A comprehensive comparison of total-order estimators for global sensitivity analysis

TL;DR

This paper compares various total-order estimators for global sensitivity analysis, revealing which are most accurate across different benchmark settings to guide analysts in selecting appropriate methods.

Contribution

It provides a comprehensive comparison of total-order estimators under randomized benchmark parameters, reducing uncertainty in estimator selection.

Findings

Razavi and Gupta's, Jansen's, Janon/Monod's estimators are most accurate for factor prioritization.

Jansen's, Janon/Monod's, Azzini and Rosati's estimators best approximate true total-order indices.

Most estimators perform poorly compared to top methods.

Abstract

Sensitivity analysis helps identify which model inputs convey the most uncertainty to the model output. One of the most authoritative measures in global sensitivity analysis is the Sobol' total-order index, which can be computed with several different estimators. Although previous comparisons exist, it is hard to know which estimator performs best since the results are contingent on the benchmark setting defined by the analyst (the sampling method, the distribution of the model inputs, the number of model runs, the test function or model and its dimensionality, the weight of higher order effects or the performance measure selected). Here we compare several total-order estimators in an eight-dimension hypercube where these benchmark parameters are treated as random parameters. This arrangement significantly relaxes the dependency of the results on the benchmark design. We observe that the most accurate estimators are Razavi and Gupta's, Jansen's or Janon/Monod's for factor prioritization, and Jansen's, Janon/Monod's or Azzini and Rosati's for approaching the "true" total-order indices. The rest lag considerably behind. Our work helps analysts navigate the myriad of total-order formulae by reducing the uncertainty in the selection of the most appropriate estimator.