Metamodel-based Variance Estimation and Global Sensitivity Analysis

We propose a multilevel Monte Carlo metamodeling approach for variance function estimation.  we show that, under some mild conditions, the proposed MLMC metamodeling approach for variance function estimation can achieve a computational complexity superior to the standard Monte Carlo while achieving a target accuracy level. Additionally, we establish the asymptotic normality of the MLMC metamodeling estimator under a set of sufficient conditions, providing valuable utility for uncertainty quantification. An application in global sensitivity analysis shows that the approach can achieve competitive performance in supporting Sobol' indices estimation.

Sobol' indices are widely used in global sensitivity analysis for assessing the input parameters' impact on the model output,  with successful applications in epidemiological modeling, defect detection in manufacturing, pollutant transport modeling, etc. We propose joint metamodel-based Sobol' index estimators  which rely on estimation of both the mean and variance functions implied by a stochastic simulation experiment. We prove the estimators' asymptotic normality, based on which asymptotic confidence intervals can be constructed for uncertainty quantification.