  In many practical cases, a sensitivity analysis or an optimization of a
complex time consuming computer code requires to build a fast running
approximation of it - also called surrogate model. We consider in this paper
the problem of building a surrogate model of a complex computer code which can
be run at different levels of accuracy. The co-kriging based surrogate model is
a promising tool to build such an approximation. The idea is to improve the
surrogate model by using fast and less accurate versions of the code. We
present here a new approach to perform a multi-fidelity co-kriging model which
is based on a recursive formulation. The strength of this new method is that
the co-kriging model is built through a series of independent kriging models.
From them, some properties of classical kriging models can naturally be
extended to the presented co-kriging model such as a fast cross-validation
procedure. Moreover, based on a Bayes linear formulation, an extension of the
universal kriging equations are provided for the co-kriging model. Finally, the
proposed model has the advantage to reduce the computational complexity
compared to the previous models. The multi-fidelity model is successfully
applied to emulate a hydrodynamic simulator. This real example illustrates the
efficiency of the recursive model.
