Quantile based global sensitivity measures

TL;DR

This paper introduces quantile-based global sensitivity measures for analyzing models where extreme output values are of interest, linking them to Sobol indices and demonstrating their efficiency through numerical tests.

Contribution

It presents novel quantile-based sensitivity measures, establishes their connection to Sobol indices, and compares Monte Carlo estimators, highlighting the efficiency of the reordering approach.

Findings

Double loop reordering estimator is more efficient than brute force.

Quantile-based measures effectively identify important variables for extreme outputs.

Numerical results confirm the method's efficiency in structural safety cases.

Abstract

New global sensitivity measures based on quantiles of the output are introduced. Such measures can be used for global sensitivity analysis of problems in which quantiles are explicitly the functions of interest and for identification of variables which are the most important in achieving extreme values of the model output. It is proven that there is a link between introduced measures and Sobol main effect sensitivity indices. Two different Monte Carlo estimators are considered. It is shown that the double loop reordering approach is much more efficient than the brute force estimator. Several test cases and practical case studies related to structural safety are used to illustrate the developed method. Results of numerical calculations show the efficiency of the presented technique.