ABSTRACT
The chapter outlines a Monte Carlo maximum likelihood procedure for parameter estimation under the PRD model. The term preferential sampling was coined by Peter J. Diggle et al. to mean that the process that generates the sampling locations xi is stochastically dependent on the spatial process S(x) that is of scientific interest. A useful exploratory device to look for evidence of preferential sampling is a scatterplot of the response variable against a non-parametric estimate of the sampling density at each measurement location. In any model for a preferentially sampled geostatistical data-set, at least one of the parameters is likely to be poorly identified. Strongly preferential sampling invalidates conventional geostatistical inferences. When analysing observational geostatistical data, investigating whether preferential sampling effects are present is a better strategy than simply ignoring them. Missingness can only be identified when the set of intended sampling locations is specified beforehand.
