COVARIANCE STRUCTURE AND CONVERGENCE RATE OF THE GIBBS SAMPLER WITH VARIOUS SCANS

This paper presents results on covariance structure and convergence fo r the Gibbs sampler with both systematic and random scans. It is shown that, under conditions that guarantee the compactness of the Markov f orward operator and irreducibility of the corresponding chain, the Gib bs sampling scheme converges geometrically in terms of Pearson chi2-di stance. In particular, for the random scan, the autocovariance can be expressed as variances of iterative conditional expectations. As a con sequence, the autocorrelations are all positive and decrease monotonic ally.