Liu Baisen, Wang Liangliang, Nie Yunlong, Cao Jiguo
School of Statistics, Dongbei University of Finance and Economics, Dalian, China.
Department of Statistics and Actuarial Science, Simon Fraser University, Burnaby, Canada.
J Agric Biol Environ Stat. 2021;26(3):428-445. doi: 10.1007/s13253-021-00446-2. Epub 2021 Apr 5.
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 materials for this article are available at10.1007/s13253-021-00446-2.
常微分方程（ODE）模型广泛用于描述复杂动力系统。从含噪声的数据中估计ODE参数时，常见的分布假设是使用高斯分布。众所周知，当存在异常数据时，高斯分布并不稳健。在本文中，我们在贝叶斯框架下为纵向数据开发了一种分层半参数混合效应ODE模型。为了对ODE参数进行稳健推断，我们考虑一类重尾分布来对ODE参数的随机效应和观测误差进行建模。提出了一种MCMC方法从后验分布中抽样ODE参数。通过研究一个基因调控实验来说明我们提出的方法。模拟研究表明，我们提出的方法对于有限样本的半参数混合效应ODE模型提供了令人满意的结果。本文的补充材料在线提供。
本文的补充材料可在10.1007/s13253-021-00446-2获取。
