{ "cells": [ { "cell_type": "markdown", "id": "d8f105f7", "metadata": {}, "source": [ "# Robust likelihoods: Student-t vs the multivariate normal\n", "\n", "The multivariate-normal likelihood penalizes a residual quadratically, so a few\n", "outliers — mislabeled points, an unreported background, a transcription error —\n", "leave it **confidently wrong**: the posterior stays narrow around a biased value.\n", "The **Student-t** likelihood keeps the same covariance $\\Sigma$ but replaces the\n", "Gaussian functional with a heavy-tailed one carrying a degrees-of-freedom\n", "parameter $\\nu$: small $\\nu$ means heavy tails, $\\nu \\to \\infty$ recovers the\n", "Gaussian. Sampling $\\nu$ lets the *data* decide how heavy the tails need to be\n", "— and, as we will see, the multivariate-t's honesty shows up as **wider,\n", "truth-covering uncertainty**, not as outlier rejection.\n" ] }, { "cell_type": "code", "execution_count": 1, "id": "2bdf89cc", "metadata": { "execution": { "iopub.execute_input": "2026-08-03T17:43:52.311562Z", "iopub.status.busy": "2026-08-03T17:43:52.311358Z", "iopub.status.idle": "2026-08-03T17:43:54.650591Z", "shell.execute_reply": "2026-08-03T17:43:54.649500Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Using database version X4-2024-12-31 located in: /home/kyle/db/exfor/unpack_exfor-2024/X4-2024-12-31\n" ] } ], "source": [ "import corner\n", "import numpy as np\n", "from matplotlib import pyplot as plt\n", "from scipy import stats\n", "\n", "import rxmc\n", "\n", "rng = np.random.default_rng(21)" ] }, { "cell_type": "markdown", "id": "8e3985d0", "metadata": {}, "source": [ "## A clean linear signal with a few gross outliers" ] }, { "cell_type": "code", "execution_count": 2, "id": "7594ebbb", "metadata": { "execution": { "iopub.execute_input": "2026-08-03T17:43:54.653141Z", "iopub.status.busy": "2026-08-03T17:43:54.652804Z", "iopub.status.idle": "2026-08-03T17:43:54.806038Z", "shell.execute_reply": "2026-08-03T17:43:54.805138Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "class LinearModel(rxmc.physical_model.PhysicalModel):\n", " def __init__(self):\n", " super().__init__(\n", " [rxmc.params.Parameter(\"m\", float), rxmc.params.Parameter(\"b\", float)]\n", " )\n", "\n", " def evaluate(self, observation, m, b):\n", " return self.y(observation.x, m, b)\n", "\n", " def y(self, x, m, b):\n", " return m * x + b\n", "\n", "\n", "model = LinearModel()\n", "m_true, b_true = 1.0, 0.5\n", "noise = 0.05\n", "\n", "x = np.linspace(0.0, 4.0, 25)\n", "y = model.y(x, m_true, b_true) + rng.normal(0.0, noise, x.size)\n", "\n", "outliers = np.array([5, 12, 19])\n", "y[outliers] += np.array([10.0, 12.0, 9.0]) * noise # one-sided: a fake background\n", "\n", "obs = rxmc.observation.Observation(x=x, y=y, y_stat_err=noise * np.ones_like(y))\n", "\n", "xg = np.linspace(-0.2, 4.2, 100)\n", "plt.plot(xg, model.y(xg, m_true, b_true), \"k:\", label=\"true signal\")\n", "plt.errorbar(x, y, noise, ls=\"none\", marker=\".\", label=\"data\")\n", "plt.plot(x[outliers], y[outliers], \"o\", mfc=\"none\", color=\"tab:red\", label=\"outliers\")\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\")\n", "plt.legend();" ] }, { "cell_type": "markdown", "id": "34ea6351", "metadata": {}, "source": [ "## The same constraint, two likelihood functionals\n", "\n", "The likelihood functional is orthogonal to the covariance: both constraints below\n", "share the identical statistical $\\Sigma$; only the function of\n", "$(d^2, \\log\\det\\Sigma, n)$ differs. The Student-t brings one likelihood-side\n", "parameter, and the **full-tuple convention** applies everywhere: every\n", "`Constraint` method takes covariance parameters followed by likelihood\n", "parameters, in `constraint.params` order — including `chi2`, even though the\n", "chi-squared statistic ignores $\\nu$.