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Adaptive Rejection Sampling for Gibbs Sampling

1992; Oxford University Press; Volume: 41; Issue: 2 Linguagem: Inglês

10.2307/2347565

1467-9876

Walter R. Gilks, Pascal Wild,

Monoclonal and Polyclonal Antibodies Research

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.