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The Controlled Thermodynamic Integral for Bayesian Model Evidence Evaluation

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  • Chris J. Oates
  • Theodore Papamarkou
  • Mark Girolami

Abstract

Approximation of the model evidence is well known to be challenging. One promising approach is based on thermodynamic integration, but a key concern is that the thermodynamic integral can suffer from high variability in many applications. This article considers the reduction of variance that can be achieved by exploiting control variates in this setting. Our methodology applies whenever the gradient of both the log-likelihood and the log-prior with respect to the parameters can be efficiently evaluated. Results obtained on regression models and popular benchmark datasets demonstrate a significant and sometimes dramatic reduction in estimator variance and provide insight into the wider applicability of control variates to evidence estimation. Supplementary materials for this article are available online.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:jnlasa:v:111:y:2016:i:514:p:634-645
    DOI: 10.1080/01621459.2015.1021006
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    Citations

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    Cited by:

    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. Marco Grzegorczyk & Andrej Aderhold & Dirk Husmeier, 2017. "Targeting Bayes factors with direct-path non-equilibrium thermodynamic integration," Computational Statistics, Springer, vol. 32(2), pages 717-761, June.
    3. 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.
    4. Mathias Drton & Martyn Plummer, 2017. "A Bayesian information criterion for singular models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 323-380, March.
    5. Jeremy Heng & Arnaud Doucet & Yvo Pokern, 2021. "Gibbs flow for approximate transport with applications to Bayesian computation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(1), pages 156-187, February.

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