\n" ] }, { "cell_type": "code", "execution_count": 3, "id": "b0ee0605", "metadata": { "execution": { "iopub.execute_input": "2026-08-03T17:43:54.807838Z", "iopub.status.busy": "2026-08-03T17:43:54.807661Z", "iopub.status.idle": "2026-08-03T17:43:54.812937Z", "shell.execute_reply": "2026-08-03T17:43:54.811975Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Gaussian constraint params: []\n", "Student-t constraint params: ['degrees_of_freedom']\n" ] } ], "source": [ "nu_param = rxmc.params.Parameter(\n", " \"degrees_of_freedom\", float, latex_name=r\"\\nu\", bounds=(1.0, 100.0)\n", ")\n", "\n", "c_gauss = rxmc.constraint.Constraint([obs], model)\n", "c_t = rxmc.constraint.Constraint(\n", " [obs], model, likelihood=rxmc.likelihood_model.StudentT(nu_parameter=nu_param)\n", ")\n", "\n", "print(\"Gaussian constraint params:\", [p.name for p in c_gauss.params])\n", "print(\"Student-t constraint params:\", [p.name for p in c_t.params])" ] }, { "cell_type": "markdown", "id": "89342ff5", "metadata": {}, "source": [ "## Sampling $\\nu$ alongside the model\n", "\n", "$\\nu$ is a likelihood parameter, so it goes to a `likelihood_samplers` entry in\n", "the `Walker` — the Gibbs framework alternates between the physics block and the\n", "nuisance block.\n" ] }, { "cell_type": "code", "execution_count": 4, "id": "08a8ecf5", "metadata": { "execution": { "iopub.execute_input": "2026-08-03T17:43:54.814637Z", "iopub.status.busy": "2026-08-03T17:43:54.814441Z", "iopub.status.idle": "2026-08-03T17:44:01.618243Z", "shell.execute_reply": "2026-08-03T17:44:01.617393Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Gaussian m = 1.002 ± 0.008 b = 0.566 ± 0.019 (truth b = 0.5 is 3.4 sigma away)\n", "Student-t m = 1.002 ± 0.028 b = 0.562 ± 0.067 (truth b = 0.5 is 0.9 sigma away)\n" ] } ], "source": [ "model_prior = stats.multivariate_normal(mean=[1.0, 0.5], cov=np.diag([0.3, 0.3]) ** 2)\n", "\n", "\n", "def make_model_sampler():\n", " return rxmc.param_sampling.BatchedAdaptiveMetropolisSampler(\n", " params=model.params,\n", " starting_location=model_prior.mean,\n", " prior=model_prior,\n", " initial_proposal_cov=model_prior.cov / 100,\n", " )\n", "\n", "\n", "nu_prior = stats.multivariate_normal(mean=[10.0], cov=[[49.0]])\n", "nu_sampler = rxmc.param_sampling.BatchedAdaptiveMetropolisSampler(\n", " params=list(c_t.params),\n", " starting_location=np.array([10.0]),\n", " prior=nu_prior,\n", " initial_proposal_cov=np.array([[4.0]]),\n", ")\n", "\n", "walker_gauss = rxmc.walker.Walker(\n", " make_model_sampler(),\n", " rxmc.evidence.Evidence([c_gauss]),\n", " rng=np.random.default_rng(1),\n", ")\n", "walker_t = rxmc.walker.Walker(\n", " make_model_sampler(),\n", " rxmc.evidence.Evidence([c_t]),\n", " likelihood_samplers=[nu_sampler],\n", " rng=np.random.default_rng(2),\n", ")\n", "\n", "for walker in (walker_gauss, walker_t):\n", " walker.walk(n_steps=6000, burnin=2000, batch_size=1000, verbose=False)\n", "\n", "chain_gauss = walker_gauss.model_sampler.chain\n", "chain_t = walker_t.model_sampler.chain\n", "nu_chain = walker_t.likelihood_samplers[0].chain\n", "\n", "for name, ch in [(\"Gaussian\", chain_gauss), (\"Student-t\", chain_t)]:\n", " z = abs(ch[:, 1].mean() - b_true) / ch[:, 1].std()\n", " print(\n", " f\"{name:10s} m = {ch[:, 0].mean():.3f} ± {ch[:, 0].std():.3f} \"\n", " f\"b = {ch[:, 1].mean():.3f} ± {ch[:, 1].std():.3f} \"\n", " f\"(truth b = {b_true} is {z:.1f} sigma away)\"\n", " )" ] }, { "cell_type": "code", "execution_count": 5, "id": "9e6a0c15", "metadata": { "execution": { "iopub.execute_input": "2026-08-03T17:44:01.620568Z", "iopub.status.busy": "2026-08-03T17:44:01.620348Z", "iopub.status.idle": "2026-08-03T17:44:01.822830Z", "shell.execute_reply": "2026-08-03T17:44:01.821741Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = corner.corner(\n", " chain_t,\n", " labels=[\"m\", \"b\"],\n", " truths=[m_true, b_true],\n", " truth_color=\"k\",\n", " color=\"tab:blue\",\n", ")\n", "corner.corner(chain_gauss, fig=fig, color=\"tab:red\")\n", "plt.plot([], [], color=\"tab:blue\", label=\"Student-t\")\n", "plt.plot([], [], color=\"tab:red\", label=\"Gaussian\")\n", "fig.legend(loc=\"upper right\");" ] }, { "cell_type": "markdown", "id": "883c01ed", "metadata": {}, "source": [ "Both posteriors are shifted by the one-sided outliers — but the Gaussian is\n", "**confidently wrong** (truth excluded at $\\sim 3.5\\sigma$) while the Student-t\n", "inflates its uncertainty until the truth is covered ($\\lesssim 1\\sigma$).\n", "\n", "This is the multivariate-t's character: it carries **one** radial tail factor\n", "for the whole stacked residual, so it cannot single out and reject individual\n", "points — it broadens the posterior instead of relocating it. Per-point outlier\n", "rejection would need per-point machinery (e.g. a free noise nuisance via\n", "`noise_term`, or explicitly masking suspect points).