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optimiz-rs/examples/notebooks/02_mcmc_tutorial.ipynb

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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "dc5d5825",
"metadata": {
"execution": {
"iopub.execute_input": "2026-02-16T16:15:08.719062Z",
"iopub.status.busy": "2026-02-16T16:15:08.718752Z",
"iopub.status.idle": "2026-02-16T16:15:10.156553Z",
"shell.execute_reply": "2026-02-16T16:15:10.155128Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"OptimizR MCMC Module Loaded!\n"
]
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from scipy import stats\n",
"from optimizr import mcmc_sample\n",
"\n",
"np.random.seed(42)\n",
"print(\"OptimizR MCMC Module Loaded!\")"
]
},
{
"cell_type": "markdown",
"id": "ddfbd617",
"metadata": {},
"source": [
"## Example 1: Inferring Parameters of a Normal Distribution\n",
"\n",
"Given observed data $\\{x_1, \\ldots, x_n\\}$, infer $\\mu$ and $\\sigma$.\n",
"\n",
"### Likelihood\n",
"$$L(\\mu, \\sigma | \\mathbf{x}) = \\prod_{i=1}^n \\frac{1}{\\sqrt{2\\pi\\sigma^2}} \\exp\\left(-\\frac{(x_i - \\mu)^2}{2\\sigma^2}\\right)$$\n",
"\n",
"### Log-Likelihood\n",
"$$\\log L(\\mu, \\sigma | \\mathbf{x}) = -\\frac{n}{2}\\log(2\\pi) - n\\log(\\sigma) - \\frac{1}{2\\sigma^2}\\sum_{i=1}^n (x_i - \\mu)^2$$"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "f929c18e",
"metadata": {
"execution": {
"iopub.execute_input": "2026-02-16T16:15:10.160126Z",
"iopub.status.busy": "2026-02-16T16:15:10.159742Z",
"iopub.status.idle": "2026-02-16T16:15:10.443829Z",
"shell.execute_reply": "2026-02-16T16:15:10.442725Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"True parameters: μ=5.0, σ=2.0\n",
"Sample mean: 4.792\n",
"Sample std: 1.807\n"
]
},
{
"data": {
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",
"text/plain": [
"<Figure size 1000x500 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Generate synthetic data\n",
"true_mu = 5.0\n",
"true_sigma = 2.0\n",
"n_obs = 100\n",
"\n",
"observed_data = np.random.normal(true_mu, true_sigma, n_obs)\n",
"\n",
"print(f\"True parameters: μ={true_mu}, σ={true_sigma}\")\n",
"print(f\"Sample mean: {observed_data.mean():.3f}\")\n",
"print(f\"Sample std: {observed_data.std():.3f}\")\n",
"\n",
"# Plot data\n",
"plt.figure(figsize=(10, 5))\n",
"plt.hist(observed_data, bins=20, density=True, alpha=0.6, color='skyblue', edgecolor='black')\n",
"x_range = np.linspace(observed_data.min(), observed_data.max(), 100)\n",
"plt.plot(x_range, stats.norm.pdf(x_range, true_mu, true_sigma), \n",
" 'r-', linewidth=2, label=f'True: N({true_mu}, {true_sigma}²)')\n",
"plt.xlabel('Value', fontsize=12)\n",
"plt.ylabel('Density', fontsize=12)\n",
"plt.title('Observed Data Distribution', fontsize=14, fontweight='bold')\n",
"plt.legend()\n",
"plt.grid(alpha=0.3)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "5626ba97",
"metadata": {},
"source": [
"### Define Log-Likelihood Function"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "37ac93a1",
"metadata": {
"execution": {
"iopub.execute_input": "2026-02-16T16:15:10.447063Z",
"iopub.status.busy": "2026-02-16T16:15:10.446784Z",
"iopub.status.idle": "2026-02-16T16:15:10.453064Z",
"shell.execute_reply": "2026-02-16T16:15:10.451933Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Log-likelihood at true params: -202.57\n"
]
}
],
"source": [
"def log_likelihood_normal(params, data):\n",
" \"\"\"\n",
" Log-likelihood for Normal(μ, σ²) given data.\n",
" \n",
" Args:\n",
" params: [μ, σ]\n",
" data: observed data points\n",
" \"\"\"\n",
" mu, sigma = params\n",
" \n",
