Inference for cluster point processes with over- or under-dispersed cluster sizes
Journal article, 2020

Cluster point processes comprise a class of models that have been used for a wide range of applications. While several models have been studied for the probability density function of the offspring displacements and the parent point process, there are few examples of non-Poisson distributed cluster sizes. In this paper, we introduce a generalization of the Thomas process, which allows for the cluster sizes to have a variance that is greater or less than the expected value. We refer to this as the cluster sizes being over- and under-dispersed, respectively. To fit the model, we introduce minimum contrast methods and a Bayesian MCMC algorithm. These are evaluated in a simulation study. It is found that using the Bayesian MCMC method, we are in most cases able to detect over- and under-dispersion in the cluster sizes. We use the MCMC method to fit the model to nerve fiber data, and contrast the results to those of a fitted Thomas process.

Thomas process

Markov chain Monte Carlo

Neyman-Scott point process

Bayesian estimation

Minimum contrast estimation

Generalized Poisson distribution


Claes Andersson

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

University of Gothenburg

Tomas Mrkvicka

University of South Bohemia

Statistics and Computing

0960-3174 (ISSN) 1573-1375 (eISSN)

Vol. 30 6 1573-1590

Subject Categories

Other Computer and Information Science

Probability Theory and Statistics

Control Engineering



More information

Latest update