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  • 1507.06807v2

    Rights statement: c 2017 International Society for Bayesian Analysis

    Accepted author manuscript, 1.2 MB, PDF document

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Bayesian inference for diffusion-driven, mixed-effects models

Research output: Contribution to journalJournal articlepeer-review

E-pub ahead of print
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<mark>Journal publication date</mark>30/09/2016
<mark>Journal</mark>Bayesian Analysis
Issue number2
Volume12
Number of pages29
Pages (from-to)435-463
Publication StatusE-pub ahead of print
Early online date30/09/16
<mark>Original language</mark>English

Abstract

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.

Bibliographic note

c 2017 International Society for Bayesian Analysis