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  • On the conditional distributions of spatial point processes

  • Part of
  • François Caron, Pierre Del Moral, Arnaud Doucet, Michele Pace
  • Journal:
    Advances in Applied Probability / Volume 43 / Issue 2 / June 2011
    Published online by Cambridge University Press:
    01 July 2016, pp. 301-307
    Print publication:
    June 2011
    • Article
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  • We consider the problem of estimating a latent point process, given the realization of another point process. We establish an expression for the conditional distribution of a latent Poisson point process given the observation process when the transformation from the latent process to the observed process includes displacement, thinning, and augmentation with extra points. Our original analysis is based on an elementary and self-contained random measure theoretic approach. This simplifies and complements previous derivations given in Mahler (2003), and Singh, Vo, Baddeley and Zuyev (2009).