Robustness of the Sobol' Indices to Marginal Distribution Uncertainty
Robustness of the Sobol' Indices to Marginal Distribution Uncertainty
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DOI：
10.1137/18m123387x
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发表时间：
2018-12
期刊：
影响因子：
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通讯作者：
Joseph L. Hart;P. Gremaud
中科院分区：
文献类型：
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作者：
Joseph L. Hart;P. Gremaud
全局敏感性分析（GSA）是对数学模型中不确定变量的影响进行量化的方法。Sobol指数是GSA中常用的工具，它试图通过将每个变量对模型输出方差的相对贡献归因于每个变量来做到这一点。为了计算Sobol指数，用户必须指定不确定变量的概率分布。这种分布通常是未知的，必须使用有限的数据和/或知识来选择。Sobol指数的有用性取决于它们对这种分布不确定性的鲁棒性。本文提出了一种利用边际概率密度函数的“最优扰动”来分析Sobol指数鲁棒性的新方法。该方法是通过合成的例子和污染物传输模型说明。
Global sensitivity analysis (GSA) quantifies the influence of uncertain variables in a mathematical model. The Sobol' indices, a commonly used tool in GSA, seek to do this by attributing to each variable its relative contribution to the variance of the model output. In order to compute Sobol' indices, the user must specify a probability distribution for the uncertain variables. This distribution is typically unknown and must be chosen using limited data and/or knowledge. The usefulness of the Sobol' indices depends on their robustness to this distributional uncertainty. This article presents a novel method which uses "optimal perturbations" of the marginal probability density functions to analyze the robustness of the Sobol' indices. The method is illustrated through synthetic examples and a model for contaminant transport.