{ "cells": [ { "cell_type": "markdown", "id": "cell-0", "metadata": {}, "source": [ "# Posterior Diagnostics Tutorial\n", "\n", "This notebook walks through all the classes and functions in `psiphy.plotting.diagnostics`,\n", "using the built-in toy models to generate realistic posteriors.\n", "\n", "## What is covered\n", "\n", "| Class / function | Description |\n", "|---|---|\n", "| `SampledDistribution` | Posterior from MCMC / IS weighted samples |\n", "| `GriddedProbabilities` | Posterior on a regular N-D grid |\n", "| `PosteriorComparison` | Side-by-side comparison: boxplot, forest, metrics table |\n", "| `plot_triangle` | Corner / triangle plot (multi-backend) |\n", "| `print_chain_stats` | Weighted mean, std, and credible intervals |\n", "\n", "### Diagnostic metrics available on every distribution\n", "\n", "| Method | What it measures |\n", "|---|---|\n", "| `credible_intervals(levels)` | Equal-tailed marginal CIs from the empirical CDF |\n", "| `z_scores()` | Per-parameter `|mean − truth| / sigma` |\n", "| `bias()` | Per-parameter `median − truth` |\n", "| `pit()` | Probability Integral Transform — `CDF(truth)` per parameter |\n", "| `mahalanobis()` | Multivariate distance from posterior mean to truth |\n", "| `kl_divergence(other)` | Per-parameter KL divergence between two posteriors |" ] }, { "cell_type": "code", "execution_count": 1, "id": "cell-1", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T13:50:50.196862Z", "iopub.status.busy": "2026-10-14T13:50:50.196649Z", "iopub.status.idle": "2026-10-14T13:50:53.015879Z", "shell.execute_reply": "2026-10-14T13:50:53.015419Z" } }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "from psiphy.mcmc import (\n", " UniformPrior,\n", " importance_sampling,\n", " sequential_monte_carlo,\n", ")\n", "from psiphy.toy_models import GaussianSignal, NoisyLine\n", "\n", "from psiphy.plotting.diagnostics import (\n", " SampledDistribution,\n", " GriddedProbabilities,\n", " PosteriorComparison,\n", " plot_triangle,\n", " print_chain_stats,\n", ")\n", "\n", "np.random.seed(42)" ] }, { "cell_type": "markdown", "id": "cell-2", "metadata": {}, "source": [ "---\n", "## 1 Generate posteriors from toy models\n", "\n", "We use `GaussianSignal` (2 parameters: mean $\\mu$, std $\\sigma$) and `NoisyLine`\n", "(2 parameters: slope $m$, intercept $b$) as test beds.\n", "Posteriors are approximated with **IS** (tight proposal) and **SMC** (broad prior)." ] }, { "cell_type": "code", "execution_count": 2, "id": "cell-3", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T13:50:53.038753Z", "iopub.status.busy": "2026-10-14T13:50:53.036442Z", "iopub.status.idle": "2026-10-14T13:50:53.222816Z", "shell.execute_reply": "2026-10-14T13:50:53.215910Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "IS particles=8000, true=[1.5 0.8]\n", "SMC particles=2000, true=[1.5 0.8]\n" ] } ], "source": [ "# ── GaussianSignal setup ──────────────────────────────────────────────────────\n", "gs = GaussianSignal(N=60)\n", "theta_true_gs = np.array([1.5, 0.8]) # [mean, sigma]\n", "x_obs = gs.simulate(theta_true_gs)\n", "\n", "prior_gs = UniformPrior([(0.0, 3.0), (0.2, 2.0)])\n", "log_post_gs = lambda t: gs.log_prob(t, x_obs) + prior_gs.log_prob(t)\n", "\n", "# IS posterior (tight proposal → good ESS)\n", "prop_is = prior_gs.sample(8000)\n", "res = importance_sampling(log_post_gs, prop_is)\n", "s_is, w_is = res['samples'], res['weights']\n", "\n", "# SMC posterior (broad prior)\n", "prior_broad = UniformPrior([(-2, 5), (0.1, 4)])\n", "res = sequential_monte_carlo(\n", " lambda t: gs.log_prob(t, x_obs),\n", " prior_broad,\n", " n_particles=2000,\n", " n_steps=12,\n", " verbose=False,\n", ")\n", "s_smc, w_smc = res['samples'], res['weights']\n", "\n", "print(f'IS particles={len(s_is)}, true={theta_true_gs}')\n", "print(f'SMC particles={len(s_smc)}, true={theta_true_gs}')" ] }, { "cell_type": "code", "execution_count": 3, "id": "cell-4", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T13:50:53.231571Z", "iopub.status.busy": "2026-10-14T13:50:53.228902Z", "iopub.status.idle": "2026-10-14T13:50:53.611218Z", "shell.execute_reply": "2026-10-14T13:50:53.606700Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "NoisyLine IS true=[-0.8 5. ]\n" ] } ], "source": [ "# ── NoisyLine setup ───────────────────────────────────────────────────────────\n", "nl = NoisyLine(Nx=50, noise_sigma=0.4)\n", "theta_true_nl = np.array([-0.8, 5.0]) # [slope, intercept]\n", "y_obs = nl.simulate(theta_true_nl)\n", "\n", "prior_nl = UniformPrior([(-3.0, 3.0), (2.0, 8.0)])\n", "log_post_nl = lambda t: nl.log_prob(t, y_obs) + prior_nl.log_prob(t)\n", "\n", "prop_nl = prior_nl.sample(8000)\n", "res = importance_sampling(log_post_nl, prop_nl)\n", "s_nl, w_nl = res['samples'], res['weights']\n", "\n", "print(f'NoisyLine IS true={theta_true_nl}')" ] }, { "cell_type": "markdown", "id": "cell-5", "metadata": {}, "source": [ "---\n", "## 2 `SampledDistribution`\n", "\n", "`SampledDistribution` wraps weighted samples (e.g. from IS or MCMC) and