Semiparametric Mixed-Effects Ordinary Differential Equation Models with Heavy-Tailed Distributions

Baisen Liu, Liangliang Wang, Yunlong Nie and Jiguo Cao ()
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Baisen Liu: Dongbei University of Finance and Economics
Liangliang Wang: Simon Fraser University
Yunlong Nie: Google Inc.
Jiguo Cao: Simon Fraser University

Journal of Agricultural, Biological and Environmental Statistics, 2021, vol. 26, issue 3, No 6, 428-445

Abstract: Abstract Ordinary differential equation (ODE) models are popularly used to describe complex dynamical systems. When estimating ODE parameters from noisy data, a common distribution assumption is using the Gaussian distribution. It is known that the Gaussian distribution is not robust when abnormal data exist. In this article, we develop a hierarchical semiparametric mixed-effects ODE model for longitudinal data under the Bayesian framework. For robust inference on ODE parameters, we consider a class of heavy-tailed distributions to model the random effects of ODE parameters and observations errors. An MCMC method is proposed to sample ODE parameters from the posterior distributions. Our proposed method is illustrated by studying a gene regulation experiment. Simulation studies show that our proposed method provides satisfactory results for the semiparametric mixed-effects ODE models with finite samples. Supplementary materials accompanying this paper appear online.

Keywords: Metropolis–Hastings; Abnormal data; Scale mixture of multivariate normal distributions (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13253-021-00446-2

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