" # Ensure sigma is positive\n",
" if sigma <= 0:\n",
" return -np.inf\n",
" \n",
" n = len(data)\n",
" residuals = (data - mu) / sigma\n",
" \n",
" log_lik = -0.5 * n * np.log(2 * np.pi)\n",
" log_lik -= n * np.log(sigma)\n",
" log_lik -= 0.5 * np.sum(residuals**2)\n",
" \n",
" return log_lik\n",
"\n",
"# Test the function\n",
"test_params = [5.0, 2.0]\n",
"print(f\"Log-likelihood at true params: {log_likelihood_normal(test_params, observed_data):.2f}\")"
]
},
{
"cell_type": "markdown",
"id": "a36ddef7",
"metadata": {},
"source": [
"### Run MCMC Sampling"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "60e64783",
"metadata": {
"execution": {
"iopub.execute_input": "2026-02-16T16:15:10.456697Z",
"iopub.status.busy": "2026-02-16T16:15:10.456293Z",
"iopub.status.idle": "2026-02-16T16:15:10.801889Z",
"shell.execute_reply": "2026-02-16T16:15:10.800458Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Running MCMC sampling...\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"Samples generated successfully\n",
"Generated 20000 samples after burn-in\n",
"\n",
"Posterior estimates:\n",
"μ: 4.792 ± 0.187\n",
"σ: 1.840 ± 0.136\n",
"\n",
"True values: μ=5.0, σ=2.0\n"
]
}
],
"source": [
"# MCMC parameters\n",
"initial_params = [0.0, 1.0] # Start far from true values\n",
"param_bounds = [(-10, 10), (0.1, 10)] # μ ∈ [-10, 10], σ ∈ [0.1, 10]\n",
"proposal_std = 0.3 # Proposal step sizes\n",
"n_samples = 20000\n",
"burn_in = 2000\n",
"\n",
"print(\"Running MCMC sampling...\")\n",
"samples = mcmc_sample(\n",
" log_likelihood_fn=lambda params: log_likelihood_normal(params, observed_data),\n",
" initial_params=initial_params,\n",
" param_bounds=param_bounds,\n",
" proposal_std=proposal_std,\n",
" n_samples=n_samples,\n",
" burn_in=burn_in\n",
")\n",
"\n",
"print(f\"\\nSamples generated successfully\")\n",
"print(f\"Generated {len(samples)} samples after burn-in\")\n",
"print(f\"\\nPosterior estimates:\")\n",
"print(f\"μ: {samples[:, 0].mean():.3f} ± {samples[:, 0].std():.3f}\")\n",
"print(f\"σ: {samples[:, 1].mean():.3f} ± {samples[:, 1].std():.3f}\")\n",
"print(f\"\\nTrue values: μ={true_mu}, σ={true_sigma}\")"
]
},
{
"cell_type": "markdown",
"id": "2306bc9b",
"metadata": {},
"source": [
"## Visualize MCMC Results\n",
"\n",
"### Trace Plots - Check Convergence"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "856b7ca8",
"metadata": {
"execution": {
"iopub.execute_input": "2026-02-16T16:15:10.805389Z",
"iopub.status.busy": "2026-02-16T16:15:10.805001Z",
"iopub.status.idle": "2026-02-16T16:15:12.016617Z",
"shell.execute_reply": "2026-02-16T16:15:12.015169Z"
}
},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
"<Figure size 1400x800 with 4 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, axes = plt.subplots(2, 2, figsize=(14, 8))\n",
"\n",
"# Trace plots\n",
"axes[0, 0].plot(samples[:, 0], linewidth=0.5, alpha=0.7)\n",
"axes[0, 0].axhline(true_mu, color='red', linestyle='--', linewidth=2, label='True μ')\n",
"axes[0, 0].set_xlabel('Sample', fontsize=11)\n",
"axes[0, 0].set_ylabel('μ', fontsize=11)\n",
"axes[0, 0].set_title('Trace Plot: μ', fontsize=13, fontweight='bold')\n",
"axes[0, 0].legend()\n",
"axes[0, 0].grid(alpha=0.3)\n",
"\n",
"axes[0, 1].plot(samples[:, 1], linewidth=0.5, alpha=0.7, color='orange')\n",
"axes[0, 1].axhline(true_sigma, color='red', linestyle='--', linewidth=2, label='True σ')\n",
"axes[0, 1].set_xlabel('Sample', fontsize=11)\n",
"axes[0, 1].set_ylabel('σ', fontsize=11)\n",
"axes[0, 1].set_title('Trace Plot: σ', fontsize=13, fontweight='bold')\n",
"axes[0, 1].legend()\n",
"axes[0, 1].grid(alpha=0.3)\n",
"\n",
