Preferential sampling and Bayesian geostatistics: Statistical modeling and examples

Preferential sampling refers to any situation in which the spatial process and the sampling locations are not stochastically independent. In this paper, we present two examples of geostatistical analysis in which the usual assumption of stochastic independence between the point process and the measurement process is violated. To account for preferential sampling, we specify a flexible and general Bayesian geostatistical model that includes a shared spatial random component. We apply the proposed model to two different case studies that allow us to highlight three different modeling and inferential aspects of geostatistical modeling under preferential sampling: (1) continuous or finite spatial sampling frame; (2) underlying causal model and relevant covariates; and (3) inferential goals related to mean prediction surface or prediction uncertainty.