全局灵敏度分析与Wasserstein空间
Global sensitivity analysis and Wasserstein spaces
摘要：
灵敏度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，我们集中在计算机代码的输出是一个累积分布函数和随机计算机代码。我们提出了一种对这类计算机代码进行全局灵敏度分析的方法。在第一种情况下，我们设计了两个指标：第一个指标基于Wasserstein Fr é chet均值，第二个指标基于Wasserstein球指标的Hoeding分解。进一步，在处理随机计算机码时，我们确定了随机计算机码的一个理想版本，它是在第一个设置的框架内。最后，我们推导出一个程序来实现第二级的全球灵敏度分析，即当一个感兴趣的灵敏度相关的输入分布，而不是在灵敏度相关的输入本身。几个数值研究提出了在dierent设置作为例证。
英文摘要：
Sensitivity indices are commonly used to quantity the relative inuence of any specic 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 rst setting, we dene two indices: the rst one is based on Wasserstein Fr{é}chet means while the second one is based on the Hoeding decomposition of the indicators of Wasserstein balls. Further, when dealing with the stochastic computer codes, we dene an ideal version of the stochastic computer code thats ts into the frame of the rst 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 in the dierent settings.
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