Semi-exact control functionals from Sard's method

• 成果类型: Article
• 署名作者: South, L. F.; Karvonen, T.; Nemeth, C.; Girolami, M.; Oates, C. J.
• 署名单位: Queensland University of Technology (QUT); Alan Turing Institute; Lancaster University; University of Cambridge; Newcastle University - UK
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asab036
• 发表日期: 2022
• 页码: 351367
• 关键词: chain monte-carlo

摘要

A novel control variate technique is proposed for the post-processing of Markov chain Monte Carlo output, based on both Stein's method and an approach to numerical integration due to Sard. The resulting estimators of posterior expected quantities of interest are proven to be polynomially exact in the Gaussian context, while empirical results suggest that the estimators approximate a Gaussian cubature method near the Bernstein-von Mises limit. The main theoretical result establishes a bias-correction property in settings where the Markov chain does not leave the posterior invariant. Empirical results across a selection of Bayesian inference tasks are presented.