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 the way of sensitivity indices, the contributions of each of its input variables in the variability of its output. Based on the functional variance analysis, the popular Sobol' indices present a difficult interpretation in the presence of statistical dependence between inputs. Recently introduced, the Shapley effects, which consist of allocating a part of the variance of the output at each input, are promising to solve this problem. In this paper, from several analytical results, we deeply study the effects of linear correlation between some Gaussian input variables on Shapley effects, comparing them to classical first-order and total Sobol' indices. This illustrates the interest, in terms of interpretation, of the Shapley effects in the case of dependent inputs. We also numerically study the numerical convergence of estimating the Shapley effects. For the engineering practical issue of computationally expensive models, we show that the substitution of the model by a metamodel (here kriging) makes it possible to estimate these indices with precision.
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Submitted on : Tuesday, July 4, 2017 - 11:08:02 PM
Last modification on : Friday, January 10, 2020 - 9:08:59 PM
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  • HAL Id : hal-01556303, version 1
  • 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-01556303v1⟩

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