Estimation of ordinary differential equations with orthogonal conditions
Nicolas Brunel (February 20, 2012)
Please install the Flash Plugin
Parameter inference of ordinary differential equations from noisy data can be seen as a nonlinear regression problem, within a parametric setting. The use of a classical statistical method such as Nonlinear Least Squares (NLS) gives rise to difficult and heavy optimization problems due to the corresponding badly posed inverse problem. Gradient Matching algorithms use a smooth (nonparametric) estimation of the solution from which is derived a nonparametric estimate of the derivative, and gives rise to a natural criterion easier than NLS to optimize. We introduce here a new class of criteria based on a weak formulation of the ODE. The estimator derived can be viewed as a generalized moment estimators which possesses nice statistical and computational properties. Finally, we consider several examples which illustrate the efficiency and the versatility of the proposed method.