Kriging and Epistemic Uncertainty: A Critical Discussion

Geostatistics is a branch of statistics dealing with spatial phenomena modelled by random functions. In particular, it is assumed that, under some wellchosen simplifying hypotheses of stationarity, this probabilistic model, i.e. the random function describing spatial dependencies, can be completely assessed from the dataset by the experts. Kriging is a method for estimating or predicting the spatial phenomenon at non sampled locations from this estimated random function. In the usual kriging approach, the data are precise and the assessment of the random function is mostly made at a glance by the experts (i.e. geostatisticians) from a thorough descriptive analysis of the dataset. However, it seems more realistic to assume that spatial data is tainted with imprecision due to measurement errors and that information is lacking to properly assess a unique random function model. Thus, it would be natural to handle epistemic uncertainty appearing in both data specification and random function estimation steps of the kriging methodology. Epistemic uncertainty consists of some meta-knowledge about the lack of information on data precision or on the model variability. The aim of this paper is to discuss the pertinence of the usual random function approach to model uncertainty in geostatistics, to survey the already existing attempts to introduce epistemic uncertainty in geostatistics and to propose some perspectives for developing new tractable methods that may handle this kind of uncertainty.