Mark Huber Publications

Likelihood based inference for Matérn type III repulsive point processes
M. L. Huber and R. L. Wolpert, Advances in Applied Probability, to appear.

Abstract: 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. He 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 mehtod 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;point process;thinning; underdispersed

2000 Mathematics Subject Classification: Primary 65C60, Secondary 62M30;68U20

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