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Thinning spatial point processes into Poisson processes

  • Jesper Møller (a1) and Frederic Paik Schoenberg (a2)

Abstract

In this paper we describe methods for randomly thinning certain classes of spatial point processes. In the case of a Markov point process, the proposed method involves a dependent thinning of a spatial birth-and-death process, where clans of ancestors associated with the original points are identified, and where we simulate backwards and forwards in order to obtain the thinned process. In the case of a Cox process, a simple independent thinning technique is proposed. In both cases, the thinning results in a Poisson process if and only if the true Papangelou conditional intensity is used, and, thus, can be used as a graphical exploratory tool for inspecting the goodness-of-fit of a spatial point process model. Several examples, including clustered and inhibitive point processes, are considered.

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Copyright

Corresponding author

Postal address: Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, DK-9220 Aalborg, Denmark.
∗∗ Postal address: Department of Statistics, 8125 Math-Science Building, University of California, Los Angeles, CA 90095-1554, USA. Email address: frederic@stat.ucla.edu

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Thinning spatial point processes into Poisson processes

  • Jesper Møller (a1) and Frederic Paik Schoenberg (a2)

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