We consider various versions of adaptive Gibbs and Metropolis-within-Gibbs samplers, which update their selection probabilities (and perhaps also their proposal distributions) on the fly during a run, by learning as they go in an attempt to optimise the algorithm. We present a cautionary example

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We consider various versions of adaptive Gibbs and Metropolis-within-Gibbs samplers, which update their selection probabilities (and perhaps also their proposal distributions) on the fly during a run, by learning as they go in an attempt to optimise the algorithm. We present a cautionary example

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... In this paper we present two general types of Gibbs samplers that can be used to fit posteriors of Bayesian hierarchical models based on stick-breaking priors. The first type of Gibbs sampler, referred to as a Polya urn Gibbs sampler, is a generalized version of a widely used Gibbs sampling

When the Gibbs sampler is used to estimate posterior distributions (Gelfand and Smith, 1990), the question of how many iterations are required is central to its implementation. When interest focuses on quantiles of functionals of the posterior distribution, we describe an easily

This paper investigates conditions under which the Gibbs sampler (Gelfand and Smith, 1990; Tanner and Wong, 1987; Geman and Geman, 1984) converges at a geometric rate. The main results appear in Sections 2 and 3, where geometric convergence results are established, with respect to total variation

Abstract. Markov chain sampling methods that automatically adapt to characteristics of the distribution being sampled can be constructed by exploiting the principle that one can sample from a distribution by sampling uniformly from the region under the plot of its density function. A Markov chain

INTRODUCTION Markov chain Monte Carlo methods have enjoyed a surge of interest since Gelfand and Smith (1990) described the Gibbs sampler and its effectiveness in providing approximate Bayesian solutions for models that had previously been approachable only with great difficulty, or that had been