A review of spatial sampling

Spatial sampling has as its major aim to collect samples in 1-, 2- or 3-dimensional space. It usually targets at the estimation of the total or mean of value in an area, to optimize estimation of values at unsampled locations, or to predict the location of a movable object. Some of the objectives are about populations, representing the “here and now”, whereas other objectives concern superpopulations that generate the populations. Data to be collected are usually spatially autocorrelated and heterogeneous, whereas sampling is usually not repeatable. In various senses it is distinct from the assumption of iid data from a population in conventional sampling. The uncertainty of spatial sample estimation propagates along a chain from spatial variation at the stochastic field, to distribution of a sample and a statistic to obtain an estimate. This uncertainty is measured by either a design or a model based method. Both methods can be used in population and superpopulation studies. The target to obtain an unbiased estimate with the lowest variance is thus a common goal in spatial sampling and inference. Reaching this objective can be addressed by sample allocation in an area in order to reach a restricted objective function.