provides\n", "all diagnostic metrics through a common interface." ] }, { "cell_type": "code", "execution_count": 4, "id": "cell-6", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T13:50:53.619972Z", "iopub.status.busy": "2026-10-14T13:50:53.619134Z", "iopub.status.idle": "2026-10-14T13:50:53.641985Z", "shell.execute_reply": "2026-10-14T13:50:53.630920Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "n_params: 2\n" ] } ], "source": [ "dist_is = SampledDistribution(\n", " s_is,\n", " weights=w_is,\n", " true_values=theta_true_gs,\n", " labels=[r'\\mu', r'\\sigma'],\n", ")\n", "\n", "dist_smc = SampledDistribution(\n", " s_smc,\n", " weights=w_smc,\n", " true_values=theta_true_gs,\n", " labels=[r'\\mu', r'\\sigma'],\n", ")\n", "\n", "print('n_params:', dist_is.n_params)" ] }, { "cell_type": "markdown", "id": "cell-7", "metadata": {}, "source": [ "### 2a `print_stats` — mean, std, and credible intervals" ] }, { "cell_type": "code", "execution_count": 5, "id": "cell-8", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T13:50:53.662181Z", "iopub.status.busy": "2026-10-14T13:50:53.656460Z", "iopub.status.idle": "2026-10-14T13:50:53.700900Z", "shell.execute_reply": "2026-10-14T13:50:53.695642Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "── IS posterior ──────────────────────────────\n", "Parameter summary\n", "==================================================\n", " \\mu: mean = 1.3756, std = 0.0967\n", " 68% CI: [1.2738, 1.4780]\n", " 95% CI: [1.1927, 1.5487]\n", " \\sigma: mean = 0.7522, std = 0.0660\n", " 68% CI: [0.6928, 0.8176]\n", " 95% CI: [0.6297, 0.8968]\n", "\n", "── SMC posterior ─────────────────────────────\n", "Parameter summary\n", "==================================================\n", " \\mu: mean = 1.3680, std = 0.0900\n", " 68% CI: [1.2955, 1.4297]\n", " 95% CI: [1.1958, 1.5856]\n", " \\sigma: mean = 0.7392, std = 0.0758\n", " 68% CI: [0.6781, 0.8302]\n", " 95% CI: [0.6253, 0.8969]\n" ] } ], "source": [ "print('── IS posterior ──────────────────────────────')\n", "dist_is.print_stats(levels=(68, 95))\n", "\n", "print()\n", "print('── SMC posterior ─────────────────────────────')\n", "dist_smc.print_stats(levels=(68, 95))" ] }, { "cell_type": "markdown", "id": "cell-9", "metadata": {}, "source": [ "### 2b Scalar metrics" ] }, { "cell_type": "code", "execution_count": 6, "id": "cell-10", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T13:50:53.707738Z", "iopub.status.busy": "2026-10-14T13:50:53.707532Z", "iopub.status.idle": "2026-10-14T13:50:53.755350Z", "shell.execute_reply": "2026-10-14T13:50:53.718579Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "IS posterior metrics\n", " z-scores : [1.286 0.723]\n", " bias : [-0.123 -0.054]\n", " PIT : [0.908 0.789]\n", " Mahalanobis D : 1.42\n", "\n", "SMC posterior metrics\n", " z-scores : [1.466 0.802]\n", " bias : [-0.138 -0.071]\n", " PIT : [0.926 0.713]\n", " Mahalanobis D : 1.748\n" ] } ], "source": [ "print('IS posterior metrics')\n", "print(' z-scores :', np.round(dist_is.z_scores(), 3))\n", "print(' bias :', np.round(dist_is.bias(), 3))\n", "print(' PIT :', np.round(dist_is.pit(), 3))\n", "print(' Mahalanobis D :', round(dist_is.mahalanobis(), 3))\n", "\n", "print()\n", "print('SMC posterior metrics')\n", "print(' z-scores :', np.round(dist_smc.z_scores(), 3))\n", "print(' bias :', np.round(dist_smc.bias(), 3))\n", "print(' PIT :', np.round(dist_smc.pit(), 3))\n", "print(' Mahalanobis D :', round(dist_smc.mahalanobis(), 3))" ] }, { "cell_type": "markdown", "id": "cell-11", "metadata": {}, "source": [ "### 2c KL divergence between IS and SMC posteriors" ] }, { "cell_type": "code", "execution_count": 7, "id": "cell-12", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T13:50:53.778597Z", "iopub.status.busy": "2026-10-14T13:50:53.774412Z", "iopub.status.idle": "2026-10-14T13:50:53.809667Z", "shell.execute_reply": "2026-10-14T13:50:53.796895Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " KL(IS || SMC) $\\mu$ = 0.1040\n", " KL(IS || SMC) $\\sigma$ = 0.3703\n" ] } ], "source": [ "kl = dist_is.kl_divergence(dist_smc)\n", "labels = [r'$\\mu$', r'$\\sigma$']\n", "for lbl, k in zip(labels, kl):\n", " print(f' KL(IS || SMC) {lbl} = {k:.4f}')" ] }, { "cell_type": "markdown", "id": "cell-13", "metadata": {}, "source": [ "---\n", "## 3 `GriddedProbabilities`\n", "\n", "`GriddedProbabilities` holds a posterior evaluated on a regular parameter grid.\n", "Credible intervals are computed directly from 1-D marginals — efficient for large grids.