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 is reasonable. However when the model itself is more complex (for instance when it is a set of partial differential equations (PDE)) it may be infeasible within a reasonable time.
In this talk, we present two variations on the stochastic approximation expectation maximisation (SAEM) method in conjunction with PDEs to estimate the parameters of a population of individuals. One is based on the building of an off line 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 Fisher-KPP equation and on a renewal (age-structured) equation.
PIMS (CNRS UMI 3069), University of British Columbia, Vancouver, Canada &
UMPA (CNRS UMR 5669), ENS de Lyon, France