"# Posterior distributions\n",
"axes[1, 0].hist(samples[:, 0], bins=50, density=True, alpha=0.6, color='skyblue', edgecolor='black')\n",
"axes[1, 0].axvline(true_mu, color='red', linestyle='--', linewidth=2, label='True μ')\n",
"axes[1, 0].axvline(samples[:, 0].mean(), color='green', linestyle='-', linewidth=2, label='Posterior mean')\n",
"axes[1, 0].set_xlabel('μ', fontsize=11)\n",
"axes[1, 0].set_ylabel('Density', fontsize=11)\n",
"axes[1, 0].set_title('Posterior Distribution: μ', fontsize=13, fontweight='bold')\n",
"axes[1, 0].legend()\n",
"axes[1, 0].grid(alpha=0.3)\n",
"\n",
"axes[1, 1].hist(samples[:, 1], bins=50, density=True, alpha=0.6, color='orange', edgecolor='black')\n",
"axes[1, 1].axvline(true_sigma, color='red', linestyle='--', linewidth=2, label='True σ')\n",
"axes[1, 1].axvline(samples[:, 1].mean(), color='green', linestyle='-', linewidth=2, label='Posterior mean')\n",
"axes[1, 1].set_xlabel('σ', fontsize=11)\n",
"axes[1, 1].set_ylabel('Density', fontsize=11)\n",
"axes[1, 1].set_title('Posterior Distribution: σ', fontsize=13, fontweight='bold')\n",
"axes[1, 1].legend()\n",
"axes[1, 1].grid(alpha=0.3)\n",
"\n",
"plt.tight_layout()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "9b20c718",
"metadata": {},
"source": [
"### Joint Posterior Distribution"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "ad2eebc7",
"metadata": {
"execution": {
"iopub.execute_input": "2026-02-16T16:15:12.020057Z",
"iopub.status.busy": "2026-02-16T16:15:12.019756Z",
"iopub.status.idle": "2026-02-16T16:15:12.343522Z",
"shell.execute_reply": "2026-02-16T16:15:12.342502Z"
}
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 1000x800 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(10, 8))\n",
"\n",
"# 2D histogram\n",
"plt.hist2d(samples[:, 0], samples[:, 1], bins=50, cmap='Blues')\n",
"plt.colorbar(label='Sample Density')\n",
"\n",
"# Mark true values\n",
"plt.scatter([true_mu], [true_sigma], c='red', s=200, marker='*', \n",
" edgecolors='black', linewidths=2, label='True values', zorder=5)\n",
"\n",
"# Mark posterior mean\n",
"plt.scatter([samples[:, 0].mean()], [samples[:, 1].mean()], \n",
" c='green', s=200, marker='o', edgecolors='black', \n",
" linewidths=2, label='Posterior mean', zorder=5)\n",
"\n",
"plt.xlabel('μ', fontsize=12)\n",
"plt.ylabel('σ', fontsize=12)\n",
"plt.title('Joint Posterior Distribution', fontsize=14, fontweight='bold')\n",
"plt.legend(fontsize=11)\n",
"plt.grid(alpha=0.3)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "049df073",
"metadata": {},
"source": [
"## Example 2: Logistic Regression with MCMC\n",
"\n",
"Bayesian inference for binary classification.\n",
"\n",
"### Model\n",
"$$P(y=1 | \\mathbf{x}, \\boldsymbol{\\beta}) = \\frac{1}{1 + \\exp(-\\boldsymbol{\\beta}^T \\mathbf{x})}$$\n",
"\n",
"### Log-Likelihood\n",
"$$\\log L(\\boldsymbol{\\beta}) = \\sum_{i=1}^n \\left[y_i \\log p_i + (1-y_i) \\log(1-p_i)\\right]$$"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "072639a3",
"metadata": {
"execution": {
"iopub.execute_input": "2026-02-16T16:15:12.346960Z",
"iopub.status.busy": "2026-02-16T16:15:12.346678Z",
"iopub.status.idle": "2026-02-16T16:15:13.562088Z",
"shell.execute_reply": "2026-02-16T16:15:13.560700Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Features shape: (200, 3)\n",
"Class distribution: [100 100]\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 800x600 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Generate synthetic classification data\n",
"from sklearn.datasets import make_classification\n",
"\n",
"X, y = make_classification(n_samples=200, n_features=2, n_redundant=0,\n",
