  Complex computer codes are widely used in science and engineering to model
physical phenomena. Furthermore, it is common that they have a large number of
input parameters. Global sensitivity analysis aims to identify those which have
the most important impact on the output. Sobol indices are a popular tool to
perform such analysis. However, their estimations 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
surrogate the computer code and the Sobol indices are estimated through it. The
aim of this paper is to provide a methodology to estimate 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
non-asymptotic confidence intervals for the Sobol index estimations.
Furthermore, we extend the suggested strategy to the case of multi-fidelity
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.
