{ "cells": [ { "cell_type": "markdown", "id": "906c5746", "metadata": {}, "source": [ "# Likelihood-free inference\n", "\n", "Often the likelihood $p(x \\mid \\theta)$ cannot be written down, but data can be\n", "**simulated** for any $\\theta$. Likelihood-free (simulation-based) inference works with the\n", "simulator alone. This notebook compares three methods from `psiphy.sbi` on a problem whose\n", "exact posterior is known:\n", "\n", "1. **Rejection ABC** (`rABC`): keep prior draws whose simulation lands close to the data.\n", " Simple, but needs many simulations.\n", "2. **BOLFI** (`BOLFI`): learn a Gaussian-process model of the discrepancy with Bayesian\n", " optimisation, then sample the resulting synthetic likelihood with any psiphy sampler.\n", " Typically needs orders of magnitude fewer simulations — what matters when each\n", " simulation is expensive.\n", "3. **LFIRE** (`LFIRE`): estimate the likelihood-to-evidence ratio\n", " $p(x \\mid \\theta)/p(x)$ with a classifier. No distance or tolerance to tune; the\n", " classifier learns how to weigh the summaries.\n", "\n", "Contents: the problem → exact reference → rejection ABC → BOLFI → LFIRE → acquisition\n", "functions and batch proposals → saving/resuming." ] }, { "cell_type": "code", "execution_count": 1, "id": "01ca1ebb", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T14:29:23.022793Z", "iopub.status.busy": "2026-10-14T14:29:23.022563Z", "iopub.status.idle": "2026-10-14T14:29:24.089605Z", "shell.execute_reply": "2026-10-14T14:29:24.089227Z" } }, "outputs": [], "source": [ "import os\n", "import tempfile\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "from psiphy.sbi.bolfi import BOLFI\n", "from psiphy.sbi.rejection_abc import rABC\n", "from psiphy.mcmc import MHSampler\n", "from psiphy.utils.prior import UniformPrior\n", "from psiphy.toy_models import GaussianSignal\n", "\n", "np.random.seed(3)" ] }, { "cell_type": "markdown", "id": "2dca855e", "metadata": {}, "source": [ "---\n", "## 1 Problem and discrepancy\n", "\n", "Data: $N = 50$ draws from $\\mathcal{N}(\\mu, \\sigma^2)$; unknowns $\\theta = (\\mu, \\sigma)$.\n", "We pretend we can only simulate.\n", "\n", "Both methods compare simulated and observed data through **summary statistics** — here\n", "the sample mean $\\bar{x}$ and standard deviation $s$ — combined into a discrepancy scaled\n", "by their expected sampling variances ($\\mathrm{Var}\\,\\bar{x} \\approx s^2/N$,\n", "$\\mathrm{Var}\\,s \\approx s^2/2N$):\n", "\n", "$$d(\\theta) = N\\left[\\frac{(\\bar{x}_\\theta - \\bar{x}_{\\rm obs})^2}{s_{\\rm obs}^2}\n", "+ \\frac{2\\,(s_\\theta - s_{\\rm obs})^2}{s_{\\rm obs}^2}\\right]$$\n", "\n", "With this scaling $d$ behaves like a $\\chi^2$, which BOLFI's default `'exp'` kernel\n", "($\\mathcal{L} \\propto e^{-d/2}$) assumes." ] }, { "cell_type": "code", "execution_count": 2, "id": "939844a8", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T14:29:24.091019Z", "iopub.status.busy": "2026-10-14T14:29:24.090914Z", "iopub.status.idle": "2026-10-14T14:29:24.093265Z", "shell.execute_reply": "2026-10-14T14:29:24.092951Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "observed: mean = 1.265, std = 0.807\n" ] } ], "source": [ "gs = GaussianSignal(N=50)\n", "theta_true = np.array([1.5, 0.8])\n", "x_obs = gs.simulate(theta_true)\n", "\n", "N = len(x_obs)\n", "m_obs, s_obs = x_obs.mean(), x_obs.std(ddof=1)\n", "\n", "def discrepancy(x_sim):\n", " return N * ((x_sim.mean() - m_obs) ** 2 / s_obs**2 + 2 * (x_sim.std(ddof=1) - s_obs) ** 2 / s_obs**2)\n", "\n", "prior = UniformPrior({'mu': (0, 3), 'sigma': (0.1, 2.5)})\n", "labels = [r'$\\mu$', r'$\\sigma$']\n", "print(f'observed: mean = {m_obs:.3f}, std = {s_obs:.3f}')" ] }, { "cell_type": "markdown", "id": "e1f8165f", "metadata": {}, "source": [ "---\n", "## 2 Exact reference posterior\n", "\n", "Because this toy model has a known likelihood, we can get the exact posterior with MCMC\n", "and use it to judge the likelihood-free results." ] }, { "cell_type": "code", "execution_count": 3, "id": "21435a96", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T14:29:24.094306Z", "iopub.status.busy": "2026-10-14T14:29:24.094250Z", "iopub.status.idle": "2026-10-14T14:29:24.966189Z", "shell.execute_reply": "2026-10-14T14:29:24.965810Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "exact mean: [1.267 0.829] std: [0.119 0.086]\n" ] } ], "source": [ "def log_post_exact(t):\n", " lp = prior.log_prob(t)\n", " return lp + gs.log_prob(t, x_obs) if np.isfinite(lp) else -np.inf\n", "\n", "exact = MHSampler(log_post_exact, n_walkers=32).run(prior.sample(32), n_steps=3000)\n", "s_exact = exact.get_chain(flat=True, discard='auto', thin=5)\n", "print('exact mean:', s_exact.mean(0).round(3), ' std:', s_exact.std(0).round(3))" ] }, { "cell_type": "markdown", "id": "be633d70", "metadata": {}, "source": [ "---\n", "## 3 Rejection ABC\n", "\n", "Draw $\\theta$ from the prior, simulate, keep $\\theta$ if $d < \\varepsilon$. Smaller\n", "$\\varepsilon$ is more accurate but accepts fewer draws." ] }, { "cell_type": "code", "execution_count": 4, "id": "acf3fea0", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T14:29:24.967377Z", "iopub.status.busy": "2026-10-14T14:29:24.967315Z", "iopub.status.idle": "2026-10-14T14:29:25.235427Z", "shell.execute_reply": "2026-10-14T14:29:25.235033Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "accepted 227 / 30000 (0.8%)\n", "ABC mean: [1.253 0.834] std: [0.147 0.095]\n" ] } ], "source": [ "n_sims_abc = 30000\n", "abc = rABC(\n", " simulator=lambda t: gs.simulate(t),\n", " distance=lambda x_o, x_s: discrepancy(x_s),\n", " observation=x_obs,\n", " prior={'mu': None, 'sigma': None},\n", " bounds={'mu': (0, 3), 'sigma': (0.1, 2.5)},\n", " N=n_sims_abc, eps=2.0, verbose=False,\n", ")\n", "abc.run()\n", "s_abc = np.array(abc.accepted_param)\n", "print(f'accepted {len(s_abc)} / {n_sims_abc} ({100 * len(s_abc) / n_sims_abc:.1f}%)')\n", "print('ABC mean:', s_abc.mean(0).round(3), ' std:', s_abc.std(0).round(3))" ] }, { "cell_type": "markdown", "id": "559c0144", "metadata": {}, "source": [ "---\n", "## 4 BOLFI\n", "\n", "1. `learn_likelihood` evaluates $d(\\theta)$ at a Latin-hypercube initial design, then\n", " repeatedly fits a GP to all evaluations and simulates where the **acquisition function**\n", " points (default: lower confidence bound, which balances low predicted $d$ against GP\n", " uncertainty).\n", "2. The GP mean $\\hat d(\\theta)$ gives a synthetic log-likelihood $-\\hat d/2$.\n", "3. `sample_posterior` samples it with `MHSampler`, `NestedSampler`, importance sampling or SMC.\n", "\n", "The `distance` argument is a function of $\\theta$ that runs the simulator and returns\n", "$d$." ] }, { "cell_type": "code", "execution_count": 5, "id": "8d1035e0", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T14:29:25.236600Z", "iopub.status.busy": "2026-10-14T14:29:25.236532Z", "iopub.status.idle": "2026-10-14T14:29:31.463642Z", "shell.execute_reply": "2026-10-14T14:29:31.463197Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "simulations used: 100\n", "BOLFI mean: [1.229 0.838] std: [0.081 0.126]\n" ] } ], "source": [ "bolfi = BOLFI(lambda t: discrepancy(gs.simulate(t)), prior, acquisition='LCB', verbose=False)\n", "bolfi.learn_likelihood(n_calls=100, random_state=0)\n", "\n", "s_bolfi = bolfi.sample_posterior(5000, method='MCMC', n_walkers=32, n_burn=500)\n", "print(f'simulations used: {len(bolfi.y)}')\n", "print('BOLFI