Geostatistical analysis under preferential sampling

In geostatistics it is commonly assumed that the selection of the sampling locations does not depend on the values of the spatial variable. One has preferential sampling when this assumption fails (e.g. maximum values search). We first show that the impact of a preferential design on the traditional prediction methods is not negligible. We address this problem by proposing a model-based approach, for stationary Gaussian processes. This new parametric model is founded on a flexible class of log-Gaussian Cox processes. A numerical study is then included to compare the performance of the model proposed and the traditional geostatistical model