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Accelerating Bayesian inference over nonlinear differential equations with Gaussian processes

Calderhead, B; Girolami, M; Lawrence, ND; (2009) Accelerating Bayesian inference over nonlinear differential equations with Gaussian processes. In: Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference. (pp. 217 - 224).

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Abstract

Identification and comparison of nonlinear dynamical system models using noisy and sparse experimental data is a vital task in many fields, however current methods are computationally expensive and prone to error due in part to the nonlinear nature of the likelihood surfaces induced. We present an accelerated sampling procedure which enables Bayesian inference of parameters in nonlinear ordinary and delay differential equations via the novel use of Gaussian processes (GP). Our method involves GP regression over time-series data, and the resulting derivative and time delay estimates make parameter inference possible without solving the dynamical system explicitly, resulting in dramatic savings of computational time. We demonstrate the speed and statistical accuracy of our approach using examples of both ordinary and delay differential equations, and provide a comprehensive comparison with current state of the art methods.

Type:Proceedings paper
Title:Accelerating Bayesian inference over nonlinear differential equations with Gaussian processes
UCL classification:UCL > School of BEAMS > Faculty of Maths and Physical Sciences > CoMPLEX - Maths and Physics in the Life Sciences and Experimental Biology

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