Rights statement: c 2017 International Society for Bayesian Analysis
Accepted author manuscript, 1.2 MB, PDF document
Accepted author manuscript
Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Bayesian inference for diffusion-driven, mixed-effects models
AU - Whitaker, Gavin A.
AU - Golightly, Andrew
AU - Boys, Richard J
AU - Sherlock, Christopher Gerrard
N1 - c 2017 International Society for Bayesian Analysis
PY - 2016/9/30
Y1 - 2016/9/30
N2 - 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.
AB - 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.
KW - Stochastic differential equation
KW - mixed-effects
KW - Markov chain Monte Carlo
KW - modified innovation scheme
KW - linear noise approximation
U2 - 10.1214/16-BA1009
DO - 10.1214/16-BA1009
M3 - Journal article
VL - 12
SP - 435
EP - 463
JO - Bayesian Analysis
JF - Bayesian Analysis
SN - 1936-0975
IS - 2
ER -