# Spatial Sampling Design for Trans-Gaussian Kriging.

Gunter SpĂ¶ck^{*}

Very often the distribution of spatial variables is skew; rainfall is one such example. Transformed-Gaussian kriging can deal with such skew spatial variables. Unfortunately, concerning spatial sampling design, - the (optimal) selection of spatial coordinates for taking samples -, almost no literature is available for skew spatial variables.$\\$ This talk will present an approach to spatial sampling design with Box-Cox transformed spatial random fields. Our methodology is based on an approximation of the investigated random field by means of a large regression model with stochastic coefficients deriving from the well-known spectral decomposition theorem for isotropic random fields. Classical Fedorov-type exchange algorithms are then used for calculating spatial sampling designs. As design criterion we will try to minimize the average of the expected lengths of 95-percent predictive intervals. The criterion takes the fact that the covariance function is uncertain and estimated by restricted maximum likelihood into account. Contrary to designs for Gaussian kriging spatial sampling designs for transformed-Gaussian kriging are dependent also on available data.$\\$ Our findings are illustrated by means of designing a rainfall monitoring network for Upper Austria.

Mathematics Subject Classification: 62K05

Keywords: Geostatistics; trans-Gaussian Kriging; Spatial Sampling Design; Experimental Design

Minisymposion: Optimal Design of Spatio-Temporal Networks and Systems