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    Rights statement: This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Biometrika following peer review. The definitive publisher-authenticated version Wentao Li, Paul Fearnhead; Convergence of regression-adjusted approximate Bayesian computation, Biometrika, Volume 105, Issue 2, 1 June 2018, Pages 301–318, https://doi.org/10.1093/biomet/asx081 is available online at: https://academic.oup.com/biomet/article/105/2/301/4827648

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Convergence of regression-adjusted approximate Bayesian computation

Research output: Contribution to journalJournal article

Published
<mark>Journal publication date</mark>1/06/2018
<mark>Journal</mark>Biometrika
Issue number2
Volume105
Number of pages18
Pages (from-to)301-318
Publication statusPublished
Early online date27/01/18
Original languageEnglish

Abstract

We present asymptotic results for the regression-adjusted version of approximate Bayesian
computation introduced by Beaumont et al. (2002). We show that for an appropriate choice of the bandwidth, regression adjustment will lead to a posterior that, asymptotically, correctly quantifies uncertainty. Furthermore, for such a choice of bandwidth we can implement an importance sampling algorithm to sample from the posterior whose acceptance probability tends to unity as the data sample size increases. This compares favourably to results for standard approximate Bayesian computation, where the only way to obtain a posterior that correctly quantifies uncertainty is to choose a much smaller bandwidth; one for which the acceptance probability tends to zero and hence for which Monte Carlo error will dominate.

Bibliographic note

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Biometrika following peer review. The definitive publisher-authenticated version Wentao Li, Paul Fearnhead; Convergence of regression-adjusted approximate Bayesian computation, Biometrika, Volume 105, Issue 2, 1 June 2018, Pages 301–318, https://doi.org/10.1093/biomet/asx081 is available online at: https://academic.oup.com/biomet/article/105/2/301/4827648