The controlled thermodynamic integral for Bayesian model evidence evaluation

Oates, C. J., Papamarkou, T. and Girolami, M. (2016) The controlled thermodynamic integral for Bayesian model evidence evaluation. Journal of the American Statistical Association, 111(514), pp. 634-645. (doi: 10.1080/01621459.2015.1021006)

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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.

Item Type:Articles
Additional Information:Supported by UK EPSRC EP/D002060/1, EP/J016934/1,EU Grant 259348 (Analyzing and Striking the Sensitivities of EmbryonalTumors), and a Royal Society Wolfson Research Merit Award.
Glasgow Author(s) Enlighten ID:Girolami, Prof Mark and Papamarkou, Dr Theodore
Authors: Oates, C. J., Papamarkou, T., and Girolami, M.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Statistics
Journal Name:Journal of the American Statistical Association
Publisher:Taylor and Francis
ISSN (Online):1537-274X
Published Online:18 August 2016

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