Statistics and Computing

, Volume 12, Issue 3, pp 229–243

# Perfect simulation for correlated Poisson random variables conditioned to be positive

• Yuzhi Cai
• Wilfrid S. Kendall
Article

## Abstract

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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