论文标题
比例边缘效应用于全球灵敏度分析
Proportional marginal effects for global sensitivity analysis
论文作者
论文摘要
具有依赖输入的表现(基于方差的)全球灵敏度分析(GSA)最近从合作游戏理论概念中受益。使用该理论,尽管输入之间存在潜在的相关性,但可以通过模型输出的分配共享对每个输入的分配共享来定义有意义的灵敏度指数。 ``莎普利效应'',即,shapley值转移到基于方差的GSA问题,允许使用这种合适的解决方案。但是,这些指数表现出可能不希望的特定行为:当模型的结构方程中未明确包含的外源输入(即,当它与内源性输入相关时)可能与严格的正索引有关。在目前的工作中,研究了不同的分配,称为``比例值''。第一个贡献是提出该分配的扩展,适用于基于方差的GSA。然后提出了新颖的GSA指数,称为``比例边缘效应''(PME)。外生性的概念在基于方差的GSA的背景下正式定义,并且表明PME允许外源变量的区别,即使它们与内源性输入相关。此外,将它们的行为与沙普利对分析玩具箱和更现实的用例的影响进行了比较。
Performing (variance-based) global sensitivity analysis (GSA) with dependent inputs has recently benefited from cooperative game theory concepts.By using this theory, despite the potential correlation between the inputs, meaningful sensitivity indices can be defined via allocation shares of the model output's variance to each input. The ``Shapley effects'', i.e., the Shapley values transposed to variance-based GSA problems, allowed for this suitable solution. 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. In the present work, the use of a different allocation, called the ``proportional values'' is investigated. A first contribution is to propose an extension of this allocation, suitable for variance-based GSA. Novel GSA indices are then proposed, called the ``proportional marginal effects'' (PME). The notion of exogeneity is formally defined in the context of variance-based GSA, and it is shown that the PME 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.