{ "cells": [ { "cell_type": "markdown", "id": "f2f86fe8", "metadata": {}, "source": [ "# MCMC sampling and priors\n", "\n", "This notebook covers the MCMC tools in `psiphy.mcmc` and the prior specifications in\n", "`psiphy.utils.prior`:\n", "\n", "1. Priors: uniform, log-uniform, Gaussian and mixtures\n", "2. Sampling a posterior with `MHSampler` (emcee backend)\n", "3. Convergence diagnostics: traces, autocorrelation time, burn-in\n", "4. Checking the result against the analytic posterior\n", "5. Saving, reloading and extending a chain\n", "6. Informative priors\n", "\n", "The test problem is `NoisyLine` (a straight line with Gaussian noise). Its posterior is\n", "Gaussian with a closed form, so every result can be checked exactly.\n", "\n", "Related notebooks: *Nested sampling and evidence* (posterior + Bayes factors),\n", "*Importance sampling and SMC*, *Likelihood-free inference* (simulator only)." ] }, { "cell_type": "code", "execution_count": 1, "id": "251a2b95", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T14:13:56.872159Z", "iopub.status.busy": "2026-10-14T14:13:56.871893Z", "iopub.status.idle": "2026-10-14T14:13:58.595266Z", "shell.execute_reply": "2026-10-14T14:13:58.594829Z" } }, "outputs": [], "source": [ "import os\n", "import tempfile\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "from psiphy.mcmc import MHSampler\n", "from psiphy.utils.prior import UniformPrior, LogUniformPrior, GaussianPrior, MixturePrior\n", "from psiphy.toy_models import NoisyLine\n", "from psiphy.plotting.diagnostics import SampledDistribution, plot_triangle\n", "\n", "np.random.seed(42)" ] }, { "cell_type": "markdown", "id": "a4550e70", "metadata": {}, "source": [ "---\n", "## 1 Priors\n", "\n", "Every prior in `psiphy.utils.prior` shares one interface, so the same object works with\n", "MCMC, nested sampling, importance sampling/SMC and BOLFI:\n", "\n", "| Method | Purpose |\n", "|---|---|\n", "| `sample(n)` | draws, shape `(n, ndim)` |\n", "| `log_prob(theta)` | single point → float; batch `(n, ndim)` → `(n,)` |\n", "| `prior_transform(u)` | unit cube → parameters (used by nested sampling) |\n", "| `to_scipy()`, `to_torch()`, `to_sbi()` | conversion to other libraries |" ] }, { "cell_type": "code", "execution_count": 2, "id": "6f224779", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T14:13:58.596887Z", "iopub.status.busy": "2026-10-14T14:13:58.596732Z", "iopub.status.idle": "2026-10-14T14:13:58.864978Z", "shell.execute_reply": "2026-10-14T14:13:58.864413Z" } }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "priors = {\n", " 'Uniform(0, 10)': UniformPrior([(0, 10)]),\n", " 'LogUniform(0.1, 10)': LogUniformPrior([(0.1, 10)]),\n", " 'Gaussian(5, 1.5²)': GaussianPrior([5.0], [1.5**2]),\n", " 'Mixture: 0.3 N(2,.5²) + 0.7 N(7,1²)': MixturePrior(\n", " [GaussianPrior([2.0], [0.25]), GaussianPrior([7.0], [1.0])], weights=[0.3, 0.7]),\n", "}\n", "\n", "grid = np.linspace(0.01, 11, 500)[:, None]\n", "fig, axes = plt.subplots(1, 4, figsize=(15, 3), sharey=False)\n", "for ax, (name, p) in zip(axes, priors.items()):\n", " ax.hist(p.sample(20000)[:, 0], bins=60, range=(0, 11), density=True, alpha=0.5, label='samples')\n", " ax.plot(grid[:, 0], np.exp(p.log_prob(grid)), 'k', lw=1.5, label='exp(log_prob)')\n", " ax.set(title=name, xlabel=r'$\\theta$')\n", "axes[0].legend(fontsize=8)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "4cabba03", "metadata": {}, "source": [ "Named bounds can be passed as a dict; the keys become `prior.names` and are picked up by\n", "the samplers. `prior_transform` maps uniform draws on $[0,1]^d$ to the prior, which is how\n", "nested samplers use it." ] }, { "cell_type": "code", "execution_count": 3, "id": "38aa8958", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T14:13:58.866370Z", "iopub.status.busy": "2026-10-14T14:13:58.866281Z", "iopub.status.idle": "2026-10-14T14:13:58.868874Z", "shell.execute_reply": "2026-10-14T14:13:58.868305Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "names : ['slope', 'intercept']\n", "log_prob (inside): -4.094344562222101\n", "log_prob (batch) : [-4.09434456 -inf]\n", "prior_transform : [0. 5.]\n" ] } ], "source": [ "prior = UniformPrior({'slope': (-3, 3), 'intercept': (0, 10)})\n", "print('names :', prior.names)\n", "print('log_prob (inside):', prior.log_prob([0.0, 5.0]))\n", "print('log_prob (batch) :', prior.log_prob(np.array([[0.0, 5.0], [9.0, 5.0]])))\n", "print('prior_transform :', prior.prior_transform([0.5, 0.5]))" ] }, { "cell_type": "markdown", "id": "f3fea2c8", "metadata": {}, "source": [ "---\n", "## 2 Problem: fitting a noisy line\n", "\n", "Data: $y_i = m x_i + b + \\varepsilon_i$ with $\\varepsilon_i \\sim \\mathcal{N}(0, \\sigma^2)$\n", "and known $\\sigma$. With a flat prior the posterior on $(m, b)$ is Gaussian with\n", "covariance $\\sigma^2 (A^\\top A)^{-1}$, where $A = [x, 1]$, centred on the least-squares fit." ] }, { "cell_type": "code", "execution_count": 4, "id": "52356705", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T14:13:58.870051Z", "iopub.status.busy": "2026-10-14T14:13:58.869973Z", "iopub.status.idle": "2026-10-14T14:13:58.904324Z", "shell.execute_reply": "2026-10-14T14:13:58.903523Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "analytic posterior mean: [-0.816 5.188]\n", "analytic posterior std : [0.043 0.248]\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "line = NoisyLine(Nx=40, noise_sigma=0.8)\n", "theta_true = np.array([-0.8, 5.0])\n", "y_obs = line.simulate(theta_true)\n", "\n", "def log_posterior(theta):\n", " lp = prior.log_prob(theta)\n", " return lp + line.log_prob(theta, y_obs) if np.isfinite(lp) else -np.inf\n", "\n", "# analytic posterior (flat prior, posterior well inside the box)\n", "A = np.column_stack([line.x, np.ones_like(line.x)])\n", "post_cov = line.noise_sigma**2 * np.linalg.inv(A.T @ A)\n", "post_mean = np.linalg.solve(A.T @ A, A.T @ y_obs)\n", "print('analytic posterior mean:', post_mean.round(3))\n", "print('analytic posterior std :', np.sqrt(np.diag(post_cov)).round(3))\n", "\n", "plt.figure(figsize=(6, 3.5))\n", "plt.plot(line.x, y_obs, '.', label='data')\n", "plt.plot(line.x, theta_true[0] * line.x + theta_true[1], 'r-', label='truth')\n", "plt.xlabel('x'); plt.ylabel('y'); plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "55404a99", "metadata": {}, "source": [ "---\n", "## 3 Running `MHSampler`\n", "\n", "`MHSampler` wraps `emcee.EnsembleSampler`. Starting from a single point, the walkers are\n", "spread into a small Gaussian ball (`init_scale`, relative). Starting from prior draws,\n", "pass an array of shape `(n_walkers, n_dim)`." ] }, { "cell_type": "code", "execution_count": 