\n", "\n", "The optional `true_ranges` parameter enables `score()`, which measures how much posterior\n", "mass falls inside a rectangular truth region (useful for challenge-style scoring)." ] }, { "cell_type": "code", "execution_count": 8, "id": "cell-14", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T13:50:53.819017Z", "iopub.status.busy": "2026-10-14T13:50:53.817647Z", "iopub.status.idle": "2026-10-14T13:50:53.946813Z", "shell.execute_reply": "2026-10-14T13:50:53.943054Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Grid shape: (80, 80)\n", "n_params : 2\n" ] } ], "source": [ "# Build a 2-D log-posterior grid for GaussianSignal\n", "n_grid = 80\n", "mu_grid = np.linspace(0.5, 2.5, n_grid)\n", "sig_grid = np.linspace(0.3, 1.5, n_grid)\n", "\n", "MU, SIG = np.meshgrid(mu_grid, sig_grid, indexing='ij')\n", "log_grid = np.vectorize(\n", " lambda mu, sig: gs.log_prob(np.array([mu, sig]), x_obs) + prior_gs.log_prob(np.array([mu, sig]))\n", ")(MU, SIG)\n", "\n", "prob_grid = np.exp(log_grid - log_grid.max()) # normalise for numerical stability\n", "\n", "dist_grid = GriddedProbabilities(\n", " prob_grid,\n", " coords=[mu_grid, sig_grid],\n", " true_values=theta_true_gs,\n", " labels=[r'\\mu', r'\\sigma'],\n", " true_ranges=[[1.2, 1.8], [0.6, 1.0]], # illustrative truth cube\n", ")\n", "\n", "print('Grid shape:', prob_grid.shape)\n", "print('n_params :', dist_grid.n_params)" ] }, { "cell_type": "code", "execution_count": 9, "id": "cell-15", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T13:50:53.974044Z", "iopub.status.busy": "2026-10-14T13:50:53.970825Z", "iopub.status.idle": "2026-10-14T13:50:53.984737Z", "shell.execute_reply": "2026-10-14T13:50:53.983264Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Grid posterior metrics\n", " z-scores : [1.282 0.813]\n", " bias : [-0.136 -0.07 ]\n", " PIT : [0.921 0.828]\n", " Mahalanobis D : 1.517\n", " score : 0.9613\n" ] } ], "source": [ "print('Grid posterior metrics')\n", "print(' z-scores :', np.round(dist_grid.z_scores(), 3))\n", "print(' bias :', np.round(dist_grid.bias(), 3))\n", "print(' PIT :', np.round(dist_grid.pit(), 3))\n", "print(' Mahalanobis D :', round(dist_grid.mahalanobis(), 3))\n", "print(' score :', round(dist_grid.score(), 4))" ] }, { "cell_type": "code", "execution_count": 10, "id": "cell-16", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T13:50:54.055952Z", "iopub.status.busy": "2026-10-14T13:50:54.053838Z", "iopub.status.idle": "2026-10-14T13:50:54.925101Z", "shell.execute_reply": "2026-10-14T13:50:54.916634Z" } }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Visualise the 2-D grid with marginals\n", "fig, axes = plt.subplots(1, 3, figsize=(13, 4))\n", "\n", "# 2-D posterior\n", "im = axes[0].pcolormesh(mu_grid, sig_grid, prob_grid.T / prob_grid.max(),\n", " cmap='Blues')\n", "axes[0].scatter(*theta_true_gs, c='red', s=80, zorder=5, label='truth')\n", "rect = plt.Rectangle((1.2, 0.6), 0.6, 0.4, fill=False, edgecolor='gray',\n", " linestyle='--', lw=1.5, label='true_ranges')\n", "axes[0].add_patch(rect)\n", "axes[0].set(xlabel=r'$\\mu$', ylabel=r'$\\sigma$', title='2-D grid posterior')\n", "axes[0].legend()\n", "plt.colorbar(im, ax=axes[0])\n", "\n", "# Marginal mu\n", "marg_mu = prob_grid.sum(axis=1)\n", "axes[1].plot(mu_grid, marg_mu / marg_mu.max())\n", "axes[1].axvline(theta_true_gs[0], c='red', ls='--', label='truth')\n", "ci_mu = dist_grid.credible_intervals()[0]\n", "axes[1].axvspan(ci_mu['lo68'], ci_mu['hi68'], alpha=0.15, label='68% CI')\n", "axes[1].axvspan(ci_mu['lo95'], ci_mu['hi95'], alpha=0.07, label='95% CI')\n", "axes[1].set(xlabel=r'$\\mu$', title=r'Marginal $\\mu$')\n", "axes[1].legend(fontsize=8)\n", "\n", "# Marginal sigma\n", "marg_sig = prob_grid.sum(axis=0)\n", "axes[2].plot(sig_grid, marg_sig / marg_sig.max())\n", "axes[2].axvline(theta_true_gs[1], c='red', ls='--', label='truth')\n", "ci_sig = dist_grid.credible_intervals()[1]\n", "axes[2].axvspan(ci_sig['lo68'], ci_sig['hi68'], alpha=0.15, label='68% CI')\n", "axes[2].axvspan(ci_sig['lo95'], ci_sig['hi95'], alpha=0.07, label='95% CI')\n", "axes[2].set(xlabel=r'$\\sigma$', title=r'Marginal $\\sigma$')\n", "axes[2].legend(fontsize=8)\n", "\n", "fig.suptitle('GriddedProbabilities — GaussianSignal posterior', y=1.02)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "cell-17", "metadata": {}, "source": [ "---\n", "## 4 `PosteriorComparison` — side-by-side diagnostics\n", "\n", "`PosteriorComparison` accepts any mix of `SampledDistribution` and `GriddedProbabilities`\n", "objects and produces aligned comparison plots.\n", "\n", "We compare three posteriors for the same `GaussianSignal` experiment:\n", "1. **IS** — importance sampling with tight proposal\n", "2. **SMC** — sequential Monte Carlo from a broad prior\n", "3. **Grid** — full 2-D grid posterior evaluated analytically" ] }, { "cell_type": "code", "execution_count": 11, "id": "cell-18", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T13:50:54.927683Z", "iopub.status.busy": "2026-10-14T13:50:54.927512Z", "iopub.status.idle": "2026-10-14T13:50:54.951925Z", "shell.execute_reply": "2026-10-14T13:50:54.943129Z" } }, "outputs": [], "source": [ "# marker=True (default) → auto-assigns from the marker cycle\n", "# color=None → auto-assigns from tab20 colour cycle\n", "comp = PosteriorComparison()\n", "comp.add(dist_is, label='IS', color='C0')\n", "comp.add(dist_smc, label='SMC', color='C2')\n", "comp.add(dist_grid, label='Grid', color='C3')" ] }, { "cell_type": "markdown", "id": "cell-19", "metadata": {}, "source": [ "### 4a Boxplot — box = 68% CI, whiskers = 95% CI, marker = median\n", "\n", "`marker=True` (default) auto-assigns a symbol from the cycle. Pass `marker=None` to suppress it." ] }, { "cell_type": "code", "execution_count": 12, "id": "cell-20", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T13:50:54.964394Z", "iopub.status.busy": "2026-10-14T13:50:54.960370Z", "iopub.status.idle": "2026-10-14T13:50:55.218827Z", "shell.execute_reply": "2026-10-14T13:50:55.210839Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = comp.plot_boxplot(levels=(68, 95))\n", "plt.suptitle('Boxplot — auto markers from cycle (default)', y=1.02)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "cell-21", "metadata": {}, "source": [ "### 4b Forest plot — errorbar style" ] }, { "cell_type": "code", "execution_count": 13, "id": "cell-22", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T13:50:55.221551Z", "iopub.status.busy": "2026-10-14T13:50:55.220724Z", "iopub.status.idle": "2026-10-14T13:50:55.541376Z", "shell.execute_reply": "2026-10-14T13:50:55.528225Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = comp.plot_forest(levels=(68, 95))\n", "plt.suptitle('Forest plot — auto markers from cycle (default)', y=1.02)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "0037074d", "metadata": {}, "source": [ "### 4c Per-entry styling: `marker`, `markersize`, `linewidth`\n", "\n", "| `marker` value | Effect |\n", "|---|---|\n", "| `True` (default) | Auto-assign from marker cycle |\n", "| `None` | No marker drawn (matplotlib convention) |\n", "| `'o'`, `'s'`, `'^'`, … | Use that specific symbol |\n", "\n", "`markersize` and `linewidth` per entry override the method-level defaults." ] }, { "cell_type": "code", "execution_count": 14, "id": "d9ba5e9f", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T13:50:55.565538Z", "iopub.status.busy": "2026-10-14T13:50:55.561151Z", "iopub.status.idle": "2026-10-14T13:50:56.011082Z", "shell.execute_reply": "2026-10-14T13:50:55.979159Z" } }, "outputs": [ { "data": { 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "comp_styled = PosteriorComparison()\n", "comp_styled.add(dist_is, label='IS (auto marker)', color='C0') # marker=True → cycle\n", "comp_styled.add(dist_smc, label='SMC (square, lw3)', color='C2', marker='s', linewidth=3) # explicit marker\n", "comp_styled.add(dist_grid, label='Grid (no marker)', color='C3', marker=None) # suppress marker\n", "\n", "fig = comp_styled.plot_boxplot(levels=(68, 95))\n", "plt.suptitle('Boxplot — auto / explicit / no marker', y=1.02)\n", "plt.show()\n", "\n", "fig = comp_styled.plot_forest(levels=(68, 95))\n", "plt.suptitle('Forest plot — auto / explicit / no marker', y=1.02)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "ca8636d7", "metadata": {}, "source": [ "### 4d Legend panel\n", "\n", "Entries with `marker=None` appear as a solid coloured line; others show their marker symbol." ] }, { "cell_type": "code", "execution_count": 15, "id": "17c8f46e", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T13:50:56.016767Z", "iopub.status.busy": "2026-10-14T13:50:56.016400Z", "iopub.status.idle": "2026-10-14T13:50:56.077665Z", "shell.execute_reply": "2026-10-14T13:50:56.063003Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = comp_styled.legend(ncol=3)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "cell-23", "metadata": {}, "source": [ "### 4e Metrics table" ] }, { "cell_type": "code", "execution_count": 16, "id": "cell-24", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T13:50:56.081795Z", "iopub.status.busy": "2026-10-14T13:50:56.080744Z", "iopub.status.idle": "2026-10-14T13:50:56.097416Z", "shell.execute_reply": "2026-10-14T13:50:56.093775Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "label mahalanobis z_1 z_2 score\n", " IS 1.420 1.286 0.723 NaN\n", " Grid 1.517 1.282 0.813 0.9613\n", " SMC 1.748 1.466 0.802 NaN\n" ] } ], "source": [ "df = comp.metrics_table(sort_by='mahalanobis')\n", "print(df.to_string(index=False))" ] }, { "cell_type": "markdown", "id": "cell-25", "metadata": {}, "source": [ "### 4f Auto-colored legend (when no markers are set)" ] }, { "cell_type": "code", "execution_count": 17, "id": "cell-26", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T13:50:56.103249Z", "iopub.status.busy": "2026-10-14T13:50:56.102718Z", "iopub.status.idle": "2026-10-14T13:50:56.143383Z", "shell.execute_reply": "2026-10-14T13:50:56.136661Z" } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = comp.legend(ncol=3)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "cell-27", "metadata": {}, "source": [ "---\n", "## 5 Comparing many posteriors — NoisyLine with varying noise\n", "\n", "A more realistic use-case: the same line observed with five different noise levels,\n", "each analysed with importance sampling. The boxplot should show the posterior widening\n", "as the noise grows. (At the lowest noise levels the posterior is so narrow that IS from\n", "the broad prior has a very small effective