Semi-Exact Control Functionals From Sard's Method

South, Leah and Karvonen, Toni and Nemeth, Christopher and Girolami, Mark and Oates, Chris J. (2022) Semi-Exact Control Functionals From Sard's Method. Biometrika, 109 (2). pp. 351-367. ISSN 0006-3444

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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.

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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 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:
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03 Jun 2021 11:10
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22 Nov 2022 10:19