{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,24]],"date-time":"2026-09-24T11:50:37Z","timestamp":1790250637843,"version":"4.1.0"},"reference-count":61,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2021,6,25]],"date-time":"2021-06-25T00:00:00Z","timestamp":1624579200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,5,25]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>A novel control variate technique is proposed for the post-processing of Markov chain Monte Carlo output, based on both Stein\u2019s 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\u2013von 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.<\/jats:p>","DOI":"10.1093\/biomet\/asab036","type":"journal-article","created":{"date-parts":[[2021,6,23]],"date-time":"2021-06-23T11:53:46Z","timestamp":1624449226000},"page":"351-367","source":"Crossref","is-referenced-by-count":10,"title":["Semi-exact control functionals from Sard\u2019s method"],"prefix":"10.1093","volume":"109","author":[{"given":"L F","family":"South","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Queensland University of Technology, 2 George Street, Brisbane, Queensland 4000, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"T","family":"Karvonen","sequence":"additional","affiliation":[{"name":"The Alan Turing Institute, British Library, 96 Euston Road, London NW1 2DB, U.K"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"C","family":"Nemeth","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Lancaster University, Bailrigg, Lancaster LA1 4YF, U.K"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M","family":"Girolami","sequence":"additional","affiliation":[{"name":"Department of Engineering, University of Cambridge, St Andrew\u2019s Street, Cambridge CB2 1PZ, U.K"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"C J","family":"Oates","sequence":"additional","affiliation":[{"name":"School of Mathematics, Statistics & Physics, Newcastle University, Newcastle upon Tyne NE1 7RU, U.K"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2021,9,22]]},"reference":[{"key":"2022052609543303100_B1","doi-asserted-by":"crossref","first-page":"4682","DOI":"10.1103\/PhysRevLett.83.4682","article-title":"Zero-variance principle for Monte Carlo algorithms","volume":"83","author":"Assaraf","year":"1999","journal-title":"Phys. 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