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Adaptive Rejection Sampling for Gibbs Sampling

W. R. Gilks and P. Wild
Journal of the Royal Statistical Society. Series C (Applied Statistics)
Vol. 41, No. 2 (1992), pp. 337-348
Published by: Wiley for the Royal Statistical Society
DOI: 10.2307/2347565
Stable URL: http://www.jstor.org/stable/2347565
Page Count: 12
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Adaptive Rejection Sampling for Gibbs Sampling
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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.

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