Model selection in a stochastic setting.

Abstract

The given data is a set of observations on functionals of a trajectory of a system of differential equations. The a priori information is that the system is a member of a parametric family of systems of increasing complexity. The problem is to use the data to identify the particular member of this family which generated the observed data. The method associates each candidate model with the analogue of a generalised smoothing spline fitted to the given data. The resulting values of the smoothing parameter as well as graphical inspection of fit provide a basis for model selection.