  Preferential sampling is a common feature in geostatistics and occurs when
the locations to be sampled are chosen based on information about the phenomena
under study. In this case, point pattern models are commonly used as the
probability law for the distribution of the locations. However, analytic
intractability of the point process likelihood prevents its direct calculation.
Many Bayesian (and non-Bayesian) approaches in non-parametric model
specifications handle this difficulty with approximation-based methods. These
approximations involve errors that are difficult to quantify and can lead to
biased inference. This paper presents an approach for performing exact Bayesian
inference for this setting without the need for model approximation. A
qualitatively minor change on the traditional model is proposed to circumvent
the likelihood intractability. This change enables the use of an augmented
model strategy. Recent work on Bayesian inference for point pattern models can
be adapted to the geostatistics setting and renders computational tractability
for exact inference for the proposed methodology. Estimation of model
parameters and prediction of the response at unsampled locations can then be
obtained from the joint posterior distribution of the augmented model.
Simulated studies showed good quality of the proposed model for estimation and
prediction in a variety of preferentiality scenarios. The performance of our
approach is illustrated in the analysis of real datasets and compares
favourably against approximation-based approaches. The paper is concluded with
comments regarding extensions of and improvements to the proposed methodology.
