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Preferential sampling is a common feature in geostatistics and occurs whenthe locations to be sampled are chosen based on information about the phenomenaunder study. In this case, point pattern models are commonly used as theprobability law for the distribution of the locations. However, analyticintractability of the point process likelihood prevents its direct calculation.Many Bayesian (and non-Bayesian) approaches in non-parametric modelspecifications handle this difficulty with approximation-based methods. Theseapproximations involve errors that are difficult to quantify and can lead tobiased inference. This paper presents an approach for performing exact Bayesianinference for this setting without the need for model approximation. Aqualitatively minor change on the traditional model is proposed to circumventthe likelihood intractability. This change enables the use of an augmentedmodel strategy. Recent work on Bayesian inference for point pattern models canbe adapted to the geostatistics setting and renders computational tractabilityfor exact inference for the proposed methodology. Estimation of modelparameters and prediction of the response at unsampled locations can then beobtained from the joint posterior distribution of the augmented model.Simulated studies showed good quality of the proposed model for estimation andprediction in a variety of preferentiality scenarios. The performance of ourapproach is illustrated in the analysis of real datasets and comparesfavourably against approximation-based approaches. The paper is concluded withcomments regarding extensions of and improvements to the proposed methodology.

Exact Bayesian Inference for Geostatistical Models under Preferential Sampling