Multiphase MCMC sampling for parameter inference in nonlinear ordinary differential equations

Lazarus, A., Husmeier, D. and Papamarkou, T. (2018) Multiphase MCMC sampling for parameter inference in nonlinear ordinary differential equations. Proceedings of Machine Learning Research, 84, pp. 1252-1260.

Abstract

Traditionally, ODE parameter inference relies on solving the system of ODEs and assessing fit of the estimated signal with the observations. However, nonlinear ODEs often do not permit closed form solutions. Using numerical methods to solve the equations results in prohibitive computational costs, particularly when one adopts a Bayesian approach in sampling parameters from a posterior distribution. With the introduction of gradient matching, we can abandon the need to numerically solve the system of equations. Inherent in these efficient procedures is an introduction of bias to the learning problem as we no longer sample based on the exact likelihood function. This paper presents a multiphase MCMC approach that attempts to close the gap between efficiency and accuracy. By sampling using a surrogate likelihood, we accelerate convergence to the stationary distribution before sampling using the exact likelihood. We demonstrate that this method combines the efficiency of gradient matching and the accuracy of the exact likelihood scheme.

• Item Type: Articles
• Additional Information: Conference paper presented at International Conference on Artificial Intelligence and Statistics, 9-11 April 2018, Playa Blanca, Lanzarote, Canary Islands.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Husmeier, Professor Dirk and Papamarkou, Dr Theodore and Lazarus, Dr Alan
• Authors: Lazarus, A., Husmeier, D., and Papamarkou, T.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Statistics
• Journal Name: Proceedings of Machine Learning Research
• Publisher: PMLR
• ISSN: 1938-7228
• Copyright Holders: Copyright © 2018 The Authors
• First Published: First published in Proceedings of Machine Learning Research 84: 1252-1260
• Publisher Policy: Reproduced under a Creative Commons License

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• Organisation

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
63329	1	Computational inference in systems biology	Dirk Husmeier	Engineering and Physical Sciences Research Council (EPSRC)	EP/L020319/1	M&S - STATISTICS
69446	1	EPSRC Centre for Multiscale soft tissue mechanics with application to heart & cancer	Raymond Ogden	Engineering and Physical Sciences Research Council (EPSRC)	EP/N014642/1	M&S - MATHEMATICS