Bayesian inference for diffusion-driven, mixed-effects models

Whitaker, Gavin A. and Golightly, Andrew and Boys, Richard J and Sherlock, Christopher Gerrard (2016) Bayesian inference for diffusion-driven, mixed-effects models. Bayesian Analysis, 12 (2). pp. 435-463. ISSN 1936-0975

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Stochastic differential equations (SDEs) provide a natural framework for modelling intrinsic stochasticity inherent in many continuous-time physical processes. When such processes are observed in multiple individuals or experimental units, SDE driven mixed-effects models allow the quantification of between (as well as within) individual variation. Performing Bayesian inference for such models, using discrete time data that may be incomplete and subject to measurement error is a challenging problem and is the focus of this paper. We extend a recently proposed MCMC scheme to include the SDE driven mixed-effects framework. Fundamental to our approach is the development of a novel construct that allows for efficient sampling of conditioned SDEs that may exhibit nonlinear dynamics between observation times. We apply the resulting scheme to synthetic data generated from a simple SDE model of orange tree growth, and real data consisting of observations on aphid numbers recorded under a variety of different treatment regimes. In addition, we provide a systematic comparison of our approach with an inference scheme based on a tractable approximation of the SDE, that is, the linear noise approximation.

Item Type:
Journal Article
Journal or Publication Title:
Bayesian Analysis
Additional Information:
c 2017 International Society for Bayesian Analysis
Uncontrolled Keywords:
?? stochastic differential equationmixed-effectsmarkov chain monte carlomodified innovation schemelinear noise approximationstatistics and probabilityapplied mathematics ??
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Deposited On:
13 Jun 2016 08:48
Last Modified:
15 Jul 2024 16:08