Convergence of regression-adjusted approximate Bayesian computation

• 成果类型: Article
• 署名作者: Li, Wentao; Fearnhead, Paul
• 署名单位: Newcastle University - UK; Lancaster University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asx081
• 发表日期: 2018
• 页码: 301318
• 关键词: chain monte-carlo; indirect inference; likelihoods; MODEL; statistics; EVOLUTION; systems; abc

摘要

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.