Delayed rejection in reversible jump Metropolis-Hastings

PJ Green, A Mira

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

161 Citations (Scopus)

Abstract

In a Metropolis-Hastings algorithm, rejection of proposed moves is an intrinsic part of ensuring that the chain converges to the intended target distribution. However, persistent rejection, perhaps in particular parts of the state space, may indicate that locally the proposal distribution is badly calibrated to the target. As an alternative to careful off-line tuning of state-dependent proposals, the basic algorithm can be modified so that, on rejection, a second attempt to move is made. A different proposal can be generated from a new distribution that is allowed to depend on the previously rejected proposal. We generalise this idea of delaying the rejection and adapting the proposal distribution, due to Tierney & Mira (1999), to generate a more flexible class of methods that applies in particular to a variable-dimension setting. The approach is illustrated by two pedagogical examples and a more realistic application to a changepoints analysis for point processes.
Translated title of the contributionDelayed rejection in reversible jump Metropolis-Hastings
Original languageEnglish
Pages (from-to)1035 - 1053
JournalBiometrika
Volume88(4)
Publication statusPublished - Dec 2001

Bibliographical note

Publisher: Biometrika Trust
Other identifier: IDS number 498YT

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