Generalized Ordinary Differential Equation Models

• 成果类型: Article
• 署名作者: Miao, Hongyu; Wu, Hulin; Xue, Hongqi
• 署名单位: University of Rochester
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2014.957287
• 发表日期: 2014
• 页码: 1672-1682
• 关键词: maximum-likelihood-estimation; time-varying coefficients; adaptive immune-response; parameter-estimation; least-squares; Identifiability; hiv-1; optimization; series; prediction

摘要

Existing estimation methods for ordinary differential equation (ODE) models are not applicable to discrete data. The generalized ODE (GODE) model is therefore proposed and investigated for the first time. We develop the likelihood-based parameter estimation and inference methods for GODE models. We propose robust computing algorithms and rigorously investigate the asymptotic properties of the proposed estimator by considering both measurement errors and numerical errors in solving ODEs. The simulation study and application of our methods to an influenza viral dynamics study suggest that the proposed methods have a superior performance in terms of accuracy over the existing ODE model estimation approach and the extended smoothing-based (ESB) method. Supplementary materials for this article are available online.