A VANILLA RAO-BLACKWELLIZATION OF METROPOLIS-HASTINGS ALGORITHMS

• 成果类型: Article
• 署名作者: Douc, Randal; Robert, Christian P.
• 署名单位: IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis; Institut Polytechnique de Paris; ENSAE Paris; Universite PSL; Universite Paris-Dauphine
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/10-AOS838
• 发表日期: 2011
• 页码: 261-277
• 关键词: weighted samples; monte-carlo

摘要

Casella and Robert [Biometrika 83 (1996) 81-94] presented a general Rao-Blackwellization principle for accept-reject and Metropolis-Hastings schemes that leads to significant decreases in the variance of the resulting estimators, but at a high cost in computation and storage. Adopting a completely different perspective, we introduce instead a universal scheme that guarantees variance reductions in all Metropolis-Hastings-based estimators while keeping the computation cost under control. We establish a central limit theorem for the improved estimators and illustrate their performances on toy examples and on a probit model estimation.