Parameter estimation in non-linear mixed effects models with SAEM algorithm: extension from ODE to PDE

¹ U.M.P.A., Ecole Normale Supérieure de Lyon, CNRS UMR 5669 & INRIA, Project-team NUMED. 46 Allée d’Italie, 69364 Lyon Cedex 07, France
emmanuel.grenier@ens-lyon.fr
² Institut Camille Jordan, CNRS UMR 5208 & Université Lyon 1 & INRIA, Project-team NUMED. 43 Boulevard du 11 novembre 1918, 69622 Villeurbanne Cedex, France

Received: 11 February 2013
Revised: 13 October 2013

Abstract

Parameter estimation in non linear mixed effects models requires a large number of evaluations of the model to study. For ordinary differential equations, the overall computation time remains reasonable. However when the model itself is complex (for instance when it is a set of partial differential equations) it may be time consuming to evaluate it for a single set of parameters. The procedures of population parametrization (for instance using SAEM algorithms) are then very long and in some cases impossible to do within a reasonable time. We propose here a very simple methodology which may accelerate population parametrization of complex models, including partial differential equations models. We illustrate our method on the classical KPP equation.