Point pattern analysis

Lee De Cola's Wikipedia page.

Point Pattern Analysis

PPA is the study of the spatial arrangements of points in (usually 2-dimensional) space. The simplest formulation is a set X = {x in D} where D is a subset of Rⁿ, an coordinate system.

Four point patterns

Description

The easiest way to visualize a 2-D point pattern is a map of the locations, which is simply a scatterplot but with the provision that the axes are equally scaled. If D is not the boundary of the map then it should also be indicated.

Modeling

The null model for point patterns is complete spatial randomness, modeled as a Poisson process in Rⁿ, which implies that the number of points in any arbitrary region A in D will be proportional to the area of A.

Inference

A fundamental problem of PPA is inferring whether a given arrangement is merely random or the result of some process. The picture illustrates patterns of 256 points using four point processes. The clustered process results in all points having the same location.

References

Cressie, N. A. C. and C. K. Wikle (2011) Statistics for spatio-temporal data. Hoboken, N.J., Wiley. ISBN 9780471692744