Derivative-based global sensitivity measures: general links with Sobol' indices and numerical tests

Matieyendou Matieyendou (1) , Bertrand Iooss (2, 3) , Anne-Laure Popelin (3) , Fabrice Gamboa (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques
3 EDF R&D - EDF R&D

The estimation of variance-based importance measures (called Sobol' indices) of the input variables of a numerical model can require a large number of model evaluations. It turns to be unacceptable for huge model involving a large number of input variables (typically more than ten). Recently, Sobol and Kucherenko have proposed the Derivative-based Global Sensitivity Measures (DGSM), defined as the integral of the squared derivatives of the model output, showing that it can help to solve the problem of dimensionality in some cases. We provide a general inequality link between DGSM and total Sobol' indices for input variables belonging in the class of Boltzmann probability measures, extending the previous results of Sobol and Kucherenko for uniform and normal measures. The special case of log-concave measures is also described. This link provides a DGSM-based maximal bound for the total Sobol indices. Numerical tests show the performance of the bound and its usefulness in practice.

Mots clés: Boltzmann measure; Derivative based global sensitivity measure; Global sensitivity analysis; Log-concave measure; Poincaré inequality; Sobol' indices

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Matieyendou Matieyendou, Bertrand Iooss, Anne-Laure Popelin, Fabrice Gamboa. Derivative-based global sensitivity measures: general links with Sobol' indices and numerical tests. 2012. ⟨hal-00666473v1⟩