B0773
Title: Parametric estimation of complex mixed models based on meta-model approach
Authors: Pierre Barbillon - AgroParisTech (France) [presenting]
Celia Barthelemy - INRIA (France)
Adeline Leclercq-Samson - LJK universite Joseph Fourier (France)
Abstract: Complex biological processes are more and more experimented along time among a collection of individuals. Longitudinal data are then available and the statistical challenge is to analyse these data to better understand the underlying biological mechanisms. The parametric statistical approach commonly used with longitudinal data is mixed-effects model methodology. In these models, the regression functions are now highly-developed to describe precisely biological processes. They may be solutions of multi-dimensional differential equations. When there is no analytical solution, a classical approach for estimating the parameters relies on the coupling of a stochastic version of the EM algorithm (SAEM) with a MCMC algorithm. This procedure needs many evaluations of the regression function which is clearly prohibitive when a time-consuming solver is used for computing it. That is why we propose to replace this regression function with a meta-model based on a Gaussian process. The new source of uncertainty due to this approximation can be incorporated in the model which leads to what we call a mixed meta-model. We guarantee a control on the distance between the maximum likelihood estimates in this mixed meta-model and the maximum likelihood estimates obtained with the exact mixed model.
