Test comparison for Sobol Indices over nested sets of variables

TL;DR

This paper introduces a new method for testing the influence of input variable sets on model output using Sobol indices, leveraging their monotonicity property without requiring direct estimation.

Contribution

It proposes a novel testing approach that exploits Sobol indices' monotonicity, avoiding direct estimation and enabling use with standard iid sampling designs.

Findings

The method effectively tests variable influence without estimating Sobol indices directly.

It works with classical iid sampling designs.

The approach leverages the monotonicity property of Sobol indices.

Abstract

Sensitivity indices are commonly used to quantify the relative influence of any specific group of input variables on the output of a computer code. One crucial question is then to decide whether a given set of variables has a significant impact on the output. Sobol indices are often used to measure this impact but their estimation can be difficult as they usually require a particular design of experiment. In this work, we take advantage of the monotonicity of Sobol indices with respect to set inclusion to test the influence of some of the input variables. The method does not rely on a direct estimation of the Sobol indices and can be performed under classical iid sampling designs.