Population parametrization of costly black box models using iterations between SAEM algorithm and kriging

Emmanuel Grenier (1, 2) , Celine Helbert (3, 4) , Violaine Louvet (2, 3, 5) , Adeline Samson (6) , Paul Vigneaux (1, 2)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
2 NUMED - Numerical Medicine
3 ICJ - Institut Camille Jordan
4 PSPM - Probabilités, statistique, physique mathématique
5 MMCS - Modélisation mathématique, calcul scientifique
6 SVH - Statistique pour le Vivant et l’Homme

In this article we focus on parametrization of black box models from repeated measurements among several individuals (population parametrization). We introduce a variant of the SAEM algorithm, called KSAEM algorithm, which couples the standard SAEM algorithm with the dynamic construction of an approximate meta model. The costly evaluation of the genuine black box is replaced by a kriging step, using a basis of precomputed values, basis which is enlarged during SAEM algorithm to improve the accuracy of the meta model in regions of interest.

Mots clés: Non-linear Mixed Effect Models; KPP equation; Parameters estimation; Kriging; Partial Differential Equations; SAEM algorithm

Domaines: Analyse numérique [math.NA]

Emmanuel Grenier, Celine Helbert, Violaine Louvet, Adeline Samson, Paul Vigneaux. Population parametrization of costly black box models using iterations between SAEM algorithm and kriging. Computational & Applied Mathematics, 2018, 37 (1), pp.161-173. ⟨10.1007/s40314-016-0337-5⟩. ⟨hal-01224004v2⟩