Bayesian inference of mixed-effects ordinary differential equations models using heavy-tailed distributions

Baisen Liu, Liangliang Wang, Yunlong Nie and Jiguo Cao

Computational Statistics & Data Analysis, 2019, vol. 137, issue C, 233-246

Abstract: A mixed-effects ordinary differential equation (ODE) model is proposed to describe complex dynamical systems. In order to make the inference of ODE parameters robust against the outlying observations and subjects, a class of heavy-tailed distributions is applied to model the random effects of ODE parameters and measurement errors in the data. The heavy-tailed distributions are so flexible that they include the conventional normal distribution as a special case. An MCMC method is proposed to make inferences on ODE parameters within a Bayesian hierarchical framework. The proposed method is demonstrated by estimating a pharmacokinetic mixed-effects ODE model. The finite sample performance of the proposed method is evaluated using some simulation studies.

Keywords: Metropolis–Hastings; Outliers; Pharmacokinetics; Scale mixtures of multivariate normal distributions; Smoothing spline (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:137:y:2019:i:c:p:233-246

DOI: 10.1016/j.csda.2019.03.001

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