Subsampling the Gibbs Sampler

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 discarded as being too difficult to work with. Ongoing research in this area includes widening the applications to ever more detailed and difficult problems, alteration and improvement of the algorithm, and improvement of estimates based on the Markov chain. See Besag and Green (1993) and Smith and Roberts (1993). One of the extraordinary features of the Gibbs sampler is that the theory behind it can be presented at an elementary level (Casella and George, 1992), giving upper level undergraduate or beginning graduate students a glimpse Steve MacEachern is Assistant Professor, Department of Statistics, Ohio State University, and Visiting Assistant Professor, Institute