Adaptive Rejection Sampler

About

Provides comprehensive guidance for implementing the Gilks et al. (1992) adaptive rejection sampling (ARS) algorithm to draw samples from complex log-concave distributions. This skill assists in constructing piecewise linear upper and lower envelopes that adapt as sampling progresses, ensuring high efficiency through squeeze tests and adaptive updates. It includes critical implementation strategies for numerical stability, proper initialization, boundary handling, and statistical verification, making it an essential resource for developing robust Monte Carlo methods and statistical computing tools.

Key Features

• Implementation steps for adaptive updating and rejection/squeeze tests
• Numerical stability guidelines for handling exponentials and floating-point noise
• 16 GitHub stars
• Statistical verification methods including Kolmogorov-Smirnov and moment-based testing
• Strategies for domain boundary handling and optimal initialization point selection
• Mathematical foundations for log-concave distribution sampling and hull construction

Use Cases

• Implementing Bayesian inference algorithms where posterior distributions are log-concave
• Developing custom Monte Carlo samplers in statistical languages like R
• Generating random variables from complex probability densities without a closed-form inverse CDF