Nonparametric Collocation ODE Parameter Estimation: Application in Biochemical Pathway Modelling

Parameter estimation of non-linear differential equations has long been an active and challenge research area. Conventionally methods are computationally intensive and often poorly conditioned. In the context of biochemical pathway modeling, a new method focused on this paper is the so-called “collocation” method, which is a nonparametric data smoothing based approach. The statistical property of a sort of linear smoothing spline based collocation methods is explicitly analyzed. It is concluded that this approach is computational efficient, but leads a non-zero estimation bias and it changes the independence assumption in the additive noise.