Statistics and Computing

, Volume 12, Issue 3, pp 229–243 | Cite as

Perfect simulation for correlated Poisson random variables conditioned to be positive

  • Yuzhi Cai
  • Wilfrid S. Kendall


In this paper we present a perfect simulation method for obtaining perfect samples from collections of correlated Poisson random variables conditioned to be positive. We show how to use this method to produce a perfect sample from a Boolean model conditioned to cover a set of points: in W.S. Kendall and E. Thönnes (Pattern Recognition 32(9): 1569–1586, 1999), this special case was treated in a more complicated way. The method is applied to several simple examples where exact calculations can be made, so as to check correctness of the program using χ2-tests, and some small-scale experiments are carried out to explore the behaviour of the conditioned Boolean model.

Markov chain Monte Carlo perfect simulation dominated CFTP extended state-space CFTP correlated Poisson random variables conditioned to be positive conditional Boolean model 


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© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Yuzhi Cai
  • Wilfrid S. Kendall

There are no affiliations available

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