Capturing spatial non-stationarity in kriging models
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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.