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Model-based geostatistical design involves the selection of locations tocollect data to minimise an expected loss function over a set of all possiblelocations. The loss function is specified to reflect the aim of datacollection, which, for geostatistical studies, could be to minimise theprediction uncertainty at unobserved locations. In this paper, we propose a newapproach to design such studies via a loss function derived through consideringthe entropy about the model predictions and the parameters of the model. Theapproach also includes a multivariate extension to generalised linear spatialmodels, and thus can be used to design experiments with more than one response.Unfortunately, evaluating our proposed loss function is computationallyexpensive so we provide an approximation such that our approach can be adoptedto design realistically sized geostatistical studies. This is demonstratedthrough a simulated study and through designing an air quality monitoringprogram in Queensland, Australia. The results show that our designs remainhighly efficient in achieving each experimental objective individually,providing an ideal compromise between the two objectives. Accordingly, weadvocate that our approach could be adopted more generally in model-basedgeostatistical design.

Bayesian design for minimising prediction uncertainty in bivariate spatial responses with applications to air quality monitoring