Targeting Bayes factors with direct-path non-equilibrium thermodynamic integration

Grzegorczyk, M., Aderhold, A. and Husmeier, D. (2017) Targeting Bayes factors with direct-path non-equilibrium thermodynamic integration. Computational Statistics, 32(2), pp. 717-761. (doi:10.1007/s00180-017-0721-7)

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Abstract

Thermodynamic integration (TI) for computing marginal likelihoods is based on an inverse annealing path from the prior to the posterior distribution. In many cases, the resulting estimator suffers from high variability, which particularly stems from the prior regime. When comparing complex models with differences in a comparatively small number of parameters, intrinsic errors from sampling fluctuations may outweigh the differences in the log marginal likelihood estimates. In the present article, we propose a thermodynamic integration scheme that directly targets the log Bayes factor. The method is based on a modified annealing path between the posterior distributions of the two models compared, which systematically avoids the high variance prior regime. We combine this scheme with the concept of non-equilibrium TI to minimise discretisation errors from numerical integration. Results obtained on Bayesian regression models applied to standard benchmark data, and a complex hierarchical model applied to biopathway inference, demonstrate a significant reduction in estimator variance over state-of-the-art TI methods.

Item Type:Articles (Other)
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Aderhold, Mr Andrej and Husmeier, Professor Dirk
Authors: Grzegorczyk, M., Aderhold, A., and Husmeier, D.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Statistics
Journal Name:Computational Statistics
Publisher:Springer
ISSN:0943-4062
ISSN (Online):1613-9658
Published Online:14 March 2017
Copyright Holders:Copyright © 2017 The Authors
First Published:First published in Computational Statistics 32(2): 717-761
Publisher Policy:Reproduced under a creative commons license

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
633291Computational inference in systems biologyDirk HusmeierEngineering & Physical Sciences Research Council (EPSRC)EP/L020319/1M&S - STATISTICS