SAEM methods for statistical PDE parameters estimation and application to biology

International audienceParameter 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 more 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. In this talk, we present two variations on the SAEM method in conjunction with PDEs : one is based on the building of an offline grid used to approximate the model (so called metamodel) and the other involves a dynamic refinement (using a kriging approach) of the metamodel along the iterations of the SAEM. These methods are illustrated on the classical KPP equation and on a renewal equation (in collaboration with Pierre Gabriel), making links with the lectures of Marie Doumic and P. Gabriel in this same CIMPA school