Approximate predetermined convergence properties of the Gibbs sampler

This article aims to provide a method for approximately predetermining conv ergence properties of the Gibbs sampler. This is to be done by first findin g an approximate rate of convergence for a normal approximation of the targ et distribution. The rates of convergence for different implementation stra tegies of the Gibbs sampler are compared to find the best one. In general, the limiting convergence properties of the Gibbs sampler on a sequence of t arget distributions (approaching a limit) are not the same as the convergen ce properties of the Gibbs sampler on the limiting target distribution. The oretical results are given in this article to justify that under conditions , the convergence properties of the Gibbs sampler can be approximated as we ll. A number of practical examples are given for illustration.