Shapley effects for sensitivity analysis with correlated inputs: comparisons with Sobol' indices, numerical estimation and applications

Bertrand Iooss 1, 2, 3 Clémentine Prieur 4
4 AIRSEA - Mathematics and computing applied to oceanic and atmospheric flows
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, UJF - Université Joseph Fourier - Grenoble 1, INPG - Institut National Polytechnique de Grenoble
Abstract : The global sensitivity analysis of a numerical model aims to quantify, by means of sensitivity indices estimate, the contributions of each uncertain input variable to the model output uncertainty. The so-called Sobol' indices, which are based on the functional variance analysis, present a difficult interpretation in the presence of statistical dependence between inputs. The Shapley effect was recently introduced to overcome this problem as they allocate the mutual contribution (due to correlation and interaction) of a group of inputs to each individual input within the group. In this paper, using several new analytical results, we study the effects of linear correlation between some Gaussian input variables on Shapley effects, and compare these effects to classical first-order and total Sobol' indices. This illustrates the interest, in terms of sensitivity analysis setting and interpretation, of the Shapley effects in the case of dependent inputs. We also investigate the numerical convergence of the estimated Shapley effects. For the practical issue of computationally demanding computer models, we show that the substitution of the original model by a metamodel (here, kriging) makes it possible to estimate these indices with precision at a reasonable computational cost.
Type de document :
Pré-publication, Document de travail
2018
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https://hal.inria.fr/hal-01556303
Contributeur : Bertrand Iooss <>
Soumis le : jeudi 17 mai 2018 - 18:43:07
Dernière modification le : mercredi 23 mai 2018 - 17:58:04

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  • HAL Id : hal-01556303, version 4
  • ARXIV : 1707.01334

Citation

Bertrand Iooss, Clémentine Prieur. Shapley effects for sensitivity analysis with correlated inputs: comparisons with Sobol' indices, numerical estimation and applications. 2018. 〈hal-01556303v4〉

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