  In decommissioning projects of nuclear facilities, the radiological
characterisation step aims to estimate the quantity and spatial distribution of
different radionuclides. To carry out the estimation, measurements are
performed on site to obtain preliminary information. The usual industrial
practice consists in applying spatial interpolation tools (as the ordinary
kriging method) on these data to predict the value of interest for the
contamination (radionuclide concentration, radioactivity, etc.) at unobserved
positions. This paper questions the ordinary kriging tool on the well-known
problem of the overoptimistic prediction variances due to not taking into
account uncertainties on the estimation of the kriging parameters (variance and
range). To overcome this issue, the practical use of the Bayesian kriging
method, where the model parameters are considered as random variables, is
deepened. The usefulness of Bayesian kriging, whilst comparing its performance
to that of ordinary kriging, is demonstrated in the small data context (which
is often the case in decommissioning projects). This result is obtained via
several numerical tests on different toy models, and using complementary
validation criteria: the predictivity coefficient (Q${}^2$), the Predictive
Variance Adequacy (PVA), the $\alpha$-Confidence Interval plot (and its
associated Mean Squared Error alpha (MSEalpha)), and the Predictive Interval
Adequacy (PIA). The latter is a new criterion adapted to the Bayesian kriging
results. Finally, the same comparison is performed on a real dataset coming
from the decommissioning project of the CEA Marcoule G3 reactor. It illustrates
the practical interest of Bayesian kriging in industrial radiological
characterisation.
