The conditional Boolean model revisited (Q2719835)

Markov chain Monte Carlo methods have established as an essential tool for statistical physics and spatial statistics. A difficult problem is to decide for how long to run the Markov chain in order to produce a sample whose distribution is sufficiently close to the target distribution. The so-called perfect simulation methods solve this problem. One of the most important perfect simulation methods is the coupling from the past which was introduced by \textit{J. G. Propp} and \textit{D. B. Wilson} [Random Struct. Algorithms 9, No. 1/2, 223-252 (1996; Zbl 0859.60067)]. In this paper different coupling from the past algorithms that have been developed for the conditional Boolean model are described. In particular, it is shown how to exploit the idea of ancestor sets to produce a perfect sample.