Inference for cluster point processes with over- or under-dispersed cluster sizes
Artikel i vetenskaplig tidskrift, 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.

Markov chain Monte Carlo

Neyman-Scott point process

Minimum contrast estimation

Thomas process

Generalized Poisson distribution

Bayesian estimation


Claes Andersson

Chalmers, Matematiska vetenskaper

Tomas Mrkvicka

University of South Bohemia

Statistics and Computing

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

Vol. 30 1573-1590


Annan data- och informationsvetenskap

Sannolikhetsteori och statistik




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