A randomized Orthogonal Array-based procedure for the estimation of first- and second-order Sobol indicesReportar como inadecuado

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1 MOISE - Modelling, Observations, Identification for Environmental Sciences Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble

Abstract : In variance-based sensitivity analysis, the method of Sobol- 1993 allows to compute Sobol- indices using Monte Carlo integration. One of the main drawbacks of this approach is that the estimation of Sobol- indices requires the use of several samples. For example, in a d-dimensional space, the estimation of all the first-order Sobol- indices requires d+1 samples. Some interesting combinatorial results have been introduced to weaken this defect, in particular by Saltelli 2002 and more recently by Owen 2012 but the quantities they estimate still require Od samples. In this paper, we introduce a new approach to estimate for any k all the k-th order Sobol- indices by using only two samples. We establish theoretical properties of such a method for the first-order Sobol- indices and discuss the generalization to higher-order indices. As an illustration, we propose to apply this new approach to a marine ecosystem model of the Ligurian sea northwestern Mediterranean in order to study the relative importance of its several parameters. The calibration process of this kind of chemical simulators is well-known to be quite intricate, and a rigorous and robust - i.e. valid without strong regularity assumptions - sensitivity analysis, as the method of Sobol- provides, could be of great help.

Keywords : variance-based sensitivity indices global sensitivity analysis orthogonal arrays numerical integration

Autor: Jean-Yves Tissot - Clémentine Prieur -

Fuente: https://hal.archives-ouvertes.fr/


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