Point Pattern Analysis on a Sphere.

Statistical methods for analysing spatial data are important in many areas of science. In particular, the theory of point processes has been extensively developed for complete separable metric spaces, especially for R. This thesis develops theory, models and methods for point processes on a sphere. Although we can adapt some of the existing general theory, models and methods for point processes to the sphere, there are instances where we need to take a different approach to take into account some of the specific properties of the sphere. The theory that we consider includes basic properties, moment measures, Campbell theorems and Palm theory. The models that we explore include Poisson, Cox, Matérn inhibition, Poisson cluster and Gibbs processes. We define and examine the properties of various summary functions and their estimators. We also discuss methods of plotting summary functions for point processes, estimating their intensities, fitting Poisson and Neyman-Scott models and examining the goodness-of-fit of models. Finally, we demonstrate the methods introduced in this thesis through the analysis of some simulated datasets and a galaxy dataset. A package of R code, called spherstat, has been developed as part of these studies.