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

Published online by Cambridge University Press:  28 July 2014

E. Grenier ,
V. Louvet  and
P. Vigneaux
E. Grenier
Affiliation:
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. [email protected]
V. Louvet
Affiliation:
Institut Camille Jordan, CNRS UMR 5208 & Université Lyon 1 & INRIA, Project-team NUMED. 43 Boulevard du 11 novembre 1918, 69622 Villeurbanne Cedex, France
P. Vigneaux
Affiliation:
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. [email protected]
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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.

Keywords

Parameter estimationSAEM algorithmpartial differential equationsKPP equation
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 48 , Issue 5 , September 2014 , pp. 1303 - 1329
Copyright
© EDP Sciences, SMAI, 2014

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