  Making good predictions of a physical system using a computer code requires
the inputs to be carefully specified. Some of these inputs called control
variables have to reproduce physical conditions whereas other inputs, called
parameters, are specific to the computer code and most often uncertain. The
goal of statistical calibration consists in estimating these parameters with
the help of a statistical model which links the code outputs with the field
measurements. In a Bayesian setting, the posterior distribution of these
parameters is normally sampled using MCMC methods. However, they are
impractical when the code runs are high time-consuming. A way to circumvent
this issue consists of replacing the computer code with a Gaussian process
emulator, then sampling a cheap-to-evaluate posterior distribution based on it.
Doing so, calibration is subject to an error which strongly depends on the
numerical design of experiments used to fit the emulator. We aim at reducing
this error by building a proper sequential design by means of the Expected
Improvement criterion. Numerical illustrations in several dimensions assess the
efficiency of such sequential strategies.
