Is it possible to improve existing sample-based algorithm to compute the total sensitivity index?

Abstract

Variance-based sensitivity indices have established themselves as a reference among practitioners of sensitivity analysis of model output. It is not unusual to consider a variance-based sensitivity analysis as informative if it produces at least the first order sensitivity indices ¿¿j and the so-called total-effect sensitivity indices ¿¿j for all the uncertain factors of the mathematical model under analysis. Computational economy is critical in sensitivity analysis. It depends mostly upon the number of model evaluations needed to obtain stable values of the estimates. While efficient estimation procedures independent from the number of factors under analysis are available for the first order indices, this is less the case for the total sensitivity indices. When estimating Tj , one can either use a sample-based approach, whose computational cost depends on the number of factors, or approaches based on meta-modelling/emulators, e.g. based on Gaussian processes. The present work focuses on sample-based estimation procedures for Tj and tries different avenues to achieve an algorithmic improvement over the designs proposed in the existing best practices. We conclude that some proposed sample-based improvements found in the literature do not work as claimed, and that improving on the existing best practice is indeed fraught with difficulties. We motivate our conclusions introducing the concepts of explorativity and efficiency of the design.