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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Licence: CC BY: Creative Commons Attribution 4.0 International License
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - Semi-Exact Control Functionals From Sard's Method
AU - South, Leah
AU - Karvonen, Toni
AU - Nemeth, Christopher
AU - Girolami, Mark
AU - Oates, Chris J.
N1 - 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
PY - 2022/6/30
Y1 - 2022/6/30
N2 - 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.
AB - 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.
U2 - 10.1093/biomet/asab036
DO - 10.1093/biomet/asab036
M3 - Journal article
VL - 109
SP - 351
EP - 367
JO - Biometrika
JF - Biometrika
SN - 0006-3444
IS - 2
ER -