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1 results

  • Thinning spatial point processes into Poisson processes

  • Part of
  • Jesper Møller, Frederic Paik Schoenberg
  • Journal:
    Advances in Applied Probability / Volume 42 / Issue 2 / June 2010
    Published online by Cambridge University Press:
    01 July 2016, pp. 347-358
    Print publication:
    June 2010
    • Article
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  • 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.