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Accurate and efficient estimation of Sobol’ sensitivity indices is a cornerstone of variance-based global sensitivity analysis, providing critical insights into how uncertainties in input parameters affect model outputs. This is particularly important for large-scale environmental, engineering, and financial models, where understanding parameter influence is essential for improving model reliability, guiding calibration, and supporting informed decision-making. However, computing Sobol’ indices requires evaluating high-dimensional integrals, presenting significant numerical and computational challenges. In this study, we present a comparative analysis of two of the best available Quasi-Monte Carlo (QMC) techniques: polynomial lattice rules (PLRs) and modified Sobol’ sequences. The performance of both approaches is systematically assessed in terms of performance and accuracy. Extensive numerical experiments demonstrate that the proposed PLR-based framework achieves superior precision for several sensitivity measures, while modified Sobol’ sequences remain competitive for lower-dimensional indices. Our results show that IPLR-α3 outperforms traditional QMC methods in estimating both dominant and weak sensitivity indices, offering a robust framework for high-dimensional models. These findings provide practical guidelines for selecting optimal QMC strategies, contributing to more reliable sensitivity analysis and enhancing the predictive power of complex computational models.
Todorov et al. (Sat,) studied this question.