Antithetic coupling of two Gibbs sampler chains

• 成果类型: Article
• 署名作者: Frigessi, A; Gåsemyr, J; Rue, H
• 署名单位: University of Oslo; Norwegian University of Science & Technology (NTNU)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2000
• 页码: 1128-1149
• 关键词: bayesian-inference; models

摘要

Two coupled Gibbs sampler chains, both with invariant probability density pi, are run in parallel so that the chains are negatively correlated. We define an asymptotically unbiased estimator of the pi -expectation E( f(X)) which achieves significant variance reduction with respect to the usual Gibbs sampler at comparable computational cost. The variance of the estimator based on the new algorithm is always smaller than the variance of a single Gibbs sampler chain, if pi is attractive and f is monotone nondecreasing in all components of X. For nonattractive targets pi, our results are not complete: The new antithetic algorithm outperforms the standard Gibbs sampler when pi is a multivariate normal density or the Ising model. More generally, nonrigorous arguments and numerical experiments support the usefulness of the antithetically coupled Gibbs samplers also for other nonattractive models. In our experiments the variance is reduced to at least a third and the efficiency also improves significantly.