVy97rrrNv9stgAAKp1Yt/Ji3auvvrr5pkFdXd0KMyy1JNYV62ZLrAtAJRLTlkdM2zRrXxT7GmNiyoMPPti8j8033zz0798/meXvP//5T/K+xX7GH/3oR8kMgF/96lfb3a+YVkybLTEtAKUiLi3fvtZYSXnZsmUpn19rrbXC+eefnxQ3TEVcKi7NlrgUoPrUhRrw2muvNf8cb0bHqegy1bZCacttlULsiEyXfEjnxU7f9hKrm8Rk2cMOO6x5+dprry35YY9J100ySZptb72mBNpi7b9l5eLO7DtbLSu/p5tSvUkcXBFHsTY5+uij210vbmv77bdPfo4jX+NAjGjXXXcN5SCX96jtui23UYz9t12vM/vvjJbVzVuePwBQicS6lRXrvvrqq61mU9p///2T6hepiHXFutkS6wJQicS05RHTzp8/v/nnRYsWNSdWH3PMMeFf//pXkqxyxhlnhMsvvzzcfvvtre7LxMdbTgnfkphWTJstMS0ApSIurby8gpgvdNRRR4Vbb701bWJ1JC4Vl2ZLXApQfaq+cnUcufbRRx+1Gv0Wq7FmasSIEa2WY6XiHXbYIZRCTPJsWTW1W7duHQZ8bT3++OPJNl566aVkKr4YPMaqu7HabQz+d9ppp7DJJpuEWtZeZei2YuXqiy++OPk5Hst4ng0YMKDVOltuuWWr0YyFFCt9NGmqmNyRtlWqW26j2PvvzL6z9cEHHzT/HM/9jkyZMqX551g1Of6dpBI/G+66665Wj+2yyy5pt1/O50jb9yneJCnlOdqZ/XfGoEGD2j1/AKASiXUrJ9adN29eOP7445tvOKyxxhrhpJNOSvsasa5YN1tiXQAqkZi2PGLa9gohHHTQQeF73/veCo+PHDkyXHrppWHPPfcMs2bNSmZR/OMf/xh+8YtfrLCumFZMmy0xLQClIi4t377WGJcuX748+TnOPB1nXZk6dWqSnB3j0DvvvDOceuqpaXN/xKXi0myJSwGqT9VXrp4+fXqr5dVWWy2r17etbNt2e8X017/+NTQ0NDQvf/aznw0rrbRSVtt48sknw7333pskasdExdgBGivsxsd/97vfJZXQjjjiiPDKK6+EWjV+/PgO14nTxDQl5sb3pGXSeym0HK0Zpx/KROzATrWNYu+/M/vOVrx4ymY0bMsKKnHgQRyQkMqYMWNW+LwZO3ZsKAe5vEdt36dsKl4X4hztzP47o+V+W54/AFCJxLqVEevGmwTHHXdceOutt5Llfv36hQsuuCD07ds37evEumLdbIl1AahEYtryiGnbPhaXv/Od76TcXixO8s1vfrN5OSa0LF26dIX1xLRi2myJaQEoFXFp+fa1nnLKKeG0005Lvs4666zwl7/8JTz00ENh0qRJSbJ2zPuJM67ceOONKbchLhWXZktcClB9qj65esGCBa2WY+XZXEcWtZ3qrphigmdMrm7psMMOK8i+HnnkkfCVr3wl3HbbbaEWZZqA33K9ltXRS6FPnz5ZV/dtu15HiRr53n/LUaWd2XehxarkTYYPH5523fXWW6/VCNuOqlYXUy7vUdt1W26jGPtvu15n9t8ZLQe1AEClE+uWf6wbE0xOPPHEZABs0w2DOBB2ww03DPkm1hXrinUBqERi2vKIadv21cUZ/zqaKbBlf2ks/JKPWf3EtGJaMS0ApSIuray8grjvo446Kvz6179OlmNl6//3//5fePvtt0M+iEvFpeJSgOrTLVS5OK1HS9lWDWtbKbW9qe4KLY7E+/73v99qRN5WW20Vdt5556wCxW233TZ53ahRo5Ik827duoU5c+aEF154Idx1113h8ccfbzUKL47ai5Wxt9tuu5zb/t5776V9Pu6/3PTu3Tvr9dqeZ8XWstP6ww8/zOg1Laexib9Ly+l0irH/2bNnt6paUiwt37dMLthajkjt6NyIxzD+fcW/qWjChAmhXLQcKBIHncSL0I4+D+Pv3vLc7sz71NlztO02iqnlBXumnw8AVL9KjHMjsW55x7qxQ/+kk04K9913X7Icr9nOP//8sOWWW2b0erGuWDdbYl2A2iamLZ5q7L9t21e37rrrdrjNoUOHhv79+zcXsXn//fdXmA1QTCumzZaYFqDyiUuLpxrj0mzFe/hbb711ePTRR5M44uqrrw4/+tGPVlhPXCouzZa4FKD6VH1ydcvEyCjbQK9t8mHb7RVDHC334osvthqNd8YZZ2ScVB2nOtl3333brfq69tprh8985jPhkEMOSSpWx4TqpiB22bJl4Xvf+16SeJ1rUuOOO+6Y9vlY5bcQFdg6I77HcdrtTNZLN0LyzTffDFdccUVe2zZu3Liw9957t/s+NnnnnXcy2lbL9dZZZ51OtSuX/b/77rt52382hgwZklXSU8uLppYDHFJpmr4oJsJsttlmHa7/05/+NORT/Fs94YQT0r5H0cyZMzs87m3fy868Ty1fGz9jMknubrn/+HtlO/NAvrSsTN/y/AGgtlVinBuJdcs71v3JT34Sbr755uTnurq68Mtf/jJ8/vOfz/j1Yt1GYt3MiXUBapuYVv9tZ2Lato9lOutcXK8pubq9oiVi2kZi2syJaQEqn7hUXFrsvIJtttkmSa6Onn766XbXEZc2EpdmTlwKUH2qPrm6rS5dunRq/WJP4/DHP/4x3HDDDa3aExOrR44cmdHrYzLiwQcfnHEAeeWVV4avfvWrzZ2bceqSP//5z0nl7FoRg/NYfTiT9dqrCtwkVt246qqr8tq2WDm9veTqllVB4sjN+NVREmhTdeV8XIS03P8rr7ySTGUek4uLtf9srL766hmPgo5i9fZMR8+++uqryVcUj0E8B4YPH572Nfk+R+Lv115ydawIE8+JppG9ccBGR8e95XsUq8pkMuggXVJSTBCK1Rjj52jc//jx48vyHGkrvo/tnT8AUInEuuUb65555pnhf//3f5uXTz/99LDnnntm1Vaxrlg3W2JdACqRmLY8YtrYVxj7PpsGIGY6u2PL9WKfZVtiWjFttsS0AJSKuLRy8wpaVsCeO3duu+uIS8Wl2RKXAlSfulDl2k573XIahkwsWrQop+oL+fDPf/4znHvuua0ei5Wlv/CFLxRsnzGY/cEPftDqseuuuy7npPIHHngg7de1114bys3kyZM7XCdWpW4KsmPC+0YbbRRKaa211grDhg1rXn7iiSc6fE3LdbbaaqtO7X/TTTdtrgofE8Cfe+65tOvHCtAtj3Nn95+NDTbYoPnnN954o8P111tvvVYXeOnceuutrZZffvnlUE5aTif/+OOPd7j+k08+mbf3KFapjpXXszlH87n/zpg2bVrzz+VYgRSA0qjEODcS65ZnrPub3/wmXH755c3LJ598cvjKV76SdVvFuo3EupkT6wLUNjFt8VRr/23Lx19//fWMkg0WLFjQvNzymDQR0zYS02ZOTAtQ+cSlxVOtcWm2mgqStU20bklc2khcmjlxKUD1qfrK1W2TobNNrm67frGSq+MFxI9//ONWSc1HHXVU+MY3vlHwfe+3335JUnesWt00dUVMEm0ZPGaqvc7RttOll5uY1H7AAQekXefGG29s/jkel/YC7pjIWqzk2pjgvdNOO4Wrr746WY7Vzr/4xS+mXP+ZZ55JEsSjWE04vrYz+vbtG7beeuvkvG3af7qqxHfddVdzhZJ47DbffPNQLLGCcqyIEquzxwT52KEfqzKnsskmm7S6QfDWW2+FNddcc4X1li1blpw7Lb300ksdTuNezATsXXbZJdxyyy3Jz7fffnvyGdOrV6+UA0viOi1fm4/9x3Ov6Rw5+uijU64bq4o3TcWUr/3nqmVSfcsEcQBqWyXGuZFYt/xi3d///vfh4osvbl6Os5AcfvjhObRUrCvWzZ5YF6C2iWn133Y2pt11112bZ96MhRJif+vAgQNTbvfuu+9u/jmut/7666+wjv5b/bfZEtMCVD5xqbi02HkF//rXv9qtpt2SuFRcmi1xKUD1qfrK1XFqupbmzJmT1etjYnFL7U1Tl29PPfVUckM9ToHSJFYti1WriyEmgrQNSjuq2FtNYifwbbfdlvL5mJTcsqpcR4nYxTJx4sQkUTp66KGHwsMPP9zuesuXLw9nn3128/Iee+wRBg8e3On9H3TQQc0/xw71V199td31Fi5cGC644ILm5a9+9asdTvWTT/EYtRzR+p///Cft+iNHjmyVYN2y7S3dfPPNzVNgtvxbLic777xzc+fEvHnzkkSeVH73u98l6zRNefS5z32u0/vfd999mweoxKrh6Sp6xnM0Jqw3jWAeM2ZMKIU4yOS1115rvmDfeOONS9IOAMgXsW55xbrxuuK8885rXo6DaY8//vgcWynWFetmR6wLQKUS05ZPTLv99tsn1Q+bqgqef/75aWOPP/zhD83Le++9d3N/dkv6b/XfZkNMC0ApiUvLIy6NFbCzKbIYC9Y9++yzrQYMtkdcKi7NhrgUoDpVfXJ12wqz7777blavj9VT2yZaFtILL7wQvvnNbyZVY1smv55++umhmGIyZbok82oWk8tPOumkFaoQR1OnTg1f//rXk0A+ih3H+++/fygHo0ePDl/60peal7/3ve+tMEVLvLD40Y9+1JxQHH/X73znOx1ut+mrqQpJe2Ly7WabbZb8XF9fH4455pgVqjLHwQ0xWSRWf26qThIrshdby2rSjz32WIfrx/e8SayGF6dtb0r8bapQ/fOf/3yFz4mY4P7II4+EchGnWPr2t7/dvPzHP/4xXHnlla0q5Mfk+5jkE59rEgd7NE3P1J5DDz20+RyJfzuprLzyyq2qMJ5xxhkrDGSIN2HOOeec5qqDTedyqcRpruIxabpZ1LVr15K1BQDyQaxbPrHuddddF84666zm5YMPPjj84Ac/CJ0l1m0k1u2YWBeASiWmLZ+YNia3tIxhY6JK7DuNfXwtvf322+HII48Ms2bNai5iEJdTEdM2EtN2TEwLQCmJS8sjLo3rTJgwIfzpT39Kmw80e/bscOaZZ4af/vSnzY/FdqSbiVpc2khc2jFxKUB16tLQMquuSsUpnJuSg+Posqeffjr07t07o9d+97vfbZX8F4OGHXbYoSDtnDZtWnJDvWUic0zmi9Vliz2t+K9//etWVSRicmMMavPtww8/TJLJozgVdky+LIUY4Df5n//5n+ZE2TXWWCOZ8jse/1i9dsqUKc3rxXPoL3/5S9opwYttwYIFSQXrlqM7Y/viVDbxuZhIHEfMNfnFL36RVBPO9NjE5I/99tsv7WCEmGweL0ya/t5iFfSYbBzP60cffbQ5MT12vMcLnPj3mU6sdnLfffetkCQ+ffr05uUNNthghdfFhOBYqbk98+fPD9tuu20ygnXIkCHhwQcfbLdKSkvxPL3//vtbDUCIv1s8rvH1TTcM4mCI+Blx8sknN58n8bFBgwaFH/7wh6EcxHa0HDwQB6GMGzcuSbKePHlycrOjSXy/Wyb9pEqujhcLUTyf4nmVSrxAjhUZWya1x+k/Y2Xq+H7EEd5N508Uk8G/9a1vpd3/vffe225F8Zj03iT+LTdVzW6y0047dTi4oOWxuuSSS8KOO+6Ydn0AKLc4NxLrll+sG28W7LPPPs2DuGKcEpe7dOmS0XsaY91U062LdcW6kVgXgHwQ0+ZfNfbfRr/61a/Cn//85+blVVZZJdlunAl0xowZSZ9f7BeMYl/7RRddlLafTUwrpo3EtAA0EZfmXzXFpS+++GLSt9ryPn68/xzvz8fY85NPPklycWKfbMsCamuvvXa44oorwqqrrpqyneJScWkkLgWoXannJ64i6623XnPiX7x5/dxzzyWBWSZaJtM2basQ3nnnnaQ6bsvE6jhK7sILLyx6YnXTSMCWUt24r0Zf+9rXkguF2MEbE3hbJvE2iQm55557blklVkf9+vVLOrFjQmhT8mpMlo1fLcXkjVNOOaXDC6BsxWm4Y9Xj73//+8lFTPx7i9Wz21bQHjx4cHJBlUnHfBxd2jJJtj3tPd/yYq+t2Km/2267hZtuuim5YIud+1tuuWXafcTp2uMgg5jIG82cOTP5amnDDTdMqsz37ds3XHvttclAjnjRF0fmxn2WS3J1rBgd23PVVVclCdVxNG/TqN8mMbHnkEMOSSqd51P8PIufa6eeemq4/fbbk8deeeWV5KvtejGpuikpLZ34Xnd0jrT3dxzfr3RisndTQv3QoUOThHwAqHRi3fKIdefOnducWN00eDBW+ctUvHZMdY0m1hXrRmJdAKqZmLa8+m+jWL16pZVWSvr9YhL1Bx980Nz311JMXDn77LPDVlttlXZ7YloxbSSmBaDciUvLIy6NydcxObupv7W9+/gtxXVjYvekSZOSGVXSEZeKSyNxKUDtqonk6m222aY5uTp66qmnMkqujqPlWgZdceTa8OHDCzLS8ogjjmg1RUms4horR/fq1SuUwrPPPttqOd1ovWoUq+XG6sPXXHNN+M9//pNMVxiD8lj9dpdddkmSTmNncTmKSaCxovbdd98dbr755vD8888nCcQxoTqev3HqmnixUIhzOYqjWf/+978nFd9vueWWpOJ37EyPxyuONI3H78tf/nJyIVRKhx12WJJcHcVE6I6Sq+Pf4u9+97vwwAMPJK975plnksEQsWJ1/F3i62PV86YLsEsvvTSpphzXjb9/OenRo0eS3Lz33nsn09HHz8f333+/+fzZYostknNk7NixBdl/vAiNyepf+cpXwo033pgk/8dzNP6NrbbaamG77bZL9h/PpVK64447wrx585Kf46wCsX0AUA3EurkT64p1OyLWBYDiENOWV0wbCzXEIgm77757UmgizvQX73fEKoFxUGCsYtjUL53pPQ/9t/pvO6L/FoByIC4tfVw6atSo8PDDDydf8R5+rFAdZ2qOBS6WLl2aFEaLMWmsZv2Zz3wm7Lnnnsk98UyJS8WlHRGXAlSvLg2xbGmVi8HTXnvt1SpIiwFaRy655JKkOnGTI488Mu+VZ+M0IoceemgyGq9l+/7617+WLPn09ddfD1/84heTirZR165dk2lXOhq1V8lT+LScoiaeL9SGOKjhkUceSZKNY4XiOF0lNIlTYcUL8JggEyuWF+IzEIDqVS5xbiTWrU1iXdIR6wKQCTEtpSamJR0xLUDtEJdSauJS0hGXAlSvulADYjJBHIXWMnk4Vp9NZ9GiRUnV4pbiCLZ8ivs45phjWiVWjxgxIlx22WUlS6yOCdVxWr6WOffjx4+XVEhV+s53vpN8j9Wnr7jiilI3hzLy5JNPJonV0eGHH+4zEACoOGJdUhHrAgCVQkxLKmJaAKCYxKWkIi4FqG41kVwdfetb32q1/LOf/Sx8/PHHKdePFatnzpzZvBynHNloo41Srh+nuotJ3E1fsRp1OvX19ckUMf/5z3+aH1t11VXDX/7yl6ymIElnypQpYfLkyRmvv3z58vDLX/4yqeDbUlPFPag2ceDAbrvtlvx81VVXhTlz5pS6SZSJiy66qPlzOY5EBgCoNGJdUhHrAgCVQkxLKmJaAKCYxKWkIi4FqG41k1y96667hk033bR5+e233w6HHHJIePnll1utN3/+/CTxumUV2549e4YTTzwxr+056aSTwoMPPti83KtXr3DGGWeELl26hBkzZmT8NW/evJT7iBW6v/rVr4bDDjssSf7+6KOP2l0vVqmOo6nierFqdksTJkwIO+ywQx5/cygv8W+xd+/eYcG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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_ecdf_pit(skewed_sbc.simulations, group=\"posterior_sbc\", visuals={\"xlabel\": False})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We shall also replot the original Posterior SBC results using the same quantity using `compute_rank_statistics`. This allows us to compare the results without need to re-run the simulations." