It is well-known that Sobol indices, which count among the most popular sensitivity indices, are based on the Sobol decomposition. Here we challenge this construction by redefining Sobol indices without the Sobol decomposition. In fact, we show that Sobol indices are a particular instance of a more general concept which we call sensitivity measures. A sensitivity measure of a system taking inputs and returning outputs is a set function that is null at a subset of inputs if and only if, with probability one, the output actually does not depend on those inputs. A sensitivity measure evaluated at the whole set of inputs represents the uncertainty about the output. We show that measuring sensitivity to a particular subset is akin to measuring the expected output's uncertainty conditionally on the fact that the inputs belonging to that subset have been fixed to random values. By considering all of the possible combinations of inputs, sensitivity measures induce an implicit symmetric factorial experiment with two levels, the factorial effects of which can be calculated. This new paradigm generalizes many known sensitivity indices, can create new ones, and defines interaction effects independently of the choice of the sensitivity measure. No assumption about the distribution of the inputs is required.
Learning Global Sensitivity Indices from Observational Data: A Metamodel-Based Approach
University of Naples Federico II（那不勒斯费德里科二世大学）；Polytechnic and Basic Sciences School（理工与基础科学学院）；Department of Electrical Engineering and Information Technology（电气与信息工程系）
Global Sensitivity Analysis for Engineering Design Based on Individual Conditional Expectations
Faculty of Mechanical and Aerospace Engineering, Institut Teknologi Bandung, Bandung, Indonesia（印度尼西亚万隆理工学院机械与航空航天工程系）；Université Toulouse Capitole, IRIT, Toulouse, France（法国图卢兹卡波利大学IRIT研究所）；Department of Mathematics, Saint Joseph’s University, Philadelphia, PA, USA（美国费城圣约瑟夫大学数学系）；Department of Mechanical Engineering, Kyushu University, Fukuoka, Japan（日本九州大学机械工程系）；Institute of Fluid Science, Tohoku University, Sendai, Japan（日本东北大学流体科学研究所）；ISAE-SUPAERO, Université de Toulouse, Toulouse, France（法国图卢兹大学ISAE-SUPAERO）
Gradient-enhanced global sensitivity analysis with Poincar{é} chaos expansions
UMR CNRS 5219, Institut de Mathématiques de Toulouse, INSA, Université de Toulouse（图卢兹数学研究所）；Chair of Risk, Safety and Uncertainty Quantification, ETH Zürich（苏黎世联邦理工学院风险、安全与不确定性量化讲席）
