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

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  • Liu, Baisen
  • Wang, Liangliang
  • Nie, Yunlong
  • Cao, Jiguo

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.

Suggested Citation

  • Liu, Baisen & Wang, Liangliang & Nie, Yunlong & Cao, Jiguo, 2019. "Bayesian inference of mixed-effects ordinary differential equations models using heavy-tailed distributions," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 233-246.
    • Handle: RePEc:eee:csdana:v:137:y:2019:i:c:p:233-246
    DOI: 10.1016/j.csda.2019.03.001
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