Abstract: |
So far, methodologies for spatial sampling design assume the investigated random field to be Gaussian. Most often the minimization of the kriging variance averaged over the investigated spatial design region is considered as a design criterion. The actual advantage of using this design criterion is that the kriging variance is independent of the actual data values but dependent only on their relative locations. The independence of data values is a result of the Gaussian assumption for the considered random field. If the data follow a skewed distribution, like for example data whose Box-Cox transformation is multivariate Gaussian, the assumption of independence of the design criterion from data values can no longer be held. Kriging with Box-Cox transformed data is also known as trans-Gaussian kriging. We consider as design criterion the average of the expected lengths of 95% predictive intervals from trans-Gaussian kriging and show how sampling designs may be calculated efficiently using recent results of the authors on the approximation of random fields by mixed linear models. To make the computations of such sampling designs faster NVIDIA CUDA technology is used and the design algorithms are implemented in parallel on fast NVIDIA graphical processing units (GPUs). Moreover, both, design criteria taking covariance function estimation by REML into account and not, are investigated. All theoretical findings are illustrated by a practical example taken from a rainfall monitoring network.
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