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Corrigendum: Adaptive Rejection Metropolis Sampling

1997; Oxford University Press; Volume: 46; Issue: 4 Linguagem: Inglês

10.1111/1467-9876.00091

1467-9876

Walter R. Gilks, Radford M. Neal, Nicky Best, Keith Tan,

Antibiotics Pharmacokinetics and Efficacy

We described a method for sampling from awkward univariate full conditional distributions encountered in applications of Gibbs sampling.The method, called adaptive rejection Metropolis sampling (ARMS), is a generalization of the adaptive rejection sampling (ARS) algorithm of Gilks (1992), the latter being restricted to logconcave distributions.ARMS deals with possible non-log-concavity in a full conditional distribution by appending a Metropolis±Hastings step following the ARS step.This note concerns the choice of initial values for the ARS step of ARMS.Let (x, y) denote the complete set of variables being sampled by the Gibbs sampler, where x is scalar and y may be vector.Let x i , y i ) denote their values at the end of iteration i of the Gibbs sampler.The task is to generate x i1 from f xjy i ), the full conditional distribution for x.To do this by ARMS, we must ®rst provide a set S i1 n of n initial x-values (starting abscissae) for the ARS step.On completion of the ARS step, additional abscissae may have been generated, yielding a set S