Global sensitivity analysis (GSA) is used to quantify the influence of uncertain variables in a mathematical model. Prior to performing GSA, the user must specific a probability distribution to model the uncertainty, and possibly statistical dependencies, of the variables. Determining this distribution is challenging in practice as the user has limited and imprecise knowledge of the uncertain variables. This article analyzes the robustness of the Sobol' indices, a commonly used tool in GSA, to changes in the distribution of the uncertain variables. A method for assessing such robustness is developed which requires minimal user specification and no additional evaluations of the model. Theoretical and computational aspects of the method are considered and illustrated through examples.

中文翻译：

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Sobol 指数对分布不确定性的稳健性

全局敏感性分析（GSA）用于量化数学模型中不确定变量的影响。在执行 GSA 之前，用户必须指定一个概率分布来模拟变量的不确定性和可能的​​统计依赖性。确定这种分布在实践中具有挑战性，因为用户对不确定变量的了解有限且不精确。本文分析了 GSA 中常用的工具 Sobol 指数对不确定变量分布变化的稳健性。开发了一种评估这种稳健性的方法，该方法需要最少的用户规范并且不需要对模型进行额外的评估。通过示例考虑并说明了该方法的理论和计算方面。