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A vanilla Rao-Blackwellisation of Metropolis-Hastings algorithms

Douc, Randal; Robert, Christian P. (2011), A vanilla Rao-Blackwellisation of Metropolis-Hastings algorithms, Annals of Statistics, 39, 1, p. 261-277. http://dx.doi.org/10.1214/10-AOS838

Type
Article accepté pour publication ou publié
External document link
http://arxiv.org/abs/0904.2144v5
Date
2011
Journal name
Annals of Statistics
Volume
39
Number
1
Publisher
Institute of Mathematical Statistics
Pages
261-277
Publication identifier
Metadata
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Author(s)
Douc, Randal
Communications, Images et Traitement de l'Information [CITI]
Services répartis, Architectures, MOdélisation, Validation, Administration des Réseaux [SAMOVAR]
Robert, Christian P.
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Centre de Recherche en Économie et Statistique [CREST]
Abstract (EN)
Casella and Robert (1996) presented a general Rao--Blackwellisation 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 computing 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 computing cost under control. We establish a central limit theorems for the improved estimators and illustrate their performances on toy examples.
Subjects / Keywords
Metropolis-Hastings algorithm; central limit theorem; Markov Chain Monte Carlo (MCMC); conditioning; variance reduction
JEL
C15 - Statistical Simulation Methods: General