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A vanilla Rao-Blackwellisation of Metropolis-Hastings algorithms

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Date
2011
Link to item file
http://arxiv.org/abs/0904.2144v5
Dewey
Probabilités et mathématiques appliquées
Sujet
Metropolis-Hastings algorithm; central limit theorem; Markov Chain Monte Carlo (MCMC); conditioning; variance reduction
JEL code
C15
Journal issue
Annals of Statistics
Volume
39
Number
1
Publication date
2011
Article pages
261-277
Publisher
Institute of Mathematical Statistics
DOI
http://dx.doi.org/10.1214/10-AOS838
URI
https://basepub.dauphine.fr/handle/123456789/3578
Collections
  • CEREMADE : Publications
Metadata
Show full item record
Author
Douc, Randal
status unknown
Robert, Christian P.
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
2579 Centre de Recherche en Économie et Statistique [CREST]
Type
Article accepté pour publication ou publié
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.

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