Geospatial uncertainties: a focus on intervals and spatial models based on inverse distance weightin

Processing geospatial data requires to manage many sources of uncertainties; some appear in classical inference problems, some others are specific to this setting. The goal of this work is to study the management of these uncertainties via standard intervals and sets when the inference model considered relies on inverse distance weighting as it is with ordinary kriging the most used method of interpolation. We provide a general discussion with examples, together with a study of the associated optimisation problems induced by different sources of uncertainty. We conclude by an illustration on a semi-synthetic use case, generated according to data recorded via real studies.