Different numerical estimators for main effect global sensitivity indices

TL;DR

This paper compares four direct formulas and the double loop reordering method for computing Sobol main effect sensitivity indices, highlighting the DLR approach's superior performance in various models.

Contribution

It introduces and evaluates four direct formulas for Sobol indices and compares them with the double loop reordering method, demonstrating the latter's effectiveness.

Findings

Double loop reordering outperforms direct formulas in accuracy and efficiency.

Direct formulas based on high-dimensional integrals vary in performance.

Monte Carlo and Quasi-Monte Carlo methods are used for integral evaluation.

Abstract

The variance-based method of global sensitivity indices based on Sobol sensitivity indices became very popular among practitioners due to its easiness of interpretation. For complex practical problems computation of Sobol indices generally requires a large number of function evaluations to achieve reasonable convergence. Four different direct formulas for computing Sobol main effect sensitivity indices are compared on a set of test problems for which there are analytical results. These formulas are based on high-dimensional integrals which are evaluated using MC and QMC techniques. Direct formulas are also compared with a different approach based on the so-called double loop reordering formula. It is found that the double loop reordering (DLR) approach shows a superior performance among all methods both for models with independent and dependent variables.