A Bayesian Approach for Global Sensitivity Analysis of (Multifidelity) Computer Codes

Abstract

Complex computer codes are widely used in science and engineering to model physical phenomena. Global sensitivity analysis aims to identify the input parameters which have the most important impact on the code output. Sobol indices are a popular tool for performing such analysis. However, their estimates require an important number of simulations and often cannot be processed under reasonable time constraint. To handle this problem, a Gaussian process regression model is built to approximate the computer code output and the Sobol indices are estimated through it. The aim of this paper is to provide a methodology for estimating the Sobol indices through a surrogate model taking into account both the estimation errors and the surrogate model errors. In particular, it allows us to derive nonasymptotic confidence intervals for the Sobol index estimates. Furthermore, we extend the suggested strategy to the case of multifidelity computer codes which can be run at different levels of accuracy. For such simulators, we use an extension of Gaussian process regression models for multivariate outputs.