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Bayesian inference of mixed-effects ordinary differential equations models using heavy-tailed distributions
- Liu, Baisen, Wang, Liangliang, Nie, Yunlong, Cao, Jiguo
- Computational statistics & data analysis 2019 v.137 pp. 233-246
- Bayesian theory, differential equation, models, normal distribution, pharmacokinetics
- 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.