Kriging with Ill-Known Variogram and Data

Kriging consists in estimating or predicting the spatial phenomenon at non sampled locations from an estimated random function. Although information necessary to properly select a unique random function model seems to be partially lacking, geostatistics in general, and the kriging methodology in particular, does not account for the incompleteness of the information that seems to pervade the procedure. On the one hand, the collected data may be tainted with errors that can be modelled by intervals or fuzzy intervals. On the other hand, the choice of parameter values for the theoretical variogram, an essential step, contains some degrees of freedom that is seldom acknowledged. In this paper we propose to account for epistemic uncertainty pervading the variogram parameters, and possibly the data set, by means of fuzzy interval uncertainty. We lay bare its impact on the kriging results, improving on previous attempts by Bardossy and colleagues in the late 1980's.