LIKELIHOOD-BASED INFERENCE FOR MAT´ ERN TYPE III RE- PULSIVE POINT PROCESSES

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 Matern 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 Matern 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.

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