Statistical Models Commons^™

Statistical Inference On Dynamical Systems, Hongyuan Wang

Theses and Dissertations--Statistics

The ordinary differential equation (ODE) is one representative and popular tool in modeling dynamical systems, which are widely implemented in physics, biology, economics, chemistry and biomedical sciences, etc. Because of the importance of dynamical systems in scientific studies, they are the main focuses of my dissertation.

The first chapter of the dissertation is introduction and literature review, which mainly focuses on numerical integration algorithms of ODEs that are difficult to solve analytically, as well as derivative-free optimization algorithms for the so-called inverse problem.

The second chapter is on the estimation method based on numerical solvers of differential equations. We start …