\n" ] }, { "cell_type": "code", "execution_count": 6, "id": "a1f32cc9", "metadata": { "execution": { "iopub.execute_input": "2026-08-03T17:44:01.825295Z", "iopub.status.busy": "2026-08-03T17:44:01.825036Z", "iopub.status.idle": "2026-08-03T17:44:02.702670Z", "shell.execute_reply": "2026-08-03T17:44:02.701239Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.hist(nu_chain[:, 0], bins=40, color=\"tab:blue\", alpha=0.7)\n", "plt.xlabel(r\"$\\nu$\")\n", "plt.ylabel(\"posterior samples\")\n", "plt.title(f\"heavy tails demanded: median $\\\\nu$ = {np.median(nu_chain):.1f}\");" ] }, { "cell_type": "markdown", "id": "fd330f6e", "metadata": {}, "source": [ "## `chi2`: the fit statistic without the normalization\n", "\n", "`Constraint.chi2` returns the generalized chi-squared (the squared Mahalanobis\n", "distance) under the same $\\Sigma$. Note the full-tuple convention: the\n", "Student-t constraint requires $\\nu$ in the tuple even though the statistic\n", "ignores it.\n" ] }, { "cell_type": "code", "execution_count": 7, "id": "b945e231", "metadata": { "execution": { "iopub.execute_input": "2026-08-03T17:44:02.704495Z", "iopub.status.busy": "2026-08-03T17:44:02.704334Z", "iopub.status.idle": "2026-08-03T17:44:02.709510Z", "shell.execute_reply": "2026-08-03T17:44:02.708453Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Gaussian chi2/n = 10.98\n", "Student-t chi2/n = 10.98\n" ] } ], "source": [ "map_gauss = chain_gauss[np.argmax(walker_gauss.model_sampler.logp_chain)]\n", "map_t = chain_t[np.argmax(walker_t.model_sampler.logp_chain)]\n", "nu_map = float(np.median(nu_chain))\n", "\n", "chi2_gauss = c_gauss.chi2(tuple(map_gauss))\n", "chi2_t = c_t.chi2(tuple(map_t), (nu_map,))\n", "print(f\"Gaussian chi2/n = {chi2_gauss / obs.n_data_pts:.2f}\")\n", "print(f\"Student-t chi2/n = {chi2_t / obs.n_data_pts:.2f}\")" ] }, { "cell_type": "markdown", "id": "1ab2a3ba", "metadata": {}, "source": [ "## Predictive comparison" ] }, { "cell_type": "code", "execution_count": 8, "id": "57661fd9", "metadata": { "execution": { "iopub.execute_input": "2026-08-03T17:44:02.711407Z", "iopub.status.busy": "2026-08-03T17:44:02.711236Z", "iopub.status.idle": "2026-08-03T17:44:02.833905Z", "shell.execute_reply": "2026-08-03T17:44:02.832486Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def band(chain, levels=(5, 95)):\n", " draws = chain[:: max(1, len(chain) // 300)]\n", " ys = np.array([model.y(xg, *p) for p in draws])\n", " return np.percentile(ys, levels, axis=0)\n", "\n", "\n", "lo_g, hi_g = band(chain_gauss)\n", "lo_t, hi_t = band(chain_t)\n", "\n", "plt.plot(xg, model.y(xg, m_true, b_true), \"k:\", label=\"true signal\")\n", "plt.errorbar(x, y, noise, ls=\"none\", marker=\".\", color=\"gray\", label=\"data\")\n", "plt.fill_between(xg, lo_g, hi_g, alpha=0.4, color=\"tab:red\", label=\"Gaussian\")\n", "plt.fill_between(xg, lo_t, hi_t, alpha=0.4, color=\"tab:blue\", label=\"Student-t\")\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\")\n", "plt.legend();" ] }, { "cell_type": "markdown", "id": "9e4a0f63", "metadata": {}, "source": [ "## Takeaways\n", "\n", "- **The likelihood functional is a drop-in choice**: `Constraint(...,\n", " likelihood=StudentT())` keeps the covariance model identical and changes only\n", " the function of $(d^2, \\log\\det\\Sigma, n)$.\n", "- **$\\nu$ is an ordinary nuisance parameter** — give it bounds on its\n", " `Parameter`, a prior, and a `likelihood_samplers` entry, and the data choose\n", " the tail weight.\n", "- **The multivariate-t buys honesty, not outlier rejection**: one shared tail\n", " factor widens the posterior to cover the truth where the Gaussian is\n", " confidently biased; rejecting individual points needs per-point terms.\n", "- **The full-tuple convention is uniform**: every method — `log_likelihood`,\n", " `chi2`, `covariance_matrix` — takes covariance parameters then likelihood\n", " parameters in `constraint.params` order, and raises on a wrong count instead\n", " of guessing.\n" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.3" } }, "nbformat": 4, "nbformat_minor": 5 }