Mark L. Huber & Robert L. Wolpert

Duke University

Revised March 2009

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 approaches to modeling repulsive point processes, and used Types I and II. The third he regarded 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 simulatin 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 past; overdispersed; point process; thinning.

The manuscript is available in PDF (383 kb) format. To appear in Advances in Applied Probability.

Cite as:

@Article{Hube:Wolp:2009,
      Author = "Mark L. Huber and Robert L. Wolpert", 
       Title = "Likelihood-based inference for {M}at{\'e}rn Type~{III}
                  Repulsive Point Processes",
     Journal = "Advances in Applied Probability",
      Volume = 41,
      Number = 4,
        Note = "958--977",
        Year = 2009,
}