mean:', s_bolfi.mean(0).round(3), ' std:', s_bolfi.std(0).round(3))" ] }, { "cell_type": "markdown", "id": "fe219c05", "metadata": {}, "source": [ "Where did BOLFI simulate? The points cluster in the high-likelihood region; the GP\n", "surrogate of the synthetic log-likelihood is shown in the background." ] }, { "cell_type": "code", "execution_count": 6, "id": "e4b25b97", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T14:29:31.464770Z", "iopub.status.busy": "2026-10-14T14:29:31.464702Z", "iopub.status.idle": "2026-10-14T14:29:31.626538Z", "shell.execute_reply": "2026-10-14T14:29:31.626140Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mu_g, sg_g = np.meshgrid(np.linspace(0, 3, 120), np.linspace(0.1, 2.5, 120))\n", "grid = np.column_stack([mu_g.ravel(), sg_g.ravel()])\n", "loglike_grid = bolfi.log_likelihood(grid).reshape(mu_g.shape)\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(12, 4.5))\n", "ax = axes[0]\n", "cf = ax.contourf(mu_g, sg_g, np.maximum(loglike_grid, -60), levels=30, cmap='Blues')\n", "plt.colorbar(cf, ax=ax, label=r'synthetic log-likelihood $-\\hat d/2$')\n", "ax.scatter(*bolfi.X[:10].T, c='C1', s=18, marker='s', label='initial design')\n", "ax.scatter(*bolfi.X[10:].T, c='k', s=10, label='acquisitions')\n", "ax.plot(*theta_true, 'r*', ms=14, label='truth')\n", "ax.set(xlabel=labels[0], ylabel=labels[1], title='BOLFI evaluations')\n", "ax.legend(fontsize=8, loc='upper right')\n", "\n", "ax = axes[1]\n", "ax.plot(*s_exact[::10].T, '.', c='0.6', ms=2, label='exact')\n", "ax.plot(*s_abc.T, '.', c='C2', ms=4, label='rejection ABC')\n", "ax.plot(*s_bolfi[::5].T, '.', c='C0', ms=2, alpha=0.5, label='BOLFI')\n", "ax.plot(*theta_true, 'r*', ms=14)\n", "ax.set(xlabel=labels[0], ylabel=labels[1], xlim=(0.8, 1.8), ylim=(0.5, 1.2), title='Posterior samples')\n", "ax.legend(fontsize=8, markerscale=4)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 7, "id": "8316f5cd", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T14:29:31.627547Z", "iopub.status.busy": "2026-10-14T14:29:31.627468Z", "iopub.status.idle": "2026-10-14T14:29:31.714835Z", "shell.execute_reply": "2026-10-14T14:29:31.714541Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "method simulations mean (mu, sigma) std (mu, sigma)\n", "exact — [1.267 0.829] [0.119 0.086]\n", "rejection ABC 30000 [1.253 0.834] [0.147 0.095]\n", "BOLFI 100 [1.229 0.838] [0.081 0.126]\n" ] } ], "source": [ "fig, axes = plt.subplots(1, 2, figsize=(11, 3.5))\n", "for i, ax in enumerate(axes):\n", " rng = (s_exact[:, i].min(), s_exact[:, i].max())\n", " ax.hist(s_exact[:, i], bins=40, range=rng, density=True, histtype='step', color='k', lw=1.5, label='exact')\n", " ax.hist(s_abc[:, i], bins=20, range=rng, density=True, alpha=0.4, color='C2', label='rejection ABC')\n", " ax.hist(s_bolfi[:, i], bins=40, range=rng, density=True, alpha=0.4, color='C0', label='BOLFI')\n", " ax.axvline(theta_true[i], c='r', lw=1)\n", " ax.set_xlabel(labels[i])\n", "axes[0].legend(fontsize=8)\n", "plt.tight_layout()\n", "plt.show()\n", "\n", "print(f\"{'method':15s} {'simulations':>12s} mean (mu, sigma) std (mu, sigma)\")\n", "for name, s, n in [('exact', s_exact, '—'), ('rejection ABC', s_abc, n_sims_abc), ('BOLFI', s_bolfi, len(bolfi.y))]:\n", " print(f\"{name:15s} {str(n):>12s} {np.round(s.mean(0), 3)} {np.round(s.std(0), 3)}\")" ] }, { "cell_type": "markdown", "id": "065e2582", "metadata": {}, "source": [ "**Why is every posterior, including the exact one, below the true $\\mu$?