AUTHOR:  Greenwood, P. E., McKeague, I. W. and Wefelmeyer, W.
DATE: 1995
TITLE: Outperforming the Gibbs Sampler Empirical
Estimator for Nearest Neighbor Random Fields

ABSTRACT:
Given a Markov chain sampling scheme, does the standard empirical estimator
make 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 with deterministic sweep, but
our approach applies to any sampler that uses  
reversible variable-at-a-time updating with deterministic sweep. 
The structure of the transition distribution of the sampler is exploited to
construct further empirical estimators that are combined with the standard
empirical estimator to reduce asymptotic variance. The extra computational
cost is negligible. When the random field is spatially homogeneous,
symmetrizations of our estimator lead to further variance reduction.
The performance of the estimators is evaluated in a simulation study
of the Ising model.