Capturing spatial non-stationarity in kriging models

Description

Kriging implicitly assumes second-order stationarity. In many practical applications, however, the data show strong evidence of a spatially non-stationary covariance structure. Nevertheless practitioners mostly use a stationary spatial model which is a simplification and strong idealization of reality. Ignoring the fact that the spatial dependence structure may vary as a function of location results in poor prediction. If our task is the prediction of all realizations of a field on the basis of only a few measurements and if we have data with spatially varying variance, we should position our design points at locations with high variability. On the other hand a trade-off has to be made between greedy information hunting and non-neglecting large regions with low variation. Using a kriging model generalized for a non-stationary covariance structure this trade-off is made automatically if we use the kriging variance as design criterion. When repeated observations of the spatial process over time are available it is easy to incorporate non-stationarity in the model and the additional computational effort is negligible. A concluding computer simulation experiment based on data provided by the Belgian institute Management Unit of the North Sea Mathematical Models compares the prediction performance of a standard stationary model with the performance of the directly generalized non-stationary model.

Period	21 Oct 2015
Event title	Statistiktage 2015
Event type	Conference
Location	AustriaShow on map