title: Bayesian geostatistical modelling with informative sampling locations.
abstract: We consider geostatistical models that allow the locations at which data are collected to be informative about the outcomes. A Bayesian approach is proposed, which models the locations using a log Gaussian Cox process, while modelling the outcomes conditionally on the locations as Gaussian with a Gaussian process spatial random effect and adjustment for the location intensity process. We prove posterior propriety under an improper prior on the parameter controlling the degree of informative sampling, demonstrating that the data are informative. In addition, we show that the density of the locations and mean function of the outcome process can be estimated consistently under mild assumptions. The methods show significant evidence of informative sampling when applied to ozone data over Eastern U.S.A.
authors: Department of Statistical Science, Duke University, 214 Old Chemistry Building, Durham, North Carolina 27708-0251, U.S.A. , dp55@stat.duke.edu.
authors: D
authors: D
authors: Pati
authors: B J
authors: BJ
authors: Reich
authors: D B
authors: DB
authors: Dunson
keywords: Cox process; Gaussian process; Joint model; Point pattern; Posterior consistency; Preferential sampling
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