Convergence Diagnostics of the Gibbs Sampler

Abstract

The emergence of the Gibbs sampler, and other associated stochastic simulation techniques, is clearly an importance advance in the generation of samples from multi-dimensional distributions, which has particular application in Bayesian statistics.The advantages of the algorithm are its ease of implementation, its speed of convergence, and the lack of regularity conditions necessary to ensure convergence. Its major drawback, however, is that although convergence is well understood theoretically, diagnosis of convergence is often difficult. In this paper, we address the issue of convergence and its diagnosis. In particular, we focus our attention on the search for a one-dimensional summary statistic which attempts to describe the convergence mechanism