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.

翻译：最近,具有依赖性投入的表演(基于差异的)全球敏感度分析(GSA)从合作游戏理论概念中受益。 尽管投入之间可能存在关联关系,但利用这一理论,可以通过模型输出差异对每种输入的分配份额来界定有意义的敏感度指数。“损耗效应”,即“沙皮值被转换为基于差异的GSA问题,允许采用这一适当的解决办法。然而,这些指数显示出一种可能不可取的特定行为:外源投入(即未明确纳入模型结构方程式的外源效应)可与严格的正向指数相联系,如果它与内生投入相关。在目前的工作中,使用不同的分配,称为“相称值”加以调查。第一种贡献是提议扩大这种分配,适合基于差异的GSA问题。然后,提出“超额全球影响”指数,称为“超比例边际效应”。在基于差异的GSA结构方程式结构方程式中正式界定了外源特性的概念,在与内生投入相关时,也显示使用不同的分配方式,在将内生变量与内生变量进行比较时,其与内生性行为是比较。