Efficient Evaluation of Sobol’ Sensitivity Indices via Polynomial Lattice Rules and Modified Sobol’ Sequences

Venelin Todorov () and Petar Zhivkov
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Venelin Todorov: Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 25A, 1113 Sofia, Bulgaria
Petar Zhivkov: Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 25A, 1113 Sofia, Bulgaria

Mathematics, 2025, vol. 13, issue 21, 1-20

Abstract: 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.

Keywords: Monte Carlo; sensitivity analysis; polynomial lattice rules; modified Sobol’ sequences (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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