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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 L F South, T Karvonen, C Nemeth, M Girolami, C J Oates, Semi-exact control functionals from Sard’s method, Biometrika, Volume 109, Issue 2, June 2022, Pages 351–367 is available online at: https://academic.oup.com/biomet/article/109/2/351/6309456

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    Available under license: CC BY-NC: Creative Commons Attribution-NonCommercial 4.0 International License

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Semi-Exact Control Functionals From Sard's Method

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<mark>Journal publication date</mark>30/06/2022
<mark>Journal</mark>Biometrika
Issue number2
Volume109
Number of pages17
Pages (from-to)351-367
Publication StatusPublished
Early online date25/06/21
<mark>Original language</mark>English

Abstract

A novel control variate technique is proposed for post-processing of Markov chain Monte Carlo output, based both on 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 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 are presented across a selection of Bayesian inference tasks.
All methods used in this paper are available in the R package ZVCV.

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 L F South, T Karvonen, C Nemeth, M Girolami, C J Oates, Semi-exact control functionals from Sard’s method, Biometrika, Volume 109, Issue 2, June 2022, Pages 351–367 is available online at: https://academic.oup.com/biomet/article/109/2/351/6309456