Shapley effects for sensitivity analysis with dependent 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
Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology, UGA - Université Grenoble Alpes, LJK - Laboratoire Jean Kuntzmann, Inria Grenoble - Rhône-Alpes
Abstract : The global sensitivity analysis of a numerical model consists in quantifying, by means of sensitivity indices, the contributions of each of its input variables to the output the variability. The popular Sobol' indices, which are based on the functional variance analysis, present a difficult interpretation in the presence of statistical dependence between inputs. The recently introduced Shapley effects (normalized variance-based Shapley values), which consist of allocating a part of the variance of the output at each input, represent a promising alternative to solve this problem. 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 expensive engineering 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.
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https://hal.inria.fr/hal-01556303
Contributor : Bertrand Iooss <>
Submitted on : Monday, October 2, 2017 - 11:29:34 AM
Last modification on : Friday, January 10, 2020 - 9:09:00 PM

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  • HAL Id : hal-01556303, version 2
  • ARXIV : 1707.01334

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Bertrand Iooss, Clémentine Prieur. Shapley effects for sensitivity analysis with dependent inputs: comparisons with Sobol' indices, numerical estimation and applications. 2017. ⟨hal-01556303v2⟩

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