Indices de Sobol généralisés aux variables dépendantes : tests de performance de l’algorithme HOGS couplé à plusieurs estimateurs paramétriques

Abstract : The algorithm " Hierarchically Orthogonal Gram-Schmidt " (HOGS) (Chastaing et al., 2015) estimates generalized Sobol indices dedicated to models with dependent inputs, quantifying explicitly the model sensitivity due to correlations. HOGS constructs a meta-model for each variable of interest by projection on a functional basis suited to indices calculation. Regression coefficients are obtained with the ordinary least-square estimator (OLS) or penalized regression methods Lasso, Ridge and Elastic Net (EN). Four study cases are proposed: three toy models allowing to investigate HOGS functioning and numerical properties, and the LNAS (Log-Normal Allocation and Senescence) model dedicated to the complex dynamics of plant growth. Several HOGS configurations and meta-model accuracy are tested by means of a consistency index. An interpretation of Sobol indices is given for LNAS. It appears that HOGS-OLS is the most efficient method when simulation resources are not limited. Otherwise, considering the issue of parameter estimation with sparsity highlights that: i) EN is more robust but more costly than Lasso, ii) the basis constructed by HOGS is too large which creates artificial sparsity. A modification of HOGS has been proposed to reduce the dimension of the basis.
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Julien Sainte-Marie, Gautier Viaud, Paul-Henry Cournède. Indices de Sobol généralisés aux variables dépendantes : tests de performance de l’algorithme HOGS couplé à plusieurs estimateurs paramétriques. Journal de la Société Française de Statistique, Société Française de Statistique et Société Mathématique de France, 2017, 158 (1), pp.68-89. ⟨hal-01630985⟩

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