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The $f$-Sensitivity Index
Journal article

The $f$-Sensitivity Index

Sharif Rahman
SIAM/ASA journal on uncertainty quantification, Vol.4(1), pp.130-162
01/2016
DOI: 10.1137/140997774
url
https://arxiv.org/pdf/1512.02303View
Open Access

Abstract

This paper presents a general multivariate f-sensitivity index, rooted in the f-divergence between the unconditional and conditional probability measures of a stochastic response, for global sensitivity analysis. Unlike the variance-based Sobol index, the f-sensitivity index is applicable to random input following dependent as well as independent probability distributions. Since the class of fdivergences supports a wide variety of divergence or distance measures, a plethora of f-sensitivity indices are possible, affording diverse choices to sensitivity analysis. Commonly used sensitivity indices or measures, such as mutual information, squared-loss mutual information, and Borgonovo's importance measure, are shown to be special cases of the proposed sensitivity index. New theoretical results, revealing fundamental properties of the f-sensitivity index and establishing important inequalities, are presented. Three new approximate methods, depending on how the probability densities of a stochastic response are determined, are proposed to estimate the sensitivity index. Four numerical examples, including a computationally intensive stochastic boundary-value problem, illustrate these methods and explain when one method is more relevant than the others.

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