language: en

Perfect Simulation of some Point Processes for the Impatient User

Elke Thonnes
Department of Statistics, University of Warwick
February 9, 1998

Abstract Recently Propp and Wilson [14] have proposed an algorithm, called Coupling from the Past (CFTP), which allows not only an approximate but perfect (i.e. exact) simulation of the stationary distribution of certain finite state space Markov chains. Perfect Sampling using CFTP has been successfully extended to the context of point processes, amongst other authors, by Haggstrom et al. [5]. In [5] Gibbs sampling is applied to a bivariate point process, the penetrable spheres mixture model [19]. However, in general the running time of CFTP in terms of number of transitions is not independent of the state sampled. Thus an impatient user who aborts long runs may introduce a subtle bias, the user impatience bias. Fill [3] introduced an exact sampling algorithm for finite state space Markov chains which, in contrast to CFTP, is unbiased for user impatience. Fill's algorithm is a form of rejection sampling and similar to CFTP requires sufficient mono-tonicity properties of the transition kernel used. We show how Fill's version of rejection sampling can be extended to an infinite state space context to produce an exact sample of the penetrable spheres mixture process and related models. Following [5] we use Gibbs sampling and make use of the partial order of the mixture model state space. Thus

[Research supported by EPSRC earmarked studentship and University of Warwick graduate award. Postal address:]

Dept. of Statistics, University