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Rao–Blackwellisation in the Markov Chain Monte Carlo Era

Robert, Christian P.; Roberts, Gareth (2021), Rao–Blackwellisation in the Markov Chain Monte Carlo Era, International Statistical Review, 89, 2, p. 237-249. 10.1111/insr.12463

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Type
Article accepté pour publication ou publié
Date
2021
Journal name
International Statistical Review
Volume
89
Number
2
Publisher
Wiley
Pages
237-249
Publication identifier
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Author(s)
Robert, Christian P.
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Roberts, Gareth
Department of Statistics [Warwick]
Abstract (EN)
Rao–Blackwellisation is a notion often occurring in the MCMC literature, with possibly different meanings and connections with the original Rao–Blackwell theorem as established by C.R. Rao in 1945 and D. Blackwell in 1947, including a reduction of the variance of the resulting Monte Carlo approximations. This survey reviews some of the meanings of the term.
Subjects / Keywords
Monte Carlo; simulation; Rao–Blackwellization; Metropolis-Hastingsalgorithm; Gibbs sampler; importance sampling; mixtures; parallelisation