Statistical Analysis on Models Defined by Differential Equations

• Activity Number: 372
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Hongyuan Wang* and David Allen
• Companies: and University of Kentucky
• Keywords: differential equations ; differential evolution ; derivative free optimization ; compartment models

Abstract

Differential equations, which describe mathematical relations between some unknown function and its derivatives, are widely used in physics, chemistry and biomedical sciences, etc. The statistical analysis of data having an underlying model defined by non-linear differential equations requires methodology from numerical analysis, numerical solution of differential equations and derivative-free optimization. In this talk we would like to present an outline for statistical inference of models based on differential equations without analytically solving them. Our methods would involve numerical integration algorithms like Runge-Kutta methods, along with optimization algorithms like Gauss-Newton, differential evolutions, etc. Examples like Compartment models, logistic models will be presented to illustrate the proposed methods. The methodology will be evaluated by both simulation study and real data analysis. The efficiency of different derivative free optimization algorithms will also be studied and compared.