OUTPERFORMING THE GIBBS SAMPLER EMPIRICAL ESTIMATOR FOR NEAREST-NEIGHBOR RANDOM-FIELDS

Given a Markov chain sampling scheme, does the standard empirical esti mator make best use of the data? We show that this is not so and const ruct better estimators. We restrict attention to nearest-neighbor rand om fields and to Gibbs samplers with deterministic sweep, but our appr oach applies to any sampler that uses reversible variable-at-a-time up dating with deterministic sweep. The structure of the transition distr ibution of the sampler is exploited to construct further empirical est imators that are combined with the standard empirical estimator to red uce asymptotic variance. The extra computational cost is negligible. W hen the random field is spatially homogeneous, symmetrizations of our estimator lead to further Variance reduction. The performance of the e stimators is evaluated in a simulation study of the Ising model.