ABSTRACT
Most standard spatial analyses assume stationarity, i.e. that the generative process producing the observed pattern is spatially homogenous, and hence its features are independent of absolute spatial locations. Under this assumption, if we wish to describe the distribution of a settlement pattern as a point process, we consider the degree of clustering or dispersion to be the same across the study region. Similarly, if we seek to measure the extent of spatial autocorrelation in our data, the assumption is that spatial dependence is homogenous across space and, hence, that a single global statistic is sufficient to describe the entirety of the phenomena of interest.
In many archaeological contexts the chances of violating the assumption of stationarity is high, and consequently global statistics are often likely to hinder the detection of meaningful outliers and deviations. With study regions increasingly covering larger spatial extents, there is in fact a higher probability that multiple generative processes coexist and differ in their magnitude in different parts of the study area. In these situations, the alternatives are appropriate partitioning of the study area into homogenous sub-regions, or the adoption of local spatial analyses, a suite of techniques that can highlight how relationships vary over space. This chapter will review archaeological applications of the latter as a powerful alternative to the more commonly adopted global spatial analysis.
