Global sensitivity analysis with dependence measures

• Published in: Journal of statistical computation and simulation Vol. 85; no. 7; pp. 1283 - 1305
• Main Author: Da Veiga, Sebastien
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 03.05.2015; Taylor & Francis Ltd
• Subjects: Computer simulation; Correlation analysis; Criteria; Dimensional measurements; global sensitivity analysis; Handles; Hilbert space; independence; kernel; Mathematical models; Mathematics; Multivariate analysis; mutual information; Random variables; Screening; Sensitivity analysis; State of the art; Statistics; Global sensitivity analysis; Independance; Kernel; Mutual information
• ISSN: 0094-9655; 1563-5163
• DOI: 10.1080/00949655.2014.945932

Global sensitivity analysis with variance-based measures suffers from several theoretical and practical limitations, since they focus only on the variance of the output and handle multivariate variables in a limited way. In this paper, we introduce a new class of sensitivity indices based on dependence measures which overcomes these insufficiencies. Our approach originates from the idea to compare the output distribution with its conditional counterpart when one of the input variables is fixed. We establish that this comparison yields previously proposed indices when it is performed with Csiszár f-divergences, as well as sensitivity indices which are well-known dependence measures between random variables. This leads us to investigate completely new sensitivity indices based on recent state-of-the-art dependence measures, such as distance correlation and the Hilbert-Schmidt independence criterion. We also emphasize the potential of feature selection techniques relying on such dependence measures as alternatives to screening in high dimension.