TY - JOUR

T1 - Convergence of regression-adjusted approximate Bayesian computation

AU - Li, Wentao

AU - Fearnhead, Paul

N1 - 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

PY - 2018/6/1

Y1 - 2018/6/1

N2 - We present asymptotic results for the regression-adjusted version of approximate Bayesiancomputation 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.

AB - We present asymptotic results for the regression-adjusted version of approximate Bayesiancomputation 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.

KW - approximate Bayesian computation

KW - Importance sampling

KW - Local-linear regression

KW - Partial information

U2 - 10.1093/biomet/asx081

DO - 10.1093/biomet/asx081

M3 - Journal article

VL - 105

SP - 301

EP - 318

JO - Biometrika

JF - Biometrika

SN - 0006-3444

IS - 2

ER -