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Adaptive Rejection Sampling for Gibbs Sampling
Author(s) -
Gilks W. R.,
Wild P.
Publication year - 1992
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.2307/2347565
Subject(s) - gibbs sampling , sampling (signal processing) , rejection sampling , adaptive sampling , mathematics , statistics , statistical physics , computer science , physics , monte carlo method , markov chain monte carlo , bayesian probability , filter (signal processing) , monte carlo molecular modeling , computer vision
SUMMARY 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.