Dimension-independent single-loop Monte Carlo simulation method for estimate of Sobol’ indices in variance-based sensitivity analysis

Abstract

This contribution presents a novel approach for estimating the Sobol’ index, which has been commonly employed in variance-based sensitivity analysis of computational models that may often involve multiple uncertain parameters. Specifically, a single-loop Monte Carlo simulation (MCS) method, which is independent of the dimensionality of inputs, is proposed to reduce the computational cost of complicated models. The proposed method is realized by developing a new estimator of the Sobol’ index computed via the two-dimensional kernel density estimation, which can be easy programming while ensuring high accuracy. Numerical examples are studied to demonstrate the advantages of the proposed method.