Better estimation of small Sobol' sensitivity indices

TL;DR

This paper introduces a novel estimation method for Sobol' sensitivity indices that uses three independent input vectors, significantly improving accuracy for small indices compared to traditional two-vector methods.

Contribution

The paper presents a new estimation technique leveraging three input vectors, enhancing accuracy for small Sobol' indices over existing methods.

Findings

Outperforms traditional methods on small Sobol' indices

Achieves higher accuracy than some oracle estimators

Less effective than oracles when indices are large

Abstract

A new method for estimating Sobol' indices is proposed. The new method makes use of 3 independent input vectors rather than the usual 2. It attains much greater accuracy on problems where the target Sobol' index is small, even outperforming some oracles which adjust using the true but unknown mean of the function. When the target Sobol' index is quite large, the oracles do better than the new method.