sample size — SMC is the better tool there.)" ] }, { "cell_type": "code", "execution_count": 18, "id": "cell-28", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T13:50:56.162841Z", "iopub.status.busy": "2026-10-14T13:50:56.162296Z", "iopub.status.idle": "2026-10-14T13:50:57.410643Z", "shell.execute_reply": "2026-10-14T13:50:57.399755Z" } }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "comp_nl = PosteriorComparison()\n", "\n", "noise_levels = [0.2, 0.4, 0.8, 1.5, 3.0]\n", "for noise in noise_levels:\n", " nl_var = NoisyLine(Nx=50, noise_sigma=noise)\n", " y_var = nl_var.simulate(theta_true_nl)\n", " prior_var = UniformPrior([(-3, 3), (2, 8)])\n", " prop_var = prior_var.sample(6000)\n", " res = importance_sampling(\n", " lambda t, _nl=nl_var, _y=y_var, _p=prior_var: _nl.log_prob(t, _y) + _p.log_prob(t),\n", " prop_var,\n", " )\n", " s_var, w_var = res['samples'], res['weights']\n", " d = SampledDistribution(\n", " s_var, weights=w_var,\n", " true_values=theta_true_nl,\n", " labels=[r'm', r'b'],\n", " )\n", " comp_nl.add(d, label=f'noise={noise}')\n", "\n", "fig = comp_nl.plot_boxplot()\n", "plt.suptitle('NoisyLine: posterior width grows with noise level', y=1.02)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 19, "id": "cell-29", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T13:50:57.444914Z", "iopub.status.busy": "2026-10-14T13:50:57.428722Z", "iopub.status.idle": "2026-10-14T13:50:57.472162Z", "shell.execute_reply": "2026-10-14T13:50:57.468966Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " label mahalanobis z_1 z_2\n", "noise=0.8 1.239 1.239 1.150\n", "noise=0.2 1.509 0.080 0.490\n", "noise=3.0 1.820 1.818 1.603\n", "noise=1.5 2.509 1.703 2.395\n", "noise=0.4 3.655 1.799 0.594\n" ] } ], "source": [ "print(comp_nl.metrics_table().to_string(index=False))" ] }, { "cell_type": "markdown", "id": "cell-30", "metadata": {}, "source": [ "---\n", "## 6 `plot_triangle` — corner / triangle plot\n", "\n", "`plot_triangle` is a standalone function that accepts raw samples and forwards to\n", "the chosen backend (`'corner'`, `'getdist'`, `'chainconsumer'`). It is also\n", "accessible directly from any `DistributionDiagnostic` via `.plot_triangle()`." ] }, { "cell_type": "code", "execution_count": 20, "id": "cell-31", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T13:50:57.478429Z", "iopub.status.busy": "2026-10-14T13:50:57.477267Z", "iopub.status.idle": "2026-10-14T13:50:57.750307Z", "shell.execute_reply": "2026-10-14T13:50:57.719069Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Standalone function — corner backend\n", "try:\n", " fig = plot_triangle(\n", " s_is,\n", " weights=w_is,\n", " labels=[r'\\mu', r'\\sigma'],\n", " true_values=theta_true_gs,\n", " engine='corner',\n", " bins=35,\n", " plot_datapoints=False,\n", " fill_contours=True,\n", " levels=(0.68, 0.95),\n", " color='C0',\n", " )\n", " plt.suptitle('plot_triangle (corner engine) — IS posterior', y=1.02)\n", " plt.show()\n", "except ImportError:\n", " print('corner not installed — skipping')" ] }, { "cell_type": "code", "execution_count": 21, "id": "cell-32", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T13:50:57.829680Z", "iopub.status.busy": "2026-10-14T13:50:57.825455Z", "iopub.status.idle": "2026-10-14T13:50:57.989337Z", "shell.execute_reply": "2026-10-14T13:50:57.978008Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Via the object method — same result\n", "try:\n", " fig = dist_smc.plot_triangle(\n", " engine='corner',\n", " bins=35,\n", " plot_datapoints=False,\n", " fill_contours=True,\n", " levels=(0.68, 0.95),\n", " color='C2',\n", " )\n", " plt.suptitle('SampledDistribution.plot_triangle — SMC posterior', y=1.02)\n", " plt.show()\n", "except ImportError:\n", " print('corner not installed — skipping')" ] }, { "cell_type": "code", "execution_count": 22, "id": "cell-33", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T13:50:57.997683Z", "iopub.status.busy": "2026-10-14T13:50:57.995804Z", "iopub.status.idle": "2026-10-14T13:50:59.083499Z", "shell.execute_reply": "2026-10-14T13:50:59.082889Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "WARNING:root:outlier fraction 0.02265475430759413 \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Removed no burn in\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# getdist backend\n", "try:\n", " g = plot_triangle(\n", " s_is,\n", " weights=w_is,\n", " labels=[r'\\mu', r'\\sigma'],\n", " true_values=theta_true_gs,\n", " engine='getdist',\n", " )\n", " plt.suptitle('plot_triangle (getdist engine) — IS posterior', y=1.02)\n", " plt.show()\n", "except ImportError:\n", " print('getdist not installed — skipping')" ] }, { "cell_type": "markdown", "id": "cell-34", "metadata": {}, "source": [ "---\n", "## 7 `print_chain_stats` — standalone summary\n", "\n", "`print_chain_stats` can be called with raw samples (it computes everything internally)\n", "or with precomputed means, sigmas, and CIs." ] }, { "cell_type": "code", "execution_count": 