5, "id": "83192da0", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T14:13:58.906433Z", "iopub.status.busy": "2026-10-14T14:13:58.906258Z", "iopub.status.idle": "2026-10-14T14:13:59.924109Z", "shell.execute_reply": "2026-10-14T14:13:59.923640Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "chain shape (steps, walkers, dim): (3000, 32, 2)\n", "mean acceptance fraction : 0.712\n" ] } ], "source": [ "sampler = MHSampler(log_posterior, n_walkers=32, param_names=prior.names)\n", "sampler.run(prior.sample(32), n_steps=3000, progress=False)\n", "\n", "print('chain shape (steps, walkers, dim):', sampler.get_chain().shape)\n", "print('mean acceptance fraction :', sampler.acceptance_fraction.mean().round(3))" ] }, { "cell_type": "markdown", "id": "e61f60eb", "metadata": {}, "source": [ "---\n", "## 4 Convergence diagnostics\n", "\n", "Walkers start spread over the whole prior and need some steps to reach the posterior.\n", "The integrated autocorrelation time $\\tau$ measures how many steps it takes for the\n", "chain to forget its state. Common practice: discard a few $\\tau$ as burn-in and run for\n", "at least ~50 $\\tau$. `discard=\"auto\"` drops $3\\,\\max(\\tau)$ steps." ] }, { "cell_type": "code", "execution_count": 6, "id": "b66bb3da", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T14:13:59.925330Z", "iopub.status.busy": "2026-10-14T14:13:59.925258Z", "iopub.status.idle": "2026-10-14T14:14:00.063744Z", "shell.execute_reply": "2026-10-14T14:14:00.063023Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "autocorrelation time: [25.7 31.6] → auto burn-in = 94 steps\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "chain = sampler.get_chain()\n", "tau = sampler.autocorr_time()\n", "burn = int(3 * tau.max())\n", "print('autocorrelation time:', tau.round(1), ' → auto burn-in =', burn, 'steps')\n", "\n", "fig, axes = plt.subplots(2, 1, figsize=(10, 5), sharex=True)\n", "for i, (ax, name) in enumerate(zip(axes, prior.names)):\n", " ax.plot(chain[:, :, i], 'k', alpha=0.1, lw=0.6)\n", " ax.axhline(theta_true[i], c='r', lw=1)\n", " ax.axvline(burn, c='C0', ls='--', label='auto burn-in')\n", " ax.set_ylabel(name)\n", "axes[0].legend(loc='upper right')\n", "axes[-1].set_xlabel('step')\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "63adfd73", "metadata": {}, "source": [ "---\n", "## 5 Posterior and comparison with the analytic result" ] }, { "cell_type": "code", "execution_count": 7, "id": "00adf9d8", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T14:14:00.065727Z", "iopub.status.busy": "2026-10-14T14:14:00.065546Z", "iopub.status.idle": "2026-10-14T14:14:00.098382Z", "shell.execute_reply": "2026-10-14T14:14:00.095232Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " param mean std median tau\n", " slope -0.8164 0.04297 -0.817 25.7\n", " intercept 5.184 0.2475 5.186 31.6\n", "acceptance fraction = 0.712, n_samples = 92992\n" ] } ], "source": [ "summary = sampler.summary(discard='auto')" ] }, { "cell_type": "code", "execution_count": 8, "id": "a5714299", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T14:14:00.100572Z", "iopub.status.busy": "2026-10-14T14:14:00.100417Z", "iopub.status.idle": "2026-10-14T14:14:00.185573Z", "shell.execute_reply": "2026-10-14T14:14:00.185047Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "MCMC mean : [-0.816 5.184] analytic: [-0.816 5.188]\n", "MCMC std : [0.043 0.247] analytic: [0.043 0.248]\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "samples = sampler.get_chain(flat=True, discard='auto', thin=5)\n", "print('MCMC mean :', samples.mean(0).round(3), ' analytic:', post_mean.round(3))\n", "print('MCMC std :', samples.std(0).round(3), ' analytic:', np.sqrt(np.diag(post_cov)).round(3))\n", "\n", "fig = plot_triangle(samples, labels=['m', 'b'], true_values=theta_true, engine='corner',\n", " bins=40, plot_datapoints=False, fill_contours=True, levels=(0.68, 0.95))\n", "# overlay the analytic 1σ/2σ ellipse in the 2-D panel\n", "ax = fig.axes[2]\n", "vals, vecs = np.linalg.eigh(post_cov)\n", "t = np.linspace(0, 2 * np.pi, 200)\n", "for k in (1, 2):\n", " ell = post_mean[:, None] + vecs @ (k * np.sqrt(vals)[:, None] * np.vstack([np.cos(t), np.sin(t)]))\n", " ax.plot(*ell, 'C1--', lw=1)\n", "fig.suptitle('MHSampler vs analytic posterior (orange dashed: 1σ, 2σ)', y=1.02)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "cf840230", "metadata": {}, "source": [ "**Why is $b$ not centred on the truth?** The MCMC result matches the analytic\n", "posterior, and that posterior is centred on the least-squares fit to *these* 40 points.\n", "The noise in this particular data set moves that fit away from the true line by a fraction\n", "of a standard deviation (printed below). Every correct method follows the data; checking\n", "for *bias* requires many data sets — see Section 7 of the *Importance sampling and SMC*\n", "tutorial." ] }, { "cell_type": "code", "execution_count": 9, "id": "7a1ddcd2", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T14:14:00.186883Z", "iopub.status.busy": "2026-10-14T14:14:00.186804Z", "iopub.status.idle": "2026-10-14T14:14:00.188974Z", "shell.execute_reply": "2026-10-14T14:14:00.188439Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "least-squares fit: [-0.816 5.188] truth: [-0.8 5. ] offset (sigma): [-0.38 0.76]\n" ] } ], "source": [ "offset = (post_mean - theta_true) / np.sqrt(np.diag(post_cov))\n", "print('least-squares fit:', post_mean.round(3), ' truth:', theta_true, ' offset (sigma):', offset.round(2))" ] }, { "cell_type": "markdown", "id": "b80b0fb7", "metadata": {}, "source": [ "The same samples plug straight into the diagnostics tools (see the *Plotting\n", "diagnostics* tutorial) for z-scores, credible intervals and comparisons." ] }, { "cell_type": "code", "execution_count": 10, "id": "ec40e2dd", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T14:14:00.190098Z", "iopub.status.busy": "2026-10-14T14:14:00.190029Z", "iopub.status.idle": "2026-10-14T14:14:00.195092Z", "shell.execute_reply": "2026-10-14T14:14:00.194632Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "slope median=-0.817 68% [-0.859, -0.774]\n", "intercept median=5.185 68% [4.941, 5.429]\n", "z-scores: [0.38 0.75]\n" ] } ], "source": [ "dist = SampledDistribution(samples, true_values=theta_true, labels=['m', 'b'])\n", "for name, ci in zip(prior.names, dist.credible_intervals(levels=(68, 95))):\n", " print(f\"{name:10s} median={ci['median']:.3f} 68% [{ci['lo68']:.3f}, {ci['hi68']:.3f}]\")\n", "print('z-scores:', np.round(dist.z_scores(), 2))" ] }, { "cell_type": "markdown", "id": "4b3fa444", "metadata": {}, "source": [ "---\n", "## 6 Saving, reloading and extending a chain\n", "\n", "Pass `filename=` to store the chain in HDF5 (needs `h5py`). The file can be reloaded, and\n", "`run(n_steps=...)