Algorithms for parameter estimation of differential equations based on nonparametric estimators
Nicolas J-B. Brunel and Florence d'Alché-Buc
In: SFDS, 30/05 - 31/06, Montreal.

Abstract

Differential equations used in biology (and in particular in systems biology) are usually nonlinear and high-dimensional (ten or more state-variables and numerous unknown parameters to estimate), which gives rise to difficult optimization problems when using classical statistical estimators. We propose to use nonparametric estimators in order to derive simple and fast estimation algorithms for the parameters. We show that this approach is theoretically justified when using consistent nonparametric estimators, but the estimators obtained suffers from slow rates of convergence. Finally, we give some directions of ameliorations for the algorithms.

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