Complete spatial randomness

Abstract: The scan statistic is commonly used to test if a one dimensional point process is purely random, or if any clusters can be detected. Here it is simultaneously extended in three directions:(i) a spatial scan statistic for the detection of clusters in a multi-dimensional point process is proposed, (ii) the area of the scanning window is allowed to vary, and (iii) the baseline process may be any inhomogeneous Poisson process or Bernoulli process with intensity pro-portional to some known function. The main interest is in detecting clusters not explained by the baseline process. These methods are illustrated on an epidemiological data set, but there are other potential areas of application as well.

Abstract: A spatial point pattern is a set of data consisting of a map of points These points might represent, for example, cases of a disease in a human or animal population, or trees in a forest, or cells in a microscopic tissue section This book provides an introduction to statistical methods for analysing data in the form of spatial point distributions Theoretical results are described in intuitive terms and statistical methods are illustrated by many applications to real data drawn from the biological and biomedical sciences

Abstract: spatstat is a package for analyzing spatial point pattern data. Its functionality includes exploratory data analysis, model-fitting, and simulation. It is designed to handle realistic datasets, including inhomogeneous point patterns, spatial sampling regions of arbitrary shape, extra covariate data, and "marks" attached to the points of the point pattern. A unique feature of spatstat is its generic algorithm for fitting point process models to point pattern data. The interface to this algorithm is a function ppm that is strongly analogous to lm and glm. This paper is a general description of spatstat and an introduction for new users.