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

Abstract

The problem of choosing spatial sampling designs for investigating an unobserved spatial phenomenon scriptS 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 scriptD. We studied randomized inhibitory spatial sampling designs to address the problem of spatial prediction while 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 disk of radius ζ. We present simulation results for the Matérn 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, 5‐year malaria transmission reduction project in Malawi.

Improved spatial ecological sampling using open data and standardization: an example from malaria mosquito surveillance

“…The effect of strong autocorrelation can reduce the overall statistical power (and the overall biological significance of the study) as it results in effectively a lower sample size (because the assumption of independence is violated), underestimates of variance, and increases in type I error (10). Geostatistical approaches, such as the one applied here (8,62), can lead to unbiased estimates of population parameters and avoid the risks and limitations of random, or haphazard, selection of sampling locations (10). Given the requirements to satisfy both parameterization and predictions (59), the simulated inhibitory design adapted from (62) in order to contain clusters of households at each sampling point, has shown that with 120 sampling houses for each site distributed across 30 sampling points, we achieve the same prediction error (main goal) as from 200 points allocated at random, albeit at the expense of parameter accuracy.…”

“…In Migori alone (where a previous sampling campaign, AIRS, took place) an adaptive sampling design was trialled in which AIRS sampling served to inform the location of the M sampling points. From the LGCP model (see above), we estimated the prediction variances at each grid cell, and attributed the M locations to the cells with highest prediction variance (27,(62)(63)(64).…”

Bayesian model based spatiotemporal survey designs and partially observed log Gaussian Cox process

“…The problem of finding an optimal design for spatial prediction when the observation process is Gaussian has received much interest in spatial statistics (e.g., Müller, 1999;Müller, 2001;Diggle and Lophaven, 2006). What has been left for lesser attention are spatiotemporal designs and designs for models with non-Gaussian observation processes (see Chipeta et al, 2016Chipeta et al, , 2017. In this work, we study observational designs for spatiotemporal log-Gaussian Cox processes (LGCPs).…”

“…Common methods to approximate these include Monte Carlo simulation (Robert, 2004;Vlachos and Gelfand, 1996;Chipeta et al, 2016) or a series of simulated annealing algorithms (Van Groenigen and Stein, 1998;Müller, 1999). Alternatively, many authors such as Müller (2001), Müller (2007), Ryan et al (2016) and Chipeta et al (2017) have aimed at developing spatially balanced designs that increase expected utility for a given class of spatial models over that of uniform random designs. In these approaches, the computation of the utility is a minor task since the expected utility of the candidate designs has to calculated only once.…”

“…Quasi-random methods use quasi-random number generators such as the Sobol and Halton sequence to generate balanced and well-distributed designs. Distance-based designs are deterministic algorithms that aim to produce space filling designs by restricting the minimum distance between any two sampling locations (Chipeta et al, 2017;Russo, 1984;Royle and Nychka, 1998). Sampling locations in the above mentioned designs are commonly selected with equal probability.…”