Variance-based sensitivity analysis in the presence of correlated input variables
This work addresses a methodological gap in sensitivity analysis for researchers dealing with correlated inputs, though it appears incremental as an extension of existing estimators.
The paper tackles the problem of estimating variance-based sensitivity indices when input variables are correlated, proposing an extension of the Sobol' estimator that decomposes contributions into correlated and uncorrelated parts, with results applicable directly to model outputs without assumptions on the response function.
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.