Sur la décomposition ANOVA et l'estimation des indices de Sobol'. Application à un modèle d'écosystème marin

Jean-Yves Tissot 1, 2
2 MOISE - Modelling, Observations, Identification for Environmental Sciences
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : In the fields of modelization and numerical simulation, simulators generally depend on several input parameters whose impact on the model outputs are not always well known. The main goal of sensitivity analysis is to better understand how the model outputs are sensisitive to the parameters variations. One of the most competitive method to handle this problem when complex and potentially highly non linear models are considered is based on the ANOVA decomposition and the Sobol' indices. More specifically the latter allow to quantify the impact of each parameters on the model response. In this thesis, we are interested in the issue of the estimation of the Sobol' indices. In the first part, we revisit in a rigorous way existing methods in light of discrete harmonic analysis on cyclic groups and randomized orthogonal arrays. It allows to study theoretical properties of this method and to intriduce generalizations. In a second part, we study the Monte Carlo method for the Sobol' indices and we introduce a new approach to reduce the number of simulations of this method. In parallel with this theoretical work, we apply these methods on a marine ecosystem model.
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Jean-Yves Tissot. Sur la décomposition ANOVA et l'estimation des indices de Sobol'. Application à un modèle d'écosystème marin. Mathématiques générales [math.GM]. Université Grenoble Alpes, 2012. Français. ⟨NNT : 2012GRENM064⟩. ⟨tel-00762800v2⟩

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