Bayesian inference for diffusion driven mixed-effects models

TL;DR

This paper develops a Bayesian inference method for diffusion-driven mixed-effects models using SDEs, enabling analysis of complex stochastic processes with individual variation, demonstrated on biological data.

Contribution

It introduces a novel MCMC scheme for efficient sampling of conditioned nonlinear SDEs within mixed-effects models, extending existing methods.

Findings

Effective inference on synthetic SDE data of orange tree growth.

Successful application to real aphid count data under different treatments.

Comparison shows advantages over linear noise approximation.

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.