Spatial Autocorrelation

Spatial autocorrelation is an assessment of the correlation between two random variables which describe the same aspect of the phenomenon under study, referred to two locations of the domain. The suffix “auto” is justified since in some sense the spatial autocorrelation quantifies the correlation of a variable with itself over space. However, the expressions “spatial autocorrelation” and “spatial correlation” are used interchangeably in literature. Most of the theoretical results of classical statistics consider the observed values, as independent realizations of a random variable: this assumption makes the statistical theory much easier. Unfortunately, this last hypothesis cannot be valid if the observations are measured in space (or in time). Historically, the concept of spatial autocorrelation has naturally been considered an extension of temporal autocorrelation: however, time is one- dimensional, and only goes in one direction, ever forward, on the other hand, the physical space has (at least) two dimensions. Any subject which regards data collected at spatial locations, such as soil science, ecology, atmospheric science, geology, image processing, epidemiology, forestry, astronomy, needs suitable tools able to analyze dependence between observations at different locations.