Statistical inference for Sobol pick freeze Monte Carlo method

TL;DR

This paper investigates the statistical properties of estimators for Sobol sensitivity indices, crucial for global sensitivity analysis, focusing on their asymptotic and non-asymptotic behaviors to improve significance testing and confidence interval estimation.

Contribution

It provides a detailed analysis of the asymptotic and non-asymptotic properties of Sobol index estimators, enhancing their reliability for sensitivity analysis.

Findings

Analyzed asymptotic behavior of Sobol index estimators.

Derived non-asymptotic properties for finite samples.

Improved significance testing and confidence interval estimation.

Abstract

Many mathematical models involve input parameters, which are not precisely known. Global sensitivity analysis aims to identify the parameters whose uncertainty has the largest impact on the variability of a quantity of interest (output of the model). One of the statistical tools used to quantify the influence of each input variable on the output is the Sobol sensitivity index. We consider the statistical estimation of this index from a finite sample of model outputs. We study asymptotic and non-asymptotic properties of two estimators of Sobol indices. These properties are applied to significance tests and estimation by confidence intervals.