Refreshments: 3.30pm, MSB 4110 (Statistics Lounge)

Speaker:            Jiguo Cao (Simon Fraser University)

Title:                Statistical Inference for Differential Equations

Abstract:        Dynamic models, usually written in forms of differential equations (DEs), describe the rate of change of a process. They are widely used in medicine, engineering, ecology and a host of other applications. One central and difficult problem is how to estimate DE parameters from noisy data. Ramsay et al. (2007) proposed the parameter cascading method to solve this problem. DE solutions are approximated by nonparametric functions, which are estimated by penalized smoothing with DE-defined penalty. A modified delta method is proposed to estimate standard errors of DE parameter estimates. We have extended the generalized profiling method to estimate time-varying parameters. A roughness penalty term is included to control the smoothness of the time-varying parameters. Simulations show that this method provides better estimates than the two-stage estimation strategy. This method is demonstrated by estimating a HIV dynamic model from clinic data.