` without a starting point continues from the last state — useful for\n", "long jobs on a cluster with wall-time limits." ] }, { "cell_type": "code", "execution_count": 11, "id": "462d3704", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T14:14:00.196077Z", "iopub.status.busy": "2026-10-14T14:14:00.196017Z", "iopub.status.idle": "2026-10-14T14:14:02.074407Z", "shell.execute_reply": "2026-10-14T14:14:02.073996Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "first job : 500 steps\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "after resume: 1500 steps stored in line_chain.h5\n" ] } ], "source": [ "tmpdir = tempfile.mkdtemp()\n", "fn = os.path.join(tmpdir, 'line_chain.h5')\n", "\n", "s1 = MHSampler(log_posterior, n_walkers=32, filename=fn)\n", "s1.run(prior.sample(32), n_steps=500)\n", "print('first job :', s1.n_steps, 'steps')\n", "\n", "# later, e.g. in a new job:\n", "s2 = MHSampler.load(fn, log_prob_fn=log_posterior)\n", "s2.run(n_steps=1000)\n", "print('after resume:', s2.n_steps, 'steps stored in', os.path.basename(fn))" ] }, { "cell_type": "markdown", "id": "fa055d99", "metadata": {}, "source": [ "---\n", "## 7 Informative priors\n", "\n", "Swapping the prior is a one-line change. A Gaussian prior on the intercept (say from an\n", "earlier measurement) tightens the intercept and, through the correlation, the slope." ] }, { "cell_type": "code", "execution_count": 12, "id": "45ec1125", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T14:14:02.075563Z", "iopub.status.busy": "2026-10-14T14:14:02.075490Z", "iopub.status.idle": "2026-10-14T14:14:03.907566Z", "shell.execute_reply": "2026-10-14T14:14:03.906835Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "std flat : [0.043 0.247]\n", "std informative: [0.029 0.128]\n" ] } ], "source": [ "prior_inf = GaussianPrior(mean=[0.0, 5.0], cov=[10.0**2, 0.15**2], names=['slope', 'intercept'])\n", "log_post_inf = lambda t: prior_inf.log_prob(t) + line.log_prob(t, y_obs)\n", "\n", "s_inf = MHSampler(log_post_inf, n_walkers=32).run(prior.sample(32), n_steps=3000)\n", "samples_inf = s_inf.get_chain(flat=True, discard='auto', thin=5)\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(10, 3.5))\n", "for i, (ax, name) in enumerate(zip(axes, prior.names)):\n", " ax.hist(samples[:, i], bins=50, density=True, alpha=0.5, label='flat prior')\n", " ax.hist(samples_inf[:, i], bins=50, density=True, alpha=0.5, label='Gaussian prior on b')\n", " ax.axvline(theta_true[i], c='r')\n", " ax.set_xlabel(name)\n", "axes[0].legend()\n", "plt.tight_layout()\n", "plt.show()\n", "print('std flat :', samples.std(0).round(3))\n", "print('std informative:', samples_inf.std(0).round(3))" ] }, { "cell_type": "markdown", "id": "5d6a6413", "metadata": {}, "source": [ "---\n", "## Summary\n", "\n", "| Task | Code |\n", "|---|---|\n", "| Define a prior | `UniformPrior({...})`, `LogUniformPrior`, `GaussianPrior`, `MixturePrior` |\n", "| Run MCMC | `MHSampler(log_prob, n_walkers=32).run(theta_init, n_steps=...)` |\n", "| Diagnose | `autocorr_time()`, `acceptance_fraction`, trace of `get_chain()` |\n", "| Samples | `get_chain(flat=True, discard='auto', thin=...)` |\n", "| Summary | `summary()` |\n", "| Checkpoint / resume | `filename='chain.h5'`, `MHSampler.load(...)`, `run(n_steps=...)` |\n", "\n", "Parallel evaluation: pass `pool=` (any object with a `map` method, e.g. a\n", "`multiprocessing.Pool`)." ] } ], "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": "3.12.11" } }, "nbformat": 4, "nbformat_minor": 5 }