23, "id": "cell-35", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T13:50:59.086996Z", "iopub.status.busy": "2026-10-14T13:50:59.086713Z", "iopub.status.idle": "2026-10-14T13:50:59.091310Z", "shell.execute_reply": "2026-10-14T13:50:59.090747Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "── From samples ─────────────────────────────\n", "Parameter summary\n", "==================================================\n", " \\mu: mean = 1.3756, std = 0.0963\n", " 68% CI: [1.2738, 1.4780]\n", " 95% CI: [1.1927, 1.5487]\n", " \\sigma: mean = 0.7522, std = 0.0658\n", " 68% CI: [0.6928, 0.8176]\n", " 95% CI: [0.6297, 0.8968]\n" ] } ], "source": [ "# From raw weighted samples\n", "print('── From samples ─────────────────────────────')\n", "print_chain_stats(s_is, weights=w_is, labels=[r'\\mu', r'\\sigma'], levels=(68, 95))" ] }, { "cell_type": "code", "execution_count": 24, "id": "cell-36", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T13:50:59.095067Z", "iopub.status.busy": "2026-10-14T13:50:59.094892Z", "iopub.status.idle": "2026-10-14T13:50:59.101467Z", "shell.execute_reply": "2026-10-14T13:50:59.100004Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "── From precomputed means / sigmas / CIs ────\n", "Parameter summary\n", "==================================================\n", " \\mu: mean = 1.3756, std = 0.0967\n", " 68% CI: [1.2738, 1.4780]\n", " 95% CI: [1.1927, 1.5487]\n", " \\sigma: mean = 0.7522, std = 0.0660\n", " 68% CI: [0.6928, 0.8176]\n", " 95% CI: [0.6297, 0.8968]\n" ] } ], "source": [ "# From precomputed statistics\n", "means_gs, _, sigmas_gs, *_ = dist_is._weighted_stats()\n", "cis_gs = dist_is.credible_intervals(levels=(68, 95))\n", "\n", "print('── From precomputed means / sigmas / CIs ────')\n", "print_chain_stats(means_gs, sigmas=sigmas_gs, cis=cis_gs,\n", " labels=[r'\\mu', r'\\sigma'], levels=(68, 95))" ] }, { "cell_type": "markdown", "id": "cell-37", "metadata": {}, "source": [ "---\n", "## 8 `score()` on `GriddedProbabilities`\n", "\n", "The `score()` method integrates posterior mass inside a rectangular parameter region\n", "defined by `true_ranges`. It is used e.g. in the SDC3b challenge to rank inference methods.\n", "\n", "Here we vary the size of the truth cube and observe how the score changes." ] }, { "cell_type": "code", "execution_count": 25, "id": "cell-38", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T13:50:59.103421Z", "iopub.status.busy": "2026-10-14T13:50:59.103304Z", "iopub.status.idle": "2026-10-14T13:50:59.281149Z", "shell.execute_reply": "2026-10-14T13:50:59.272321Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " half_width=0.05 score=0.0718\n", " half_width=0.10 score=0.2701\n", " half_width=0.20 score=0.7891\n", " half_width=0.40 score=0.9979\n", " half_width=0.60 score=1.0000\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "half_widths = [0.05, 0.1, 0.2, 0.4, 0.6]\n", "scores = []\n", "\n", "for hw in half_widths:\n", " d = GriddedProbabilities(\n", " prob_grid,\n", " coords=[mu_grid, sig_grid],\n", " true_values=theta_true_gs,\n", " true_ranges=[\n", " [theta_true_gs[0] - hw, theta_true_gs[0] + hw],\n", " [theta_true_gs[1] - hw, theta_true_gs[1] + hw],\n", " ],\n", " )\n", " scores.append(d.score())\n", " print(f' half_width={hw:.2f} score={d.score():.4f}')\n", "\n", "fig, ax = plt.subplots(figsize=(6, 3.5))\n", "ax.plot(half_widths, scores, 'o-', c='steelblue')\n", "ax.set(xlabel='Truth-cube half-width', ylabel='Score',\n", " title='GriddedProbabilities.score() vs truth-cube size')\n", "ax.axhline(1.0, ls='--', c='k', lw=0.8, label='perfect (score=1)')\n", "ax.legend()\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "cell-39", "metadata": {}, "source": [ "---\n", "## 9 Mixing `SampledDistribution` and `GriddedProbabilities` in one comparison\n", "\n", "`PosteriorComparison` works with any `DistributionDiagnostic` subclass, so you can\n", "put grid-based and sample-based posteriors side by side directly." ] }, { "cell_type": "code", "execution_count": 26, "id": "cell-40", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T13:50:59.329939Z", "iopub.status.busy": "2026-10-14T13:50:59.326233Z", "iopub.status.idle": "2026-10-14T13:50:59.649101Z", "shell.execute_reply": "2026-10-14T13:50:59.641303Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", " label mahalanobis z_1 z_2 score\n", " IS samples 1.420 1.286 0.723 NaN\n", " Grid 1.517 1.282 0.813 0.9613\n", "SMC samples 1.748 1.466 0.802 NaN\n" ] } ], "source": [ "comp_mixed = PosteriorComparison()\n", "comp_mixed.add(dist_is, label='IS samples', color='C0', marker='o', markersize=9)\n", "comp_mixed.add(dist_smc, label='SMC samples', color='C2', marker='s', markersize=9)\n", "comp_mixed.add(dist_grid, label='Grid', color='C3', marker='^', markersize=9)\n", "\n", "fig = comp_mixed.plot_boxplot(levels=(68, 95), figsize=(9, 3.5))\n", "plt.suptitle('Mixed posteriors: samples vs grid — GaussianSignal', y=1.02)\n", "plt.show()\n", "\n", "print()\n", "print(comp_mixed.metrics_table().to_string(index=False))" ] }, { "cell_type": "markdown", "id": "61393d84", "metadata": {}, "source": [ "---\n", "## 10 Derived (pseudo) parameters — `add_derived`\n", "\n", "`add_derived(func, label, true_value)` registers a parameter computed from\n", "the original samples. After that it appears everywhere: contour plots,\n", "triangle plots, and metric methods.