GEOSTATISTICAL INFERENCE UNDER PREFERENTIAL SAMPLING

Geostatistics involves the fitting of spatially continuous models to spatially discrete data (Chil`es and Delfiner, 1999). Preferential sampling arises when the process that determines the data-locations and the process being modelled are stochastically dependent. Conventional geostatistical methods assume, if only implicitly, that sampling is non-preferential. However, these methods are often used in situations where sampling is likely to be preferential. For example, in mineral exploration samples may be concentrated in areas thought likely to yield high-grade ore. We give a general expression for the likelihood function of preferentially sampled geostatistical data and describe how this can be evaluated approximately using Monte Carlo methods. We present a model for preferential sampling, and demonstrate through simulated examples that ignoring preferential sampling can lead to seriously misleading inferences. We describe an application of the model to a set of bio-monitoring data from Galicia, northern Spain, in which making allowance for preferential sampling materially changes the inferences.

Bayesian Geostatistical Design

This paper describes the use of model-based geostatistics for choosing the optimal set of sampling locations, collectively called the design, for a geostatistical analysis. Two types of design situations are considered. These are retrospective design, which concerns the addition of sampling locations to, or deletion of locations from, an existing design, and prospective design, which consists of choosing optimal positions for a new set of sampling locations. We propose a Bayesian design criterion which focuses on the goal of efficient spatial prediction whilst allowing for the fact that model parameter values are unknown. The results show that in this situation a wide range of inter-point distances should be included in the design, and the widely used regular design is therefore not the optimal choice.