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

• 成果类型: Article
• 署名作者: Greenwood, PE; McKeague, IW; Wefelmeyer, W
• 署名单位: State University System of Florida; Florida State University; Universitat Siegen
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1996
• 页码: 1433-1456
• 关键词: exploring posterior distributions; markov-chains; stochastic relaxation; bayesian computation; DYNAMICS; models

摘要

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.