Reliable error estimation for Sobol’ indices

Abstract

A practical problem concerning the estimation of Sobol' indices is how large to choose the number of evaluations to ensure that estimates are accurate enough. This paper addresses this challenge by proposing a reliable error bound for Sobol' indices based on digital sequences. The error bound is defined in terms of the discrete Walsh coefficients of the integrands involved in the Sobol' indices definition. We propose a sequential estimation procedure of first-order and total effect Sobol' indices using the error bound as stopping criterion. The procedure operates under the assumption that all integrands lie inside a particular cone of functions