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Inhibitory geostatistical designs for spatial prediction taking account of uncertain covariance structure

The problem of choosing spatial sampling designs for investigating unobserved spatial phenomenon S arises in many contexts, for example in identifying households to select for a prevalence survey to study disease burden and heterogeneity in a study region D. We studied randomised inhibitory spatial sampling designs to address the problem of spatial prediction whilst taking account of the need to estimate covariance structure. Two specific classes of design are inhibitory designs and inhibitory designs plus close pairs. In an inhibitory design, any pair of sample locations must be separated by at least an inhibition distance {$δ$}. In an inhibitory plus close pairs design, n - k sample locations in an inhibitory design with inhibition distance {$δ$} are augmented by k locations each positioned close to one of the randomly selected n - k locations in the inhibitory design, uniformly distributed within a disc of radius {$ζ$}. We present simulation results for the Matern class of covariance structures. When the nugget variance is non-negligible, inhibitory plus close pairs designs demonstrate improved predictive efficiency over designs without close pairs. We illustrate how these findings can be applied to the design of a rolling Malaria Indicator Survey that forms part of an ongoing large-scale, five-year malaria transmission reduction project in Malawi.