Adaptive Rejection Sampling for Gibbs Sampling

TLDR

The authors propose an adaptive rejection sampling method for univariate log‑concave densities, aimed at reducing expensive density evaluations in Gibbs sampling for Bayesian models with non‑conjugacy. The method adaptively constructs piecewise exponential rejection envelopes and squeezing functions that converge to the target density, and is applied to Gibbs sampling of monoclonal antibody reactivity.

Abstract

We propose a method for rejection sampling from any univariate log‐concave probability density function. The method is adaptive: As sampling proceeds, the rejection envelope and the squeezing function converge to the density function. The rejection envelope and squeezing function are piece‐wise exponential functions, the rejection envelope touching the density at previously sampled points, and the squeezing function forming arcs between those points of contact. The technique is intended for situations where evaluation of the density is computationally expensive, in particular for applications of Gibbs sampling to Bayesian models with non‐conjugacy. We apply the technique to a Gibbs sampling analysis of monoclonal antibody reactivity.