A design utility approach for preferentially sampled spatial data

Spatial preferential sampling occurs when the choice of sampling locations depends stochastically on the process of interest. Ignoring this dependence leads to inaccurate inferences. Our framework models experimenter preferences jointly with the spatial process to adjust for this. We dispense with the unrealistic assumption (required by existing methods) of conditional independence of sampling locations by defining a whole design distribution proportional to a utility function on the space of designs. The proposed model likelihood is generally intractable. We provide fitting techniques based on the noisy Markov chain Monte Carlo and demonstrate their usage on a data set of spatially distributed ammonia concentrations.