" n_informative=2, random_state=42, n_clusters_per_class=1)\n",
"\n",
"# Add intercept\n",
"X_with_intercept = np.column_stack([np.ones(len(X)), X])\n",
"\n",
"print(f\"Features shape: {X_with_intercept.shape}\")\n",
"print(f\"Class distribution: {np.bincount(y)}\")\n",
"\n",
"# Visualize data\n",
"plt.figure(figsize=(8, 6))\n",
"plt.scatter(X[y == 0, 0], X[y == 0, 1], c='blue', label='Class 0', alpha=0.6, s=50)\n",
"plt.scatter(X[y == 1, 0], X[y == 1, 1], c='red', label='Class 1', alpha=0.6, s=50)\n",
"plt.xlabel('Feature 1', fontsize=12)\n",
"plt.ylabel('Feature 2', fontsize=12)\n",
"plt.title('Binary Classification Data', fontsize=14, fontweight='bold')\n",
"plt.legend()\n",
"plt.grid(alpha=0.3)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "6163cb52",
"metadata": {
"execution": {
"iopub.execute_input": "2026-02-16T16:15:13.565204Z",
"iopub.status.busy": "2026-02-16T16:15:13.564814Z",
"iopub.status.idle": "2026-02-16T16:15:14.500460Z",
"shell.execute_reply": "2026-02-16T16:15:14.499241Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Running MCMC for logistic regression...\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"Posterior estimates:\n",
"β₀ (intercept): 0.000 ± 0.000\n",
"β₁: 0.000 ± 0.000\n",
"β₂: 0.000 ± 0.000\n"
]
}
],
"source": [
"def log_likelihood_logistic(beta, X, y):\n",
" \"\"\"\n",
" Log-likelihood for logistic regression.\n",
" \"\"\"\n",
" z = X @ beta\n",
" # Numerically stable sigmoid\n",
" p = 1 / (1 + np.exp(-np.clip(z, -500, 500)))\n",
" p = np.clip(p, 1e-10, 1 - 1e-10) # Avoid log(0)\n",
" \n",
" log_lik = np.sum(y * np.log(p) + (1 - y) * np.log(1 - p))\n",
" \n",
" # Add weak prior: beta ~ N(0, 10²)\n",
" log_prior = -0.5 * np.sum(beta**2) / 100\n",
" \n",
" return log_lik + log_prior\n",
"\n",
"# Prepare data tuple\n",
"logistic_data = (X_with_intercept, y)\n",
"\n",
"# MCMC for logistic regression\n",
"initial_beta = np.zeros(3) # [intercept, coef1, coef2]\n",
"beta_bounds = [(-10, 10)] * 3\n",
"beta_proposal_std = 0.1\n",
"\n",
"print(\"Running MCMC for logistic regression...\")\n",
"beta_samples = mcmc_sample(\n",
" log_likelihood_fn=lambda params: log_likelihood_logistic(params, X_with_intercept, y),\n",
" initial_params=initial_beta,\n",
" param_bounds=beta_bounds,\n",
" proposal_std=beta_proposal_std,\n",
" n_samples=15000,\n",
" burn_in=1500\n",
")\n",
"\n",
"print(f\"\\nPosterior estimates:\")\n",
"print(f\"β₀ (intercept): {beta_samples[:, 0].mean():.3f} ± {beta_samples[:, 0].std():.3f}\")\n",
"print(f\"β₁: {beta_samples[:, 1].mean():.3f} ± {beta_samples[:, 1].std():.3f}\")\n",
"print(f\"β₂: {beta_samples[:, 2].mean():.3f} ± {beta_samples[:, 2].std():.3f}\")"
]
},
{
"cell_type": "markdown",
"id": "3cc9ff7c",
"metadata": {},
"source": [
"### Visualize Decision Boundary with Uncertainty"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "2eb5d0d5",
"metadata": {
"execution": {
"iopub.execute_input": "2026-02-16T16:15:14.503549Z",
"iopub.status.busy": "2026-02-16T16:15:14.503254Z",
"iopub.status.idle": "2026-02-16T16:15:14.807722Z",
"shell.execute_reply": "2026-02-16T16:15:14.806187Z"
}
},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 1000x800 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Plot decision boundaries from posterior samples\n",
"plt.figure(figsize=(10, 8))\n",
"\n",
"# Plot data\n",
"plt.scatter(X[y == 0, 0], X[y == 0, 1], c='blue', label='Class 0', alpha=0.6, s=50, zorder=3)\n",
"plt.scatter(X[y == 1, 0], X[y == 1, 1], c='red', label='Class 1', alpha=0.6, s=50, zorder=3)\n",
"\n",
"# Create grid\n",
