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Semi-exact control functionals from Sard’s method
[Zero-variance principle for Monte Carlo algorithms]

Author

Listed:
  • L F South
  • T Karvonen
  • C Nemeth
  • M Girolami
  • C J Oates

Abstract

SummaryA 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.

Suggested Citation

  • L F South & T Karvonen & C Nemeth & M Girolami & C J Oates, 2022. "Semi-exact control functionals from Sard’s method [Zero-variance principle for Monte Carlo algorithms]," Biometrika, Biometrika Trust, vol. 109(2), pages 351-367.
    • Handle: RePEc:oup:biomet:v:109:y:2022:i:2:p:351-367.
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    File URL: http://hdl.handle.net/10.1093/biomet/asab036
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    References listed on IDEAS

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    1. Chris J. Oates & Mark Girolami & Nicolas Chopin, 2017. "Control functionals for Monte Carlo integration," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(3), pages 695-718, June.
    2. Chris J. Oates & Theodore Papamarkou & Mark Girolami, 2016. "The Controlled Thermodynamic Integral for Bayesian Model Evidence Evaluation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 634-645, April.
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