Title: Spatial point processes
Authors: Janine Illian - University of Glasgow (United Kingdom) [presenting]
Abstract: In recent years point process methodology has become increasingly familiar to applied users. Spatial point processes have been originally developed within mathematical statistics as stochastic processes that have spatial point patterns as realisations. Nowadays, there has been a shift towards using them as a tool for modelling the locations of objects or events in space (and time) in practical scientific applications. This shift implies a change in the aims of the statistical analysis and in the focus of the associated statistical research. Within mathematical statistics, point processes form part of stochastic geometry and hence the aim is to define mathematically tractable processes that best mimic the geometric properties of a certain type of point pattern. In the context of applied statistics, however, the main aim of a modelling exercise is to answer scientific questions. Hence appropriate inference, model interpretation and model assessment are of primary concern. We explore this shift in focus, reviews recent progress in making point process methodology more relevant in practice and highlights opportunities for research. In the light of this, we discuss issues concerning model assumptions, model construction and model assessment and draw on a number of concrete examples from ecology and beyond for illustration.