Model selection via marginal likelihood estimation by combining thermodynamic integration and gradient matching

Macdonald, B. and Husmeier, D. (2019) Model selection via marginal likelihood estimation by combining thermodynamic integration and gradient matching. Statistics and Computing, 29(5), pp. 853-867. (doi: 10.1007/s11222-018-9840-4)

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Conducting statistical inference on systems described by ordinary differential equations (ODEs) is a challenging problem. Repeatedly numerically solving the system of equations incurs a high computational cost, making many methods based on explicitly solving the ODEs unsuitable in practice. Gradient matching methods were introduced in order to deal with the computational burden. These methods involve minimising the discrepancy between predicted gradients from the ODEs and those from a smooth interpolant. Work until now on gradient matching methods has focused on parameter inference. This paper considers the problem of model selection. We combine the method of thermodynamic integration to compute the log marginal likelihood with adaptive gradient matching using Gaussian processes, demonstrating that the method is robust and able to outperform BIC and WAIC.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Husmeier, Professor Dirk and Macdonald, Dr Benn
Authors: Macdonald, B., and Husmeier, D.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Statistics
Journal Name:Statistics and Computing
ISSN (Online):1573-1375
Published Online:14 December 2018
Copyright Holders:Copyright © 2018 The Authors
First Published:First published in Statistics and Computing 29(5): 853-867
Publisher Policy:Reproduced under a Creative Commons License

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
694461EPSRC Centre for Multiscale soft tissue mechanics with application to heart & cancerRaymond OgdenEngineering and Physical Sciences Research Council (EPSRC)EP/N014642/1M&S - MATHEMATICS