Estimating the Approximation Error when Fixing Unessential Factors in Global Sensitivity Analysis

Abstract

One of the major settings of global sensitivity analysis is that of fixing non influential factors, in order to reduce the dimensionality of a model. However, this is usually done without knowing the magnitude of the approximation error being produced. This paper presents and proves a new theorem for the estimation of the average approximation error generated when fixing non influential factors. A simple function where analytical solutions are available is used as test case to illustrate the theorem; furthermore this function is used to show the theorem applicability to sensitivity analysis by groups of factors. Improved formulas for the estimation of sensitivity indices are presented; such formulas allow for more accurate estimations at a lower computational cost with respect to the original method of Sobol’.