Abstract We introduce original sensitivity analysis metrics with the aim of assistingdiagnosis of the functioning of a given model. We do so by characterizing model-induced dependencies between a target model output and selected model input(s) through the associated bivariate copuladensity. The latter fully characterizes the dependencies between two random variables at any order (i.e., without being limited to linear dependence), independent of the marginal behavior of the two variables. As a metric to assess sensitivity, we rely on the absolute distance betweenthe copuladensity associated with the target model output and a model input and its counterpart associated with two independent variables. We then provide two sensitivity indices which allow characterizing (i) the global (with respect to the input) value of the sensitivity and (ii) the degree of variability (across the range of the input values) of the sensitivity for each value that the prescribed model output can possibly undertake, as driven by the governing model. In this sense, our approach to sensitivity is global with respect to model input(s) and local with respect to model output, thus enabling one to discriminate the relevance of an input across the entire range of values of the modeling goal of interest. We exemplify the use of our approach and illustrate the type of information it can provide by focusing on an analytical test function and on two scenarios related to flow and transport in porous media.

中文翻译：

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用于敏感性分析的 Copula 密度驱动指标：多孔介质中流动和传输的理论和应用。

摘要 我们引入了原始敏感性分析指标，目的是帮助诊断给定模型的功能。我们通过相关联的双变量 copuladensity 表征目标模型输出和选定模型输入之间的模型诱导依赖性来做到这一点。后者完全表征两个随机变量之间任意阶次的依赖关系（即，不限于线性依赖关系），与两个变量的边际行为无关。作为评估灵敏度的指标，我们依赖于与目标模型输出和模型输入相关联的 copuladensity 之间的绝对距离，以及与两个自变量相关联的对应项之间的绝对距离。然后，我们提供两个敏感度指数，它们允许表征（i）敏感度的全局（相对于输入）值和（ii）每个值的敏感度的可变性程度（跨输入值范围）在管理模型的驱动下，规定的模型输出可能会进行。从这个意义上说，我们的敏感性方法对于模型输入是全局的，而对于模型输出是局部的，从而使人们能够在感兴趣的建模目标的整个值范围内区分输入的相关性。我们举例说明了我们的方法的使用，并通过关注分析测试功能和与多孔介质中的流动和传输相关的两个场景来说明它可以提供的信息类型。