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 |
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Status: | Published |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | Husmeier, Professor Dirk and Aderhold, Mr Andrej |
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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