** The 50\n", "observed values have a sample mean about two standard errors below the true mean (printed\n", "below). All methods correctly follow the data there; the comparison that matters is with\n", "the exact posterior, not with the true value. Calibration over many data sets is shown\n", "in Section 7 of the *Importance sampling and SMC* tutorial." ] }, { "cell_type": "code", "execution_count": 8, "id": "bff0b7fb", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T14:29:31.715945Z", "iopub.status.busy": "2026-10-14T14:29:31.715865Z", "iopub.status.idle": "2026-10-14T14:29:31.717442Z", "shell.execute_reply": "2026-10-14T14:29:31.717141Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sample mean = 1.265, true mean = 1.5, standard error = 0.114 -> data offset = -2.1 sigma\n" ] } ], "source": [ "se = s_obs / np.sqrt(N)\n", "print(f'sample mean = {m_obs:.3f}, true mean = {theta_true[0]}, standard error = {se:.3f}'\n", " f' -> data offset = {(m_obs - theta_true[0]) / se:+.1f} sigma')" ] }, { "cell_type": "markdown", "id": "f4a36a4b", "metadata": {}, "source": [ "BOLFI finds the right region and gives a posterior of the right size with 300× fewer\n", "simulations than rejection ABC. It is less precise: because each $d(\\theta)$ comes from a\n", "single noisy simulation, the GP surrogate — and with it the posterior widths — varies from\n", "run to run (the means stay within about 1σ). Averaging several simulations per $\\theta$ with\n", "`n_repeats` is the most effective fix. Measured over 6 runs on this problem:\n", "\n", "| setting | simulations | run-to-run spread of posterior std |\n", "|---|---|---|\n", "| `n_repeats=1`, `n_calls=100` | 100 | ~20% |\n", "| `n_repeats=4`, `n_calls=100` | 400 | ~10% |\n", "| `n_repeats=1`, `n_calls=400` | 400 | ~17% |\n", "\n", "For the same budget, averaging beats adding more points (and is faster: fewer GP fits).\n", "The repeats at one $\\theta$ are independent, so they can run in parallel.\n", "\n", "Both likelihood-free posteriors are approximations: they depend on the chosen summaries\n", "and discrepancy." ] }, { "cell_type": "markdown", "id": "34ce745a", "metadata": {}, "source": [ "---\n", "## 5 LFIRE: likelihood-free inference by ratio estimation\n", "\n", "For a given $\\theta$, LFIRE simulates `n_theta` data sets at $\\theta$ and compares them\n", "with `n_m` data sets from the marginal (prior predictive, simulated once) using an\n", "L1-regularised logistic regression. The classifier's log-odds at the observed data\n", "estimate\n", "\n", "$$\\log r(x_{\\rm obs}, \\theta) = \\log p(x_{\\rm obs} \\mid \\theta) - \\log p(x_{\\rm obs}),$$\n", "\n", "so $p(\\theta \\mid x_{\\rm obs}) \\propto \\pi(\\theta)\\, r(x_{\\rm obs}, \\theta)$.\n", "\n", "The log ratio is **linear in the classifier features**, so the `summary` must be rich\n", "enough: here the sample mean and log-std plus their squares and product (a change in\n", "$\\sigma$ changes the spread of the data, which a linear function of the mean alone cannot\n", "pick up). L1 regularisation drops features that don't help.\n", "\n", "Each evaluation costs `n_theta` simulations, so — as with BOLFI — a GP surrogate of the\n", "log ratio is learned with Bayesian optimisation (`learn_posterior`) and then sampled.\n", "For one or two parameters `run_grid` evaluates a grid directly instead." ] }, { "cell_type": "code", "execution_count": 9, "id": "f964e190", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T14:29:31.718359Z", "iopub.status.busy": "2026-10-14T14:29:31.718301Z", "iopub.status.idle": "2026-10-14T14:29:41.388789Z", "shell.execute_reply": "2026-10-14T14:29:41.388387Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "log-ratio evaluations: 50, simulations: 25500\n", "LFIRE mean: [1.256 0.827] std: [0.121 0.088]\n", "at the truth: log r = 2.74, classifier accuracy = 0.98\n" ] } ], "source": [ "from psiphy.sbi.lfire import LFIRE\n", "from sklearn.preprocessing import PolynomialFeatures\n", "\n", "poly = PolynomialFeatures(degree=2, include_bias=False)\n", "lfire_summary = lambda x: poly.fit_transform([[x.mean(), np.log(x.std())]])[0]\n", "\n", "lfire = LFIRE(gs.simulate, x_obs, prior, n_m=500, n_theta=500, summary=lfire_summary,\n", " verbose=False, random_state=0)\n", "lfire.learn_posterior(n_calls=50, random_state=0)\n", "s_lfire = lfire.sample_posterior(5000, method='MCMC', n_walkers=32, n_burn=500)\n", "\n", "n_sims_lfire = lfire.n_m + len(lfire.y) * lfire.n_theta\n", "print(f'log-ratio evaluations: {len(lfire.y)}, simulations: {n_sims_lfire}')\n", "print('LFIRE mean:', s_lfire.mean(0).round(3), ' std:', s_lfire.std(0).round(3))\n", "log_r, acc = lfire.log_ratio(theta_true, return_score=True)\n", "print(f'at the truth: log r = {log_r:.2f}, classifier accuracy = {acc:.2f}')" ] }, { "cell_type": "code", "execution_count": 10, "id": "56a8b893", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T14:29:41.389845Z", "iopub.status.busy": "2026-10-14T14:29:41.389778Z", "iopub.status.idle": "2026-10-14T14:29:41.514311Z", "shell.execute_reply": "2026-10-14T14:29:41.513964Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "method simulations mean (mu, sigma) std (mu, sigma)\n", "exact — [1.267 0.829] [0.119 0.086]\n", "rejection ABC 30000 [1.253 0.834] [0.147 0.095]\n", "BOLFI 100 [1.229 0.838] [0.081 0.126]\n", "LFIRE 25500 [1.256 0.827] [0.121 0.088]\n" ] } ], "source": [ "fig, axes = plt.subplots(1, 2, figsize=(11, 3.5))\n", "for i, ax in enumerate(axes):\n", " rng = (s_exact[:, i].min(), s_exact[:, i].max())\n", " ax.hist(s_exact[:, i], bins=40, range=rng, density=True, histtype='step', color='k', lw=1.5, label='exact')\n", " ax.hist(s_bolfi[:, i], bins=40, range=rng, density=True, alpha=0.35, color='C0', label='BOLFI')\n", " ax.hist(s_lfire[:, i], bins=40, range=rng, density=True, alpha=0.35, color='C3', label='LFIRE')\n", " ax.axvline(theta_true[i], c='r', lw=1)\n", " ax.set_xlabel(labels[i])\n", "axes[0].legend(fontsize=8)\n", "plt.tight_layout()\n", "plt.show()\n", "\n", "print(f\"{'method':15s} {'simulations':>12s} mean (mu, sigma) std (mu, sigma)\")\n", "for name, s, n in [('exact', s_exact, '—'), ('rejection ABC', s_abc, n_sims_abc),\n", " ('BOLFI', s_bolfi, len(bolfi.y)), ('LFIRE', s_lfire, n_sims_lfire)]:\n", " print(f\"{name:15s} {str(n):>12s} {np.round(s.mean(0), 3)} {np.round(s.std(0), 3)}\")" ] }, { "cell_type": "markdown", "id": "54130489", "metadata": {}, "source": [ "LFIRE reproduces the exact posterior most closely of the three methods here, without a\n", "hand-tuned distance or tolerance. It uses a similar number of simulations as rejection ABC, though: every log-ratio\n", "evaluation needs its own `n_theta` simulations. It pays off when good summaries are hard\n", "to combine by hand (many candidate summaries, L1 picks the useful ones) and when\n", "simulations at one $\\theta$ can be generated in parallel.\n", "\n", "`plot_lfire` from `psiphy.plotting.corner` draws the grid posterior after\n", "`lfire.posterior_grid()` or `lfire.run_grid()`." ] }, { "cell_type": "markdown", "id": "1bf46cc2", "metadata": {}, "source": [ "---\n", "## 6 Acquisition functions and batch proposals\n", "\n", "`acquisition` chooses where to simulate next (all implemented in\n", "`psiphy.utils.bayesian_opt`):\n", "\n", "| Name | Picks points with | Behaviour |\n", "|---|---|---|\n", "| `'LCB'` (default) | low $\\mu - \\kappa\\sigma$ | explores in proportion to `kappa` (default 1.96) |\n", "| `'EI'` | high expected improvement over the best $\\hat d$ | concentrates near the minimum; `xi` adds exploration |\n", "| `'PI'` | high probability of improvement | most exploitative |\n", "\n", "`batch_size=q` proposes $q$ points per round (kriging believer: each pick is added to the\n", "GP as a fake observation at its predicted mean, so the