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2008

Accelerating Bayesian Inference over Nonlinear Differential Equations with Gaussian Processes

10 years 2 months ago
Accelerating Bayesian Inference over Nonlinear Differential Equations with Gaussian Processes
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.
Ben Calderhead, Mark Girolami, Neil D. Lawrence
Added 30 Oct 2010
Updated 30 Oct 2010
Type Conference
Year 2008
Where NIPS
Authors Ben Calderhead, Mark Girolami, Neil D. Lawrence
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