Global Activity Scores

TL;DR

The paper introduces a new global sensitivity measure called global activity scores, which are based on finite differences and are more stable under noisy conditions compared to derivative-based measures.

Contribution

It establishes the theoretical connection of global activity scores with Sobol' indices and demonstrates their superior stability in noisy environments.

Findings

Global activity scores outperform derivative-based measures in noisy settings.

In noiseless cases, all sensitivity measures perform similarly.

Numerical examples validate the stability and reliability of global activity scores.

Abstract

We introduce a new global sensitivity measure, the global activity scores. The measure is based on finite differences of the underlying function, in contrast to several sensitivity measures in the literature that are based on derivatives of the function. We establish its theoretical connection with Sobol' sensitivity indices and demonstrate its performance through numerical examples. In these examples, we compare global activity scores with Sobol' sensitivity indices, derivative-based sensitivity measures, and activity scores. The results show that in the presence of additive noise or high variability, global activity scores provide more stable and reliable identification of influential variables than derivative-based measures and activity scores, which are more sensitive to noise. In noiseless settings, however, all three approaches yield comparable results.