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

Abstract : 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 high-dimensional 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 to the class of Boltzmann probability measures, thus 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.
Type de document :
Article dans une revue
Mathematics and Computers in Simulation, Elsevier, 2013, 87, pp.45-54
Liste complète des métadonnées

Littérature citée [5 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-00666473
Contributeur : Bertrand Iooss <>
Soumis le : dimanche 1 juillet 2012 - 23:12:20
Dernière modification le : vendredi 26 octobre 2018 - 10:35:44
Document(s) archivé(s) le : mardi 2 octobre 2012 - 09:33:51

Fichiers

Art_Math_Comp.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-00666473, version 2
  • ARXIV : 1202.0943

Citation

Matieyendou Lamboni, Bertrand Iooss, Anne-Laure Popelin, Fabrice Gamboa. Derivative-based global sensitivity measures: general links with Sobol' indices and numerical tests. Mathematics and Computers in Simulation, Elsevier, 2013, 87, pp.45-54. 〈hal-00666473v2〉

Partager

Métriques

Consultations de la notice

478

Téléchargements de fichiers

468