Spatially-restricted random sampling designs for design-based and model-based estimation

Studying natural resources and environmental problems in most situations requires that information be collected over space and time. Given the typical infeasibility of acquiring data continuously in space, a scheme for site selection is necessary. We focus on probability designs that incorporate randomization in site selection. Traditional designs include simple random sampling, spatially stratified random sampling, and systematic sampling. In some cases, survey designs have constructed a linear ordering of two-dimensional space and then used systematic sampling of the linear ordering to help spread the sample over space. Hierarchial randomization designs explicitly incorporate space in the randomization process. The resulting designs have better spatial properties in their ability to match the spatial pattern of the population being sampled. We provide a comparison of these properties with the traditional designs. We discuss how these designs spatially distribute sites, and how both design-based and model-based statistical inferences can be applied.