A review of spatial sampling

The main aim of spatial sampling is to collect samples in 1-, 2- or 3-dimensional space. It is typically used to estimate the total or mean for a parameter in an area, to optimize parameter estimations for unsampled locations, or to predict the location of a movable object. Some objectives are for 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 independent and identically distributed (i.i.d.) data from a population in conventional sampling. The uncertainty for spatial sample estimation propagates along a chain from spatial variation in the stochastic field to sample distribution and statistical tools used to obtain an estimate. This uncertainty is measured using either a design-based or modelbased method. Both methods can be used in population and superpopulation studies. 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 to obtain a restricted objective function.