The $f$-Sensitivity Index
Abstract
This article presents a general multivariate -sensitivity index, rooted in the -divergence between the unconditional and conditional probability measures of a stochastic response, for global sensitivity analysis. Unlike the variance-based Sobol index, the -sensitivity index is applicable to random input following dependent as well as independent probability distributions. Since the class of -divergences supports a wide variety of divergence or distance measures, a plethora of -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 -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.
Cite
@article{arxiv.1512.02303,
title = {The $f$-Sensitivity Index},
author = {Sharif Rahman},
journal= {arXiv preprint arXiv:1512.02303},
year = {2015}
}
Comments
32 pages, 5 figures, accepted by SIAM/ASA Journal on Uncertainty Quantification, 2015