Convergence of regression-adjusted approximate Bayesian computation

Li, Wentao and Fearnhead, Paul (2018) Convergence of regression-adjusted approximate Bayesian computation. Biometrika, 105 (2). pp. 301-318. ISSN 0006-3444

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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.

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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, is available online at:
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?? approximate bayesian computationimportance samplinglocal-linear regressionpartial informationgeneral agricultural and biological sciencesapplied mathematicsstatistics and probabilitystatistics, probability and uncertaintygeneral mathematicsagricultural an ??
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07 Oct 2016 10:40
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16 Jul 2024 10:17