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 this http URL 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. 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.

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相关输入敏感性分析的沙普利效应：与 Sobol 指数、数值估计和应用的比较

数值模型的全局敏感性分析旨在通过敏感性指数估计量化每个不确定输入变量对模型输出不确定性的贡献。所谓的 Sobol' 指数基于函数方差分析，在输入之间存在统计相关性的情况下很难解释。最近引入了 Shapley 效应来解决这个问题，因为他们将一组输入的相互贡献（由于相关性和交互作用）分配给本文 http URL 中的每个单独输入，使用几个新的分析结果，我们研究了这些影响一些高斯输入变量对 Shapley 效应的线性相关性，并将这些效应与经典的一阶和总 Sobol 指数进行比较。这说明了兴趣，在敏感性分析设置和解释方面，在依赖输入的情况下，沙普利效应。对于计算要求高的计算机模型的实际问题，我们表明用元模型（这里是克里金法）替换原始模型可以以合理的计算成本精确地估计这些指标。