Outperforming the Gibbs sampler empirical estimator for nearest-neighbor random fields

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Abstract
Given a Markov chain sampling scheme, does the standard empirical estimatormake best use of the data? We show that this is not so and construct better estimators.We restrict attention to nearest neighbor random fields and to Gibbs samplers withdeterministic sweep, but our approach applies to any sampler that uses reversiblevariable-at-a-time updating with deterministic sweep. The structure of the transitiondistribution of the sampler is exploited to construct further empirical estimators...

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