  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, could be to minimise the
prediction uncertainty at unobserved locations. In this paper, we propose a new
approach to design such studies via a loss function derived through considering
the entropy about the model predictions and the parameters of the model. The
approach also includes a multivariate extension to generalised linear spatial
models, and thus can be used to design experiments with more than one response.
Unfortunately, evaluating our proposed loss function is computationally
expensive so we provide an approximation such that our approach can be adopted
to design realistically sized geostatistical studies. This is demonstrated
through a simulated study and through designing an air quality monitoring
program in Queensland, Australia. The results show that our designs remain
highly efficient in achieving each experimental objective individually,
providing an ideal compromise between the two objectives. Accordingly, we
advocate that our approach could be adopted more generally in model-based
geostatistical design.