next pick goes elsewhere). The $q$\n", "simulations of a round are independent, so on a cluster they can run in parallel." ] }, { "cell_type": "code", "execution_count": 11, "id": "c70460eb", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T14:29:41.515456Z", "iopub.status.busy": "2026-10-14T14:29:41.515372Z", "iopub.status.idle": "2026-10-14T14:29:50.189962Z", "shell.execute_reply": "2026-10-14T14:29:50.189535Z" } }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "runs = {\n", " 'LCB': dict(acquisition='LCB'),\n", " 'EI': dict(acquisition='EI'),\n", " 'LCB, batch_size = 5': dict(acquisition='LCB', batch_size=5),\n", "}\n", "fig, axes = plt.subplots(1, 3, figsize=(15, 4), sharex=True, sharey=True)\n", "for ax, (name, kw) in zip(axes, runs.items()):\n", " batch = kw.pop('batch_size', 1)\n", " b = BOLFI(lambda t: discrepancy(gs.simulate(t)), prior, verbose=False, **kw)\n", " b.learn_likelihood(n_calls=60, batch_size=batch, random_state=1)\n", " s = b.sample_posterior(3000, method='MCMC', n_walkers=32, n_burn=500)\n", " ax.plot(*s_exact[::10].T, '.', c='0.75', ms=2)\n", " ax.scatter(*b.X.T, c=np.arange(len(b.X)), cmap='viridis', s=14, zorder=3)\n", " ax.plot(*theta_true, 'r*', ms=12)\n", " ax.set(title=f'{name}\\nmean {np.round(s.mean(0), 2)}, std {np.round(s.std(0), 2)}', xlabel=labels[0])\n", "axes[0].set_ylabel(labels[1])\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "1a316ff3", "metadata": {}, "source": [ "Colour shows the order of evaluation (dark = early). Grey: exact posterior samples." ] }, { "cell_type": "markdown", "id": "a3f45b55", "metadata": {}, "source": [ "---\n", "## 7 Saving and resuming\n", "\n", "With `filename=`, the evaluated points are stored after learning. A later call with the\n", "same file continues from them, adding `n_calls` new simulations — so the expensive part\n", "can be split across jobs." ] }, { "cell_type": "code", "execution_count": 12, "id": "87a27232", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T14:29:50.191172Z", "iopub.status.busy": "2026-10-14T14:29:50.191100Z", "iopub.status.idle": "2026-10-14T14:29:51.956647Z", "shell.execute_reply": "2026-10-14T14:29:51.956359Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "evaluations after resume: 50\n" ] } ], "source": [ "fn = os.path.join(tempfile.mkdtemp(), 'bolfi.pkl')\n", "b1 = BOLFI(lambda t: discrepancy(gs.simulate(t)), prior, verbose=False)\n", "b1.learn_likelihood(n_calls=30, filename=fn, random_state=0)\n", "\n", "b2 = BOLFI(lambda t: discrepancy(gs.simulate(t)), prior, verbose=False)\n", "b2.learn_likelihood(n_calls=20, filename=fn, random_state=1) # resumes from the 30 stored points\n", "print('evaluations after resume:', len(b2.y))" ] }, { "cell_type": "markdown", "id": "e0db368e", "metadata": {}, "source": [ "---\n", "## Summary\n", "\n", "| Task | Code |\n", "|---|---|\n", "| Rejection ABC | `rABC(simulator, distance, x_obs, prior, bounds, N, eps).run()` |\n", "| LFIRE | `LFIRE(simulator, x_obs, prior, summary=...)`, then `learn_posterior(n_calls)` or `run_grid(n_grid)` |\n", "| BOLFI | `BOLFI(distance_fn, prior, acquisition='LCB')` |\n", "| Learn | `learn_likelihood(n_calls, batch_size=1, filename=None)` |\n", "| Sample | `sample_posterior(n, method='MCMC' \\| 'NestedSampling' \\| 'IS' \\| 'SMC')` |\n", "| Surrogate | `log_likelihood(theta)`, `predict_distance(theta, return_std=True)` |\n", "\n", "BOLFI and LFIRE share `sample_posterior`, `save_model` / `load_model` (resumable\n", "learning) and `batch_size`. Options worth knowing: `distance_kernel='exp' | 'gaussian' | callable` (maps $d$ to\n", "$\\log\\mathcal{L}$), `learn_log_dist=True` (model $\\log d$ when $d$ spans orders of magnitude)." ] } ], "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 }