Pe. Greenwood et al., OUTPERFORMING THE GIBBS SAMPLER EMPIRICAL ESTIMATOR FOR NEAREST-NEIGHBOR RANDOM-FIELDS, Annals of statistics, 24(4), 1996, pp. 1433-1456
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.