Bayesian design for minimising uncertainty in spatial processes
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Model-based geostatistical design involves the selection of locations to collect data to minimise an expected loss function over a set of all possible locations. The loss function is specified to reflect the aim of data collection, which, for geostatistical studies, would typically be to minimise the uncertainty in a spatial process. In this paper, we propose a new approach to design such studies via a loss function derived through considering the entropy of model predictions, and we show that this simultaneously addresses the goal of precise parameter estimation. One drawback of this loss function is that is it computationally expensive to evaluate, so we provide an efficient approximation such that it can be used within realistically sized geostatistical studies. To demonstrate our approach, we apply the proposed approach to design the collection of spatially dependent multiple responses, and compare this with either designing for estimation or prediction only. The results show that our designs remain highly efficient in achieving each experimental objective individually, and provide an ideal compromise between the two objectives. Accordingly, we advocate that our design approach should be used more generally in model-based geostatistical studies.
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