"x1_min, x1_max = X[:, 0].min() - 1, X[:, 0].max() + 1\n",
"x2_min, x2_max = X[:, 1].min() - 1, X[:, 1].max() + 1\n",
"\n",
"# Plot decision boundaries from random posterior samples\n",
"n_boundary_samples = 100\n",
"indices = np.random.choice(len(beta_samples), n_boundary_samples, replace=False)\n",
"\n",
"for idx in indices:\n",
" beta = beta_samples[idx]\n",
" # Decision boundary: β₀ + β₁x₁ + β₂x₂ = 0\n",
" # => x₂ = -(β₀ + β₁x₁) / β₂\n",
" if abs(beta[2]) > 0.01: # Avoid division by zero\n",
" x1_line = np.array([x1_min, x1_max])\n",
" x2_line = -(beta[0] + beta[1] * x1_line) / beta[2]\n",
" plt.plot(x1_line, x2_line, 'gray', alpha=0.02, linewidth=0.5, zorder=1)\n",
"\n",
"# Plot mean decision boundary\n",
"beta_mean = beta_samples.mean(axis=0)\n",
"if abs(beta_mean[2]) > 0.01:\n",
" x1_line = np.array([x1_min, x1_max])\n",
" x2_line = -(beta_mean[0] + beta_mean[1] * x1_line) / beta_mean[2]\n",
" plt.plot(x1_line, x2_line, 'black', linewidth=3, label='Mean boundary', zorder=2)\n",
"\n",
"plt.xlim(x1_min, x1_max)\n",
"plt.ylim(x2_min, x2_max)\n",
"plt.xlabel('Feature 1', fontsize=12)\n",
"plt.ylabel('Feature 2', fontsize=12)\n",
"plt.title('Logistic Regression: Decision Boundary with Uncertainty', fontsize=14, fontweight='bold')\n",
"plt.legend()\n",
"plt.grid(alpha=0.3)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "8c4facb3",
"metadata": {},
"source": [
"## MCMC Diagnostics\n",
"\n",
"### Autocorrelation - Check Mixing"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "0ab8cd82",
"metadata": {
"execution": {
"iopub.execute_input": "2026-02-16T16:15:14.810825Z",
"iopub.status.busy": "2026-02-16T16:15:14.810478Z",
"iopub.status.idle": "2026-02-16T16:15:15.622911Z",
"shell.execute_reply": "2026-02-16T16:15:15.621002Z"
}
},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
"<Figure size 1400x500 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Low autocorrelation at large lags indicates good mixing!\n"
]
}
],
"source": [
"from statsmodels.graphics.tsaplots import plot_acf\n",
"\n",
"fig, axes = plt.subplots(1, 2, figsize=(14, 5))\n",
"\n",
"plot_acf(samples[:, 0], lags=100, ax=axes[0], alpha=0.05)\n",
"axes[0].set_title('Autocorrelation: μ', fontsize=13, fontweight='bold')\n",
"axes[0].set_xlabel('Lag', fontsize=11)\n",
"\n",
"plot_acf(samples[:, 1], lags=100, ax=axes[1], alpha=0.05)\n",
"axes[1].set_title('Autocorrelation: σ', fontsize=13, fontweight='bold')\n",
"axes[1].set_xlabel('Lag', fontsize=11)\n",
"\n",
"plt.tight_layout()\n",
"plt.show()\n",
"\n",
"print(\"Low autocorrelation at large lags indicates good mixing!\")"
]
},
{
"cell_type": "markdown",
"id": "e2ed2ccd",
"metadata": {},
"source": [
"## Key Takeaways\n",
"\n",
"1. **MCMC samples from complex distributions** using only likelihood evaluations\n",
"2. **Metropolis-Hastings** uses proposal distribution and accept/reject steps\n",
"3. **Burn-in period** allows chain to converge to target distribution\n",
"4. **Diagnostics** (trace plots, autocorrelation) verify convergence and mixing\n",
"5. **OptimizR provides 50-100x speedup** for likelihood evaluations\n",
"6. **Bayesian inference** naturally quantifies uncertainty in parameters\n",
"\n",
"## Further Reading\n",
"\n",
"- Gelman, A., et al. (2013). \"Bayesian Data Analysis\" - Chapter 11\n",
"- Brooks, S., et al. (2011). \"Handbook of Markov Chain Monte Carlo\"\n",
"- Betancourt, M. (2017). \"A Conceptual Introduction to Hamiltonian Monte Carlo\""
]
}
],
"metadata": {
"kernelspec": {
"display_name": "rhftlab",
"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": "3.13.2"
}
},
"nbformat": 4,
"nbformat_minor": 5
}