Variance-based sensitivity analysis in the presence of correlated input variables

TL;DR

This paper extends Sobol' sensitivity analysis to handle correlated input variables by decomposing their contributions into correlated and uncorrelated parts, enabling more accurate variance-based sensitivity estimates.

Contribution

It introduces a novel extension of the Sobol' estimator that accounts for input correlations using a linear correlation model, improving sensitivity analysis accuracy.

Findings

Decomposes input contributions into correlated and uncorrelated parts.

Uses sampling matrices that follow the original joint distribution.

Provides a direct computation method without model response assumptions.

Abstract

In this paper we propose an extension of the classical Sobol' estimator for the estimation of variance based sensitivity indices. The approach assumes a linear correlation model between the input variables which is used to decompose the contribution of an input variable into a correlated and an uncorrelated part. This method provides sampling matrices following the original joint probability distribution which are used directly to compute the model output without any assumptions or approximations of the model response function.