Analysing highly complex and highly structured point patterns in space

The purpose of this paper is to discuss two recently introduced approaches that focus on structures of different events that occur randomly in space: spatial dependence graph models (SDGMs), and network intensity functions. While SDGMs are undirected graphical models which capture the conditional independence structure between components of multivariate spatial point processes, network intensity functions describe the first-order properties of point patterns that occur on arbitrary network structures.