Methods for preferential sampling in geostatistics

Preferential sampling in geostatistics occurs when the locations at which observations are made may depend on the spatial process that underlines the correlation structure of the measurements. We show that previously proposed Monte Carlo estimates for the likelihood function may not be approximating the desired function. Furthermore, we argue that, for preferential sampling of moderate complexity, alternative and widely available numerical methods to approximate the likelihood function produce better results than Monte Carlo methods. We illustrate our findings on the Galicia data set analysed previously in the literature.