Semi-exact control functionals from Sard’s method-Reference-Cited by-同舟云学术

Semi-exact control functionals from Sard’s method

Published:2021-09-22 Issue: Volume: Page:
ISSN:0006-3444
Container-title:Biometrika
language:en
Short-container-title:

Author:

South L F¹,Karvonen T²,Nemeth C³,Girolami M⁴,Oates C J⁵

Affiliation:

1. School of Mathematical Sciences, Queensland University of Technology, 2 George Street, Brisbane, Queensland 4000, Australia

2. The Alan Turing Institute, British Library, 96 Euston Road, London NW1 2DB, U.K

3. Department of Mathematics and Statistics, Lancaster University, Bailrigg, Lancaster LA1 4YF, U.K

4. Department of Engineering, University of Cambridge, St Andrew’s Street, Cambridge CB2 1PZ, U.K

5. School of Mathematics, Statistics & Physics, Newcastle University, Newcastle upon Tyne NE1 7RU, U.K

Abstract

Summary 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.

Publisher

Oxford University Press (OUP)

Subject

Applied Mathematics,Statistics, Probability and Uncertainty,General Agricultural and Biological Sciences,Agricultural and Biological Sciences (miscellaneous),General Mathematics,Statistics and Probability

Link

http://academic.oup.com/biomet/advance-article-pdf/doi/10.1093/biomet/asab036/40469505/asab036.pdf

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