language: en

Structured Markov Chain Monte Carlo

by Daniel J. SARGENT 1 , James S. HODGES 2 , and Bradley P. CARLIN 2
1 Section of Biostatistics, Mayo Clinic
2 Division of Biostatistics, School of Public Health, University of Minnesota
January 9, 1998

Abstract In this paper we introduce a general method for Bayesian computing in richly-parameterized models, Structured Markov Chain Monte Carlo (SMCMC), that is based on a blocked hybrid of the Gibbs sampling and Metropolis-Hastings algorithms. SMCMC speeds algorithm convergence by using the structure that is present in the problem to suggest an appropriate Metropolis-Hastings candidate distribution. While the approach is easiest to describe for hierarchical normal linear models, we show its extension to both non-normal and nonlinear cases to be straightforward. After describing the method in detail we compare its performance (both in terms of runtime and autocorrelation in the samples produced) to several other existing methods, including the traditional single-site updating Gibbs sampler available in the popular BUGS software package. Our results suggest significant improvements in convergence for many problems using SMCMC, as well as broad applicability of the method, including previously intractable hierarchical nonlinear model settings.

KEY WORDS: Blocking; Convergence acceleration; Gibbs sampling; Hierarchical model; Metropolis-Hastings algorithm.