\n", "\n", "A cosmology-style example: $S_8 = \\sigma_8 \\sqrt{\\Omega_m / 0.3}$.\n", "Here we use the two GaussianSignal parameters $(\\mu, \\sigma)$ and define\n", "a pseudo-parameter $P = \\mu \\cdot \\sqrt{|\\sigma|}$ to mimic the idea." ] }, { "cell_type": "code", "execution_count": 27, "id": "6002e512", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T13:50:59.662891Z", "iopub.status.busy": "2026-10-14T13:50:59.658377Z", "iopub.status.idle": "2026-10-14T13:50:59.682479Z", "shell.execute_reply": "2026-10-14T13:50:59.677919Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Full labels : ['\\\\mu', '\\\\sigma', 'P']\n", "Full truths : [np.float64(1.5), np.float64(0.8), 1.3416407864998738]\n", "Sample shape : (8000, 3)\n" ] } ], "source": [ "from psiphy.plotting.diagnostics import SampledDistribution\n", "\n", "# Re-use the IS samples from Section 1\n", "# true_values = [mu_true, sigma_true] = theta\n", "dist_derived = SampledDistribution(\n", " s_is,\n", " weights=w_is,\n", " true_values=theta_true_gs,\n", " labels=[r'\\mu', r'\\sigma'],\n", ")\n", "\n", "# Register a derived parameter: P = mu * sqrt(|sigma|)\n", "true_P = float(theta_true_gs[0] * theta_true_gs[1] ** 0.5)\n", "dist_derived.add_derived(\n", " lambda s: s[:, 0] * np.abs(s[:, 1]) ** 0.5,\n", " label=r'P',\n", " true_value=true_P,\n", ")\n", "\n", "print('Full labels :', dist_derived._full_labels())\n", "print('Full truths :', dist_derived._full_true_values())\n", "\n", "full_s, full_w = dist_derived.get_full_samples()\n", "print('Sample shape :', full_s.shape) # (N, 3) — 2 original + 1 derived" ] }, { "cell_type": "markdown", "id": "c12d4ad5", "metadata": {}, "source": [ "### 10a Credible intervals on the derived parameter" ] }, { "cell_type": "code", "execution_count": 28, "id": "9bd6bce8", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T13:50:59.694510Z", "iopub.status.busy": "2026-10-14T13:50:59.689311Z", "iopub.status.idle": "2026-10-14T13:50:59.707630Z", "shell.execute_reply": "2026-10-14T13:50:59.706381Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "P median=1.1854 68% [1.0883, 1.2987] true=1.3416\n" ] } ], "source": [ "cis = dist_derived.credible_intervals() # original params only\n", "cis_full = []\n", "# credible_intervals() operates on get_samples(); for derived params, use\n", "# the full sample column directly via plot_contour_1d or a manual CI:\n", "from psiphy.plotting.diagnostics import SampledDistribution as SD\n", "# Wrap derived column as its own 1-D posterior to get CI numbers:\n", "derived_col = full_s[:, 2]\n", "dist_P = SD(derived_col, weights=full_w, true_values=[true_P], labels=[r'P'])\n", "ci_P = dist_P.credible_intervals()[0]\n", "print(f'P median={ci_P[\"median\"]:.4f}'\n", " f' 68% [{ci_P[\"lo68\"]:.4f}, {ci_P[\"hi68\"]:.4f}]'\n", " f' true={true_P:.4f}')" ] }, { "cell_type": "markdown", "id": "63c095d5", "metadata": {}, "source": [ "---\n", "## 11 Single-panel contour plots\n", "\n", "`plot_contour_1d(param)` and `plot_contour_2d(param1, param2)` draw\n", "individual marginal panels using a KDE.\n", "\n", "* `param` can be an **integer index** or a **label string** (including\n", " derived parameters).\n", "* Both methods accept an `ax=` argument for embedding into existing figures.\n", "* `PosteriorComparison` provides the same two methods to **overlay** all\n", " registered posteriors on a shared axes." ] }, { "cell_type": "code", "execution_count": 29, "id": "edd89e3f", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T13:50:59.709179Z", "iopub.status.busy": "2026-10-14T13:50:59.709120Z", "iopub.status.idle": "2026-10-14T13:50:59.868753Z", "shell.execute_reply": "2026-10-14T13:50:59.860847Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# ── 11a 1-D marginal of an original parameter ────────────────────────────\n", "fig = dist_derived.plot_contour_1d(param=0) # mu\n", "plt.title(r'1-D marginal: $\\mu$')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 30, "id": "a4141dcd", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T13:50:59.886573Z", "iopub.status.busy": "2026-10-14T13:50:59.886452Z", "iopub.status.idle": "2026-10-14T13:51:00.001205Z", "shell.execute_reply": "2026-10-14T13:50:59.995760Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# ── 11b 1-D marginal of the derived parameter ────────────────────────────\n", "fig = dist_derived.plot_contour_1d(param=r'P')\n", "plt.title(r'1-D marginal: derived $P = \\mu\\,|\\sigma|^{1/2}$')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 31, "id": "94d8fe59", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T13:51:00.006724Z", "iopub.status.busy": "2026-10-14T13:51:00.006530Z", "iopub.status.idle": "2026-10-14T13:51:01.191506Z", "shell.execute_reply": "2026-10-14T13:51:01.184436Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# ── 