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Fast approximate Bayesian computation for estimating parameters in differential equations

Fast approximate Bayesian computation for estimating parameters in differential equations
Fast approximate Bayesian computation for estimating parameters in differential equations
Approximate Bayesian computation (ABC) using a sequential Monte Carlo method provides a comprehensive platform for parameter estimation, model selection and sensitivity analysis in differential equations. However, this method, like other Monte Carlo methods, incurs a significant computational cost as it requires explicit numerical integration of differential equations to carry out inference. In this paper we propose a novel method for circumventing the requirement of explicit integration by using derivatives of Gaussian processes to smooth the observations from which parameters are estimated. We evaluate our methods using synthetic data generated from model biological systems described by ordinary and delay differential equations. Upon comparing the performance of our method to existing ABC techniques, we demonstrate that it produces comparably reliable parameter estimates at a significantly reduced execution time.
0960-3174
1-20
Ghosh, Sanmitra
012cd6b2-63ac-4821-afe3-9b208ba6fd82
Maharatna, Koushik
93bef0a2-e011-4622-8c56-5447da4cd5dd
Dasmahapatra, Srinandan
eb5fd76f-4335-4ae9-a88a-20b9e2b3f698
Ghosh, Sanmitra
012cd6b2-63ac-4821-afe3-9b208ba6fd82
Maharatna, Koushik
93bef0a2-e011-4622-8c56-5447da4cd5dd
Dasmahapatra, Srinandan
eb5fd76f-4335-4ae9-a88a-20b9e2b3f698

Ghosh, Sanmitra, Maharatna, Koushik and Dasmahapatra, Srinandan (2016) Fast approximate Bayesian computation for estimating parameters in differential equations. Statistics and Computing, 1-20. (doi:10.1007/s11222-016-9643-4).

Record type: Article

Abstract

Approximate Bayesian computation (ABC) using a sequential Monte Carlo method provides a comprehensive platform for parameter estimation, model selection and sensitivity analysis in differential equations. However, this method, like other Monte Carlo methods, incurs a significant computational cost as it requires explicit numerical integration of differential equations to carry out inference. In this paper we propose a novel method for circumventing the requirement of explicit integration by using derivatives of Gaussian processes to smooth the observations from which parameters are estimated. We evaluate our methods using synthetic data generated from model biological systems described by ordinary and delay differential equations. Upon comparing the performance of our method to existing ABC techniques, we demonstrate that it produces comparably reliable parameter estimates at a significantly reduced execution time.

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Accepted/In Press date: 22 February 2016
e-pub ahead of print date: 26 March 2016
Organisations: Electronics & Computer Science

Identifiers

Local EPrints ID: 393166
URI: https://eprints.soton.ac.uk/id/eprint/393166
ISSN: 0960-3174
PURE UUID: cd9bb67f-58ff-478f-9bb3-fbb762e39d5f

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Date deposited: 22 Apr 2016 08:50
Last modified: 09 Sep 2019 18:25

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Author: Sanmitra Ghosh

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