Workshop on Statistical Methods for Dynamic
Vancouver, June 4-6 2009
System Models
The standard least squares (LS) estimation approach is widely used to estimate the unknown parameters in a nonlinear ODE model. It requires repeatedly evaluation of the ODEs in order to obtain the LS estimate using numerical methods. However, rigorous statistical theories and asymptotic properties need to be established with consideration of both numerical errors and measurement errors of data. We derive the estimates for both constant and time-varying parameters in the nonlinear ODE models and establish the asymptotic properties for the proposed estimators. In addition, if the parameter space is high-dimensional, the LS approach may require high computational cost and the LS estimates may not be reliable due to the convergence problem of the computational algorithm. In this case, we have developed numerical algorithm-based regression approaches to estimate the unknown parameters. We demonstrate that the numerical algorithm-based regression approaches are computationally efficient and stable although some price, a lower estimation efficiency, has to be paid. The trade-off between the computational efficiency/stability and estimation efficiency for different methods is studied via Monte Carlo simulations. Application examples in modeling infectious diseases such as HIV and influenza will be used to illustrate the usefulness of the proposed methodology. A user-friendly software, DEDiscover developed by our group, for differential equation model simulations and parameter estimation will be introduced.
Statistical Methods and Theories for Nonlinear Differential Equation Models with Applications to Infectious Disease Modeling
Professor of Biostatistics and Computational Biology,
Director, Center for Biodefense Immune Modeling
Department of Biostatistics and
Computational Biology
University of Rochester
School of Medicine and Dentistry
Rochester, New York
