Accounting for Preferential Sampling in Geostatistical Inference

In geostatistical inference, preferential sampling takes place when the locations of point‐referenced data are related to the latent spatial process of interest. Traditional geostatistical models can lead to biased inferences and predictions under preferential sampling. We introduce an extended Bayesian hierarchical framework that models both the observed locations and the responses jointly, using a spatial point process for the locations and a geostatistical process for the responses. We illustrate extensions beyond the classical log‐Gaussian Cox process for the sampling locations, combined with a Gaussian process for the responses. We also introduce simpler methods for accounting for preferential sampling that are less computationally demanding at the expense of prediction accuracy. We validate our models through simulation, demonstrating their effectiveness in correcting biases and improving prediction accuracy. We apply our models to decadal average temperature data from the Global Historical Climate Network in the Southwestern United States and show that preferential sampling could be present in some spatial regions.