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Likelihood-based inference for Matérn type-III repulsive point processes

Part of: Probabilistic methods, simulation and stochastic differential equations Inference from stochastic processes

Published online by Cambridge University Press:  01 July 2016

Mark L. Huber  and
Robert L. Wolpert
Mark L. Huber*
Affiliation:
Duke University
Robert L. Wolpert*
Affiliation:
Duke University
*
∗ Current address: Department of Mathematics and Computer Science, Claremont McKenna College, 850 Columbia Avenue, Claremont, CA 91711, USA. Email address: mhuber@cmc.edu
∗∗ Postal address: Department of Statistical Science and Nicholas School of the Environment, Duke University, Durham, NC 27708-0251, USA. Email address: wolpert@stat.duke.edu
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Abstract

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In a repulsive point process, points act as if they are repelling one another, leading to underdispersed configurations when compared to a standard Poisson point process. Such models are useful when competition for resources exists, as in the locations of towns and trees. Bertil Matérn introduced three models for repulsive point processes, referred to as types I, II, and III. Matérn used types I and II, and regarded type III as intractable. In this paper an algorithm is developed that allows for arbitrarily accurate approximation of the likelihood for data modeled by the Matérn type-III process. This method relies on a perfect simulation method that is shown to be fast in practice, generating samples in time that grows nearly linearly in the intensity parameter of the model, while the running times for more naive methods grow exponentially.

Keywords

Coupling from the pastpoint processthinningunderdispersed

MSC classification

Primary: 65C60: Computational problems in statistics
Secondary: 62M30: Spatial processes 68U20: Simulation
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 41 , Issue 4 , December 2009 , pp. 958 - 977
Copyright
Copyright © Applied Probability Trust 2009 

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