Bayesian geostatistical modelling with informative sampling locations

摘要

We consider geostatistical models that allow the locations at which data are collected to beninformative about the outcomes. A Bayesian approach is proposed, which models the locationsnusing a log Gaussian Cox process, while modelling the outcomes conditionally on the locationsnas Gaussian with a Gaussian process spatial random effect and adjustment for the location intensitynprocess. We prove posterior propriety under an improper prior on the parameter controllingnthe degree of informative sampling, demonstrating that the data are informative. In addition, wenshow that the density of the locations and mean function of the outcome process can be estimatednconsistently undermild assumptions. The methods showsignificant evidence of informative samplingnwhen applied to ozone data over Eastern U.S.A.