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": 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46eRcyJBx4zH94Ac/WCVYXV8MRN93331h/PiVf/SvvvpqePTRR8Mee+yRMVT+5ptv1t0ePnx4OOaYY9IuP2DAgGQcv/jFL5LbMZQdx3n11VeHarNsxYowZ3FuwdJyvkrFlTYtV2s7ocX+efMNcJfz3xkUS2vveMftxL/NWvrMAwAAANJ3ic4nzFCMC7jLaSwAAEDxtVY39mLkEMoxHK4RHuTHcQVqNlwdw8VvvfVW3e0NN9ww7Lrrrhmf06VLl3DYYYeFSy+9tO6+u+++u2Dh6s8++yw8/fTTDbpWH3TQQRmfEztUx4D16aef3mBMmcLV99xzT4Pb8fmZOl1HBx98cLj88svDnDlzkttPPvlk0sm6R48eoVo8OuXTcPG498OsLFv/V8JVKtleaRONGjow7J3hZ8g2qA3NqbXAOlTCjjcAAABAfTHEkO/xiEJfwF1OYwEAAFpHJecKyjEcrhEetaqlTe0cV6Amw9WPP/54g9v77bdfVs/7+te/3iBcHTtZn3nmmQUZ01NPPRWWLv3ff6x77bVX6NSpU7PPi0HqGPxesGBBcvuZZ54JixcvDh07dlxl2Xh/fDyla9euGYPYKXEcI0aMCP/4xz+S20uWLEnGu++++4ZqccHL7+b1QVotV6lcPmFS8gVAbex4x4tmcrkIBwAAAAAAAIDKDIeX45ig2DS1o9BqIlz97LPPNri9zTbbZPW8ddZZJ6y77rph6tSpye33338/fPjhh6Ffv34tHtNzzz2X15hi8HnLLbcMY8aMSW7PmzcvTJgwocnnjxs3LsyfP7/udnxeUyHspsT1pcLVqdewmsLVLVEOV6m09EobAMqTnVwAAACgHIweMSys3sQx8FJcwF1OYwEAAACqo6md4wo0pybC1e+8807d923btg1bbLFF1s8dNmxYXbg6ta5ChKvffvvtBrdj8DmXMaXC1al1NRWubryNoUOH5rSNdK9hNfjJFzYKF497P8xatCRUota+0iYGuWOgGwAAAACA6hfDzOXS5aycxsJKS5evKPq058WaIh0AcrFax/ZJHZLKFcTv430AQPnS1I5Cqfqq77PPPgszZ86su73GGmuELl26ZP38/v37N7gdu1fvsssuLR5XXE9KmzZtwoABA1o0pua2ERVjG5Vq9/5rhC+v2zvMWVy5V6nkcqVN9MDkGeHyCZPyClbHILcDkwDVJf7/lg0npwAAAACqWy5h6XzPNRRT6jxGPG8CAIXUrk2b8KPhG4QLXn43uR2/j/cBAFD9qj5cPXny5Aa311lnnZye37dv34zry0cMe8+bN6/udu/evUPHjh0LPqYPPvgg4/My6dSpU+jVq1eYNWtWcnvOnDnJ9/G+ahF3eiq920UuV9ocPqhfOGSjdXLuJiFUB1Cdsr1wyMkpAAAAoFIu4C6nsVSK+yfPaLVZMosljj3+DLEhjd8rAMVo3Ba/AIDq57gCNRWurh9iTgWZc9E4TDx37tySj6nx8unG1Pj+fLaTClenxl1N4eoFCxZktdzCRauGkZcuXRpCmlBztuvNtP4ml1u4MKxYsSLko127dkmAv6kw9qJFi8Ly5cvTPnfJoqUh3eHotm3bJkH8pjS33kwyrXfx4sVh2bL8DvLGLvGdO3du8rElS5as/L3mKV1H/LjOuO5Crze+BvG1yFd8HeLrUej1xt9b/P01Ft8L8T2Rr/j+je/jxuLfRPzbKPR68/lbrq9Dhw6hffv2BV9vXGdcd7E+I1rzb9lnROt+RmT7f01zJ6farFjuM6LKPiNiZ6rmTp62bde2wWdEnPJQZ47yVy3v0Wz4f2wlte7/qHVXUuv6jKjPZ4TPiFr8jMi11lXnlp9qeS8WuqbN5r2d0rZtm9Ax3XHWZL0rx/tZEw05Fi5YGBYsb+L+Jo4xZHsBd7f2bcP3h/QPe67b9LmK5Hhlm3ZZH79tyVhSF5OP6Nerpo/fxvdTpQerU+LPMGPOvLB6p/Y1/RmRC8dv/8c5npWc4ym/zwg1bXlQl67k/5yV5ApWkivwGdGYzwifEZX8GdHSYxzNHWvN5VhOfb26dg6dOxYmn1ifXEH2qj5c/fnnnze4nS7klU7jIOb8+fNbPKbG68ila3VTP0O6MTW+v6U/e+PXMhsff/xxxsfrh7db2/XXX5/VcgvbtA+hz9AG9738+lthuy03b3L5W/7vb2HRwuw/yBe2bR/CWk2vq7477rgj79driy22CLvuumuTj913333hww8/zGu9G220Udh7772bfOzxxx8P7767cnqkXPXr1y+MHDmyyceef/75MHHixLzWGy8OOOKII5p8bOzYseE///lPXuuNfyvf/va3m3zs9ddfD0899VTI1ymnnNLk/e+//3548MEH817vt771rSYPFsa/2X/+8595r/ewww4La6yx6pXb8b07evTovNd7wAEHhHXXXbfJg03Z/i03Za+99gobb7xxk4+1ZL277LJL2HLLLZt87NZbb807EL7tttuG7bbbrsnHfEas5DOi6c+IeHqlw9pDw5L4f04eYqEfZz6Y/8l0nxFV9BnxXufe4YXV+uf8vogXasWpD2u9U0c517nV8h7Nllp3JbXu/6h1V1Lr+oyoz2eEz4ha+4zIp9atxTpXTVt5NW2++3H5iH+znVcszep4ebY+X7o8XDz2vTD5wX+Gtmn+v9rnoEOyPn7bkrGkLiZfZ/ZH4dmnnw61evw2Hu+phmB1c+/bcv3/Klv2e1dS0/6P/d6V1LTVU9OqS3Pn/5yV5Aqqpy5NkSv4H3XpSrJHK8keFfczoqXHOPbJcKz1nFv/mfexnC5tQ/jx1huHfdZbq+KOtVZybVpT4erGKf2WBplbkvovVOg523B147Hmup3Gr1U+P3u6A8Ip8erczTbbLFSan02aH8KkF5t+sOfgEHq29ogAIL14wnL7OVNa7QQs5S8G7vN9P8xatCRc8PK7Fb0TVAjVWucCANRqrVuLda6atnb24wqp44qloVNYHhY1GY9uXhz/4jbtswrAZjOWDsuXtuhi8vnVkysuiW3mTAkbLpgZ9vnqPmGdddZpsgN6POGbr6/s9pWwwQYbNPnYNTfcFO7KonENQCWqtZpWXQoAlEKPDu2Tma3yveg4dYwjndixuiXHchYsD3WzjLdvu+rsVq1heY3nCmouXdPUNGq5LJ/vlF25bKPQy5fzzw4AtI4NF84M6y+cmbG4T9n3kG+EY596o1XGRWnE90GpT8gDAEAxqHWpVq353o6B5RhcbkqMVI9oMyc80X6Nknc8djF5cew347XQeXnz4ff4HklF7Ht2aJd0pGpswfKlLQrSr9a+bZPrjbIZI0ClUtMCABRfDCyfMXyDpAN17ERdaHG2qJYey0nNMp5u37jYFtd4rqDqf/LG01MsWrQop+c3bp/etWvXFo+p8TpybdGe7Zga/+y5bqfxa5XPz/7kk09mfDy2kf/Zz34WyllLu1/kKl4RE6+MAYBCiye8sjmh1dP/Q2QxfU+tq4Y6FwCA2q5z1bQ0JR4Lj7NfZepLvUWbheHsr22bnNxr7LnnngtvvP6/C7YXtm1f1O7C2VxM3qlzp3DkkUeG2YuWhMMeHl+0sVSLGFouRGdxAFpfpda06lIAoFT2WW+tsNMa3cJ1N97c7LLFPsZRbXpVaG1aX5sVVd6OOB7IO+644+puf/nLXw5/+MMfsn7+/fffH0aNGlV3e//99w+/+c1vWjSmSZMmhT333LPu9qBBg8I999yT9fMnTJgQDjnkkLrb22yzTbjllltWWe7www8PL7/8ct3t22+/PWy55ZZZb2ffffcN77zzTt3tRx55JAwYMCAU0qeffhq++93vJt9fe+21YY01Wq8N/IIFC7Je9qGpM8MVr04pylUq9XVv3y6csdUGyQd3YzEcn++fa7t27ULHjh3ThuiXL8/v52rbtm3o1KlTq6538eLFYdmy/DqixG7snTt3bvKxJUuWhKVL8z9g3PhihpS4zrjuQq83vgbxtchXfB2a6mbf0vXG31v8/TUW3wu5XtxSX3z/xvdxY/FvItcLR7JZb66fEY116NAhtG/fvuDrjeuM626Kz4iVfEYU5m95QZt2YZ97X2pw3wNf2ybpFuQzojo+I2YvWhoOeHRig2Vu3GXTJoP1bdu1bVBHrNaxfWiX50wqtaSUdW41vEdzodZdSa37P2rdldS6PiPq8xnhM6KWPiPyrXXVuatS07bsvVjomjaX93ZK27ZtQsd0x1mT9a5osvlHc1PN5nL8tqlx/3P3LcLqndo3+f9VPCax9z0vrnJMonvblcdaW3KcNU5H23jd9+w9PFl3S9Zbycdvm3pN0v1+yu347Uez5+b8N5F6j3fp1LHk/1/lwn7vSmra/7Hfu5KatnZqWnXpqvyfs5JcQfXUpSlyBf+jLl1J9mgl2aPy+IxId4xj7R5dm1xvU/vcze23frZk6SqzjMfjIo07V5f7sdZqqU2rvj1u9+7dV+kgl4uZM2c2uN2jR48Wj6nxOnIdU+Pl042ppdtp/LM3fi0rXbrisin7b7xu2HfDfk124iik2LE63YHrdKHglkp3ELxc15vuJENLxf800v3H0RLxP6R0B2lbIv6nnMt7uNTrjTtGxVhv3JErxnqjSluvz4iVfEYU5m954aKmLwrxGVE9nxEL2676O+6zWveSTSdE4VX6e7RQ1LorqXVX8v/Y//iM8BlRn88InxHV9hmh1q0elf5eLHRNW/D3dpH2/xofm2lq3J27dA5d0mx/QZpjEsX8/yrdWGrp+G22v59yOn4bx9lY4xPQ6cLVcdrnpprcVPJnRKWs1/HbyvyMcI7nf9S0tUldupL/c1ZyHGUl/+f4jGjMZ4TPiFr4jEh3jCPdRcFNae5YTuc0x0UaU5e2jqoPVw8cOLDB7Y8++iin53/88ccNbheic3Pv3r2ToPK8efPqrrSMV3Rle0Ch8c+Qbkzrrbdexp8lk3iVR/1wdQxq9+rVK9SyGHoWOAKgVsWpc1t6oVBjS5evyPnCpVzWDwA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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sbc.compute_rank_statistics(lambda _, param_value: param_value)\n", "plot_ecdf_pit(sbc.simulations, group=\"posterior_sbc\", visuals={\"xlabel\": False})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "\n", "- Säilynoja, T., Schmitt, M., Bürkner, P.-C., & Vehtari, A. (2025).\n", " *Posterior SBC: Simulation-Based Calibration Checking Conditional on Data*.\n", " [arXiv:2502.03279](https://arxiv.org/abs/2502.03279)\n", "- Talts, S., Betancourt, M., Simpson, D., Vehtari, A., & Gelman, A. (2020).\n", " *Validating Bayesian Inference Algorithms with Simulation-Based Calibration*.\n", " [arXiv:1804.06788](https://arxiv.org/abs/1804.06788)" ] } ], "metadata": { "kernelspec": { "display_name": "simuk_dev", "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": "3.14.4" }, "tags": [ "skip-execution" ] }, "nbformat": 4, "nbformat_minor": 4 }