Course information

A spatial point process is a mathematical model for randomly distributed points in two or higher dimensional space, e.g. the locations of restaurants in a city, trees in a forest, cases of a disease in a country or galaxies in the Universe. The model may be extended to include information about covariates such as soil conditions in case of trees and random `marks´ such as `types of points´ (e.g. different types of restaurants or species of trees), `size of associated object´ (e.g. the diameter of a tree at breast height) or `direction of associated object´ (e.g. the direction from the center of a brain cell to its apex). Fig. 1 shows three. While the mathematical theory for point processes on two or higher dimensional Euclidean space is fairly well-developed with accompanying user-friendly software for statistical analysis, notably the R package spatstat, the research on point processes defined on more general spaces such as linear networks and the sphere is in its infancy. The theory for marked point processes is also less developed. The extension to space-time point processes gives rise to further basic research problems.

Fig. 1: (a) locations of Western-style and Chinese restaurants in Beijing.  (b) pyramidal brain cells’ nucleolus locations and their directions. (c) spine locations on a dendrite network of neurons. 

The summer school provides an state-of-the-art introduction to statistics for point patterns in first Euclidean space and second on the sphere and linear networks. Along with this relevant software using the spatstat package will be introduced. Furthermore, two separate topics will be treated: statistics for space-time processes and topological tools for analyzing point patterns.

The lectures will be given by five members of the spatial point process group at Department of Mathematical Sciences, Aalborg University, which is recognized as an international leading group at the forefront of development of spatial point process theory and its applications. Professors Jesper Møller (JM) and Rasmus Waagepetersen (RW) have contributed with a number of influential papers and a research monograph which is a key reference. Associate Professor Jakob G. Rasmussen (JGR) is a specialist on spatial and temporal point processes, Associate Professor Ege Rubak (ER) has a strong background in computational methods for spatial point processes and is a co-author of a recent monograph about spatstat, and Associate Professor Christophe A.N. Biscio (CB) works with topological data analysis methods for spatial point processes.

Prerequisites: Basic knowledge in probability theory and mathematical statistics. Some knowledge about spatial statistics/point processes will be an advantage but is not requested.