11c 2-D joint contour (original params) ──────────────────────────────\n", "fig = dist_derived.plot_contour_2d(param1=0, param2=1)\n", "plt.title(r'Joint: $\\mu$ vs $\\sigma$')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 32, "id": "0a74a132", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T13:51:01.195008Z", "iopub.status.busy": "2026-10-14T13:51:01.194210Z", "iopub.status.idle": "2026-10-14T13:51:02.366326Z", "shell.execute_reply": "2026-10-14T13:51:02.361543Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# ── 11d 2-D joint contour (original vs derived) ─────────────────────────\n", "fig = dist_derived.plot_contour_2d(param1=0, param2=r'P')\n", "plt.title(r'Joint: $\\mu$ vs derived $P$')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "c83f59ed", "metadata": {}, "source": [ "### 11e Embedding into a multi-panel figure" ] }, { "cell_type": "code", "execution_count": 33, "id": "68a438fc", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T13:51:02.376056Z", "iopub.status.busy": "2026-10-14T13:51:02.372683Z", "iopub.status.idle": "2026-10-14T13:51:03.024843Z", "shell.execute_reply": "2026-10-14T13:51:03.018617Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(1, 2, figsize=(10, 4))\n", "\n", "dist_derived.plot_contour_1d(param=0, ax=axes[0], color='C0')\n", "axes[0].set_title(r'$\\mu$ marginal')\n", "\n", "dist_derived.plot_contour_1d(param=r'P', ax=axes[1], color='C1')\n", "axes[1].set_title(r'Derived $P$ marginal')\n", "\n", "fig.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "cdf41e85", "metadata": {}, "source": [ "### 11f `PosteriorComparison` overlay" ] }, { "cell_type": "code", "execution_count": 34, "id": "d370f3ca", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T13:51:03.032681Z", "iopub.status.busy": "2026-10-14T13:51:03.032483Z", "iopub.status.idle": "2026-10-14T13:51:03.359927Z", "shell.execute_reply": "2026-10-14T13:51:03.352738Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Build a comparison: IS vs SMC, both with the derived parameter\n", "dist_smc_d = SampledDistribution(\n", " s_smc, weights=w_smc, true_values=theta_true_gs, labels=[r'\\mu', r'\\sigma'],\n", ")\n", "dist_smc_d.add_derived(\n", " lambda s: s[:, 0] * np.abs(s[:, 1]) ** 0.5,\n", " label=r'P', true_value=true_P,\n", ")\n", "\n", "from psiphy.plotting.diagnostics import PosteriorComparison\n", "comp_d = PosteriorComparison()\n", "comp_d.add(dist_derived, label='IS', color='C0')\n", "comp_d.add(dist_smc_d, label='SMC', color='C2')\n", "\n", "# 1-D overlay\n", "fig = comp_d.plot_contour_1d(param=r'P', fill=True, alpha=0.2)\n", "plt.title(r'Overlay: derived $P$ — IS vs SMC')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 35, "id": "608eba3b", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T13:51:03.367006Z", "iopub.status.busy": "2026-10-14T13:51:03.366397Z", "iopub.status.idle": "2026-10-14T13:51:04.568123Z", "shell.execute_reply": "2026-10-14T13:51:04.562068Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# 2-D overlay (filled=False keeps colours readable)\n", "fig = comp_d.plot_contour_2d(param1=0, param2=r'P', filled=False)\n", "plt.title(r'Overlay: $\\mu$ vs $P$ — IS vs SMC')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "cell-41", "metadata": {}, "source": [ "---\n", "## Summary\n", "\n", "| What | How |\n", "|---|---|\n", "| Wrap IS/MCMC samples | `SampledDistribution(samples, weights, true_values, labels)` |\n", "| Wrap a grid posterior | `GriddedProbabilities(grid, coords, true_values, labels, true_ranges)` |\n", "| Metrics | `.z_scores()`, `.bias()`, `.pit()`, `.mahalanobis()`, `.kl_divergence(other)` |\n", "| Per-parameter CIs | `.credible_intervals(levels=(68, 95))` |\n", "| Print summary | `.print_stats()` or `print_chain_stats(samples)` |\n", "| Triangle plot | `.plot_triangle(engine='corner')` or standalone `plot_triangle(...)` |\n", "| Compare posteriors | `PosteriorComparison` → `.plot_boxplot()`, `.plot_forest()`, `.metrics_table()` |\n", "| Posterior mass in truth cube | `GriddedProbabilities(..., true_ranges=...).score()` |\n", "\n", "### Styling controls for `PosteriorComparison.add()`\n", "\n", "| Argument | Default | Effect |\n", "|---|---|---|\n", "| `color` | `None` → tab20 cycle | Bar / box / line colour |\n", "| `marker` | `True` → auto from marker cycle | `None` = no marker (matplotlib convention); any string = that symbol |\n", "| `markersize` | `None` → method default (8) | Per-entry override |\n", "| `linewidth` | `None` → method default (2) | Per-entry override |\n", "| Single-panel KDE | `dist.plot_contour_1d(param)`, `dist.plot_contour_2d(p1, p2)` |\n", "| Overlay contours | `comp.plot_contour_1d(param)`, `comp.plot_contour_2d(p1, p2)` |\n", "| Derived parameters | `dist.add_derived(func, label, true_value)` |\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": "3.12.11" } }, "nbformat": 4, "nbformat_minor": 5 }