Semiparametric Mixed-Effects Ordinary Differential Equation Models with Heavy-Tailed Distributions
| Autor: | Jiguo Cao, Baisen Liu, Yunlong Nie, Liangliang Wang |
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| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
Dynamical systems theory Applied Mathematics Gaussian Ode Markov chain Monte Carlo Random effects model Agricultural and Biological Sciences (miscellaneous) Abnormal data Article Scale mixture of multivariate normal distributions symbols.namesake Distribution (mathematics) Metropolis–Hastings algorithm Ordinary differential equation symbols Applied mathematics Statistics Probability and Uncertainty General Agricultural and Biological Sciences Metropolis–Hastings General Environmental Science Mathematics |
| Zdroj: | Journal of Agricultural, Biological, and Environmental Statistics |
| ISSN: | 1085-7117 |
| Popis: | 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. Supplementary Information Supplementary materials for this article are available at10.1007/s13253-021-00446-2. |
| Databáze: | OpenAIRE |
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