Statistical Models and Methods for Spatial Point Processes

Course
5 – 8 February, 2017, Les Diablerets, Switzerland
Abstract:
Rasmus Waagepetersen gives a PhD-course on spatial point processes 5 – 8 February 2017 in Les Diablerets, Switzerland. The course is part of a winterschool, organized by Yves Tillé. For more information about the winterschool, see https://statistique.cuso.ch/index.php?id=2688&tx_displaycontroller[showUid]=3302.


Summary of lectures

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) or size of associated object (e.g. the diameter of a tree at breast height).

In the lectures we will cover the following spatial point process topics:

  • First and second order characteristics of spatial point processes: this includes summary statistics such as the intensity-, pair correlation and K-function.
  • The Poisson process: the Poisson process is the basic model for point patterns with absence of interaction between points. It is of great interest in its own right and is furthermore the basic building block for construction of more flexible models allowing interactions between points.
  • Cox and cluster point processes: in many applications, clustering between points prevents the use of a Poisson process model. In such cases Cox and cluster point process models are useful alternatives.
  • Estimating functions for spatial point processes: we discuss non-parametric estimation of the K-function as well as estimation for parametric Poisson, Cox and cluster point process models.
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Revised 03.06.2016