Accelerating Metropolis-Hastings algorithms by Delayed Acceptance

Marco Banterle, Clara Grazian, Anthony Lee, Christian Robert

Research output: Contribution to journalArticle (Academic Journal)peer-review

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Abstract

MCMC algorithms such as Metropolis--Hastings algorithms are slowed down by the computation of complex target distributions as exemplified by huge datasets. We offer a useful generalisation of the Delayed Acceptance approach, devised to reduce such computational costs by a simple and universal divide-and-conquer strategy. The generic acceleration stems from breaking the acceptance step into several parts, aiming at a major gain in computing time that out-ranks a corresponding reduction in acceptance probability. Each component is sequentially compared with a uniform variate, the first rejection terminating this iteration. We develop theoretical bounds for the variance of associated estimators against the standard Metropolis--Hastings and produce results on optimal scaling and general optimisation of the procedure.
Original languageEnglish
Pages (from-to)103-128
Number of pages25
JournalFoundations of Data Science
Volume1
Issue number2
Early online date19 Mar 2019
DOIs
Publication statusPublished - 1 Jun 2019

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