统计与管理学院2015年学术报告第28期

【主  题】 Numerical Error and Measurement Error in Statistical Analysis for Ordinary Differential Equation Models

【报告人】 Hongqi Xue 博士

Department of Biostatistics and Computational Biology，University of Rochester

【时  间】 2015年6月26日（星期五）16:00－17:00

【地  点】 上海财经大学统计与管理学院大楼1208室

【语  言】 英文

【摘  要】 We consider parameter estimation of nonlinear ordinary differential equation (ODE) models where analytic closed-form solutions are not available. The numerical solution-based nonlinear least squares (NLS) estimator is proposed. A numerical algorithm such as the Runge-Kutta algorithm is used to approximate the ODE solution. The asymptotic properties are established for the proposed estimators with consideration of both numerical error and measurement error. Our results show that if the maximum step size of the numerical algorithm goes to zero faster than a special rate, which depends on the order of the ODEs, then the numerical error is negligible compared to the measurement error. This provides a theoretical guidance in selection of the step size for numerical evaluations of ODEs. We illustrate our approach with both simulation studies and clinical data on HIV viral dynamics. Finally, we extend the above model and method to their generalized ODE versions for fitting discrete data.