Statistical inference for Sobol pick-freeze Monte Carlo method

Abstract

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