Proportional Marginal Effects for Global Sensitivity Analysis

IF 2.1 3区工程技术 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2024-06-26 DOI:10.1137/22m153032x

Margot Herin, Marouane Il Idrissi, Vincent Chabridon, Bertrand Iooss

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引用次数: 0

Abstract

SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 2, Page 667-692, June 2024.
Abstract.Performing (variance-based) global sensitivity analysis (GSA) with dependent inputs has recently benefited from cooperative game theory concepts, leading to meaningful sensitivity indices suitable with dependent inputs. The “Shapley effects,” i.e., the Shapley values transposed to variance-based GSA problems, are an example of such indices. However, these indices exhibit a particular behavior that can be undesirable: an exogenous input (i.e., which is not explicitly included in the structural equations of the model) can be associated with a strictly positive index when it is correlated to endogenous inputs. This paper investigates using a different allocation, called the “proportional values” for GSA purposes. First, an extension of this allocation is proposed to make it suitable for variance-based GSA. A novel GSA index is then defined: the proportional marginal effect (PME). The notion of exogeneity is formally defined in the context of variance-based GSA. It is shown that the PMEs are more discriminant than the Shapley values and allow the distinction of exogenous variables, even when they are correlated to endogenous inputs. Moreover, their behavior is compared to the Shapley effects on analytical toy cases and more realistic use cases.

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全球敏感性分析的比例边际效应

SIAM/ASA 不确定性量化期刊》，第 12 卷，第 2 期，第 667-692 页，2024 年 6 月。摘要.最近，利用合作博弈论概念对依赖性输入进行（基于方差的）全局灵敏度分析（GSA）已获益匪浅，从而产生了适合依赖性输入的有意义的灵敏度指数。夏普利效应"，即基于方差的 GSA 问题的夏普利值，就是此类指数的一个例子。然而，这些指数表现出一种可能不可取的特殊行为：当外生性输入（即未明确包含在模型结构方程中）与内生性输入相关时，外生性输入可能与严格的正指数相关联。本文研究了一种不同的分配方法，为 GSA 目的称之为 "比例值"。首先，本文提出了该分配的扩展方案，使其适用于基于方差的 GSA。然后定义了一种新的 GSA 指数：比例边际效应（PME）。在基于方差的 GSA 的背景下，正式定义了外生性概念。结果表明，PME 比 Shapley 值更具区分性，即使外生变量与内生输入相关，也能区分外生变量。此外，在分析玩具案例和更现实的使用案例中，它们的行为与夏普利效应进行了比较。

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来源期刊

Siam-Asa Journal on Uncertainty Quantification Mathematics-Statistics and Probability

CiteScore

3.70

自引率

0.00%

发文量

期刊介绍： SIAM/ASA Journal on Uncertainty Quantification (JUQ) publishes research articles presenting significant mathematical, statistical, algorithmic, and application advances in uncertainty quantification, defined as the interface of complex modeling of processes and data, especially characterizations of the uncertainties inherent in the use of such models. The journal also focuses on related fields such as sensitivity analysis, model validation, model calibration, data assimilation, and code verification. The journal also solicits papers describing new ideas that could lead to significant progress in methodology for uncertainty quantification as well as review articles on particular aspects. The journal is dedicated to nurturing synergistic interactions between the mathematical, statistical, computational, and applications communities involved in uncertainty quantification and related areas. JUQ is jointly offered by SIAM and the American Statistical Association.