  Complex computer codes are widely used in science to model physical systems.
Sensitivity analysis aims to measure the contributions of the inputs on the
code output variability. An efficient tool to perform such analysis are the
variance-based methods which have been recently investigated in the framework
of dependent inputs. One of their issue is that they require a large number of
runs for the complex simulators. To handle it, a Gaussian process regression
model may be used to approximate the complex code. In this work, we propose to
decompose a Gaussian process into a high dimensional representation. This leads
to the definition of a variance-based sensitivity measure well tailored for
non-independent inputs. We give a methodology to estimate these indices and to
quantify their uncertainty. Finally, the approach is illustrated on toy
functions and on a river flood model.
