SIAM/ASA Journal on Uncertainty Quantification, Volume 9, Issue 2, Page 880-921, January 2021.
Sensitivity indices are commonly used to quantify the relative influence of any specific group of input variables on the output of a computer code. In this paper, we focus both on computer codes, the output of which is a cumulative distribution function, and on stochastic computer codes. We propose a way to perform a global sensitivity analysis for these kinds of computer codes. In the first setting, we define two indices: the first one is based on Wasserstein Fréchet means, while the second one is based on the Hoeffding decomposition of the indicators of Wasserstein balls. Further, when dealing with the stochastic computer codes, we define an “ideal version” of the stochastic computer code that fits into the framework of the first setting. Finally, we deduce a procedure to realize a second level global sensitivity analysis, namely, when one is interested in the sensitivity related to the input distributions rather than in the sensitivity related to the inputs themselves. Several numerical studies are proposed as illustrations of the different settings.

中文翻译：

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全局敏感性分析和 Wasserstein 空间

SIAM/ASA 不确定性量化杂志，第 9 卷，第 2 期，第 880-921 页，2021 年 1 月。
敏感性指数通常用于量化任何特定输入变量组对计算机代码输出的相对影响。在本文中，我们既关注计算机代码，其输出是累积分布函数，也关注随机计算机代码。我们提出了一种对这些类型的计算机代码进行全局敏感性分析的方法。在第一个设置中，我们定义了两个指标：第一个基于 Wasserstein Fréchet 均值，而第二个基于 Wasserstein 球指标的 Hoeffding 分解。此外，在处理随机计算机代码时，我们定义了适合第一个设置框架的随机计算机代码的“理想版本”。最后，我们推导出实现二级全局敏感性分析的过程，即：当人们对与输入分布相关的敏感性而不是与输入本身相关的敏感性感兴趣时。提出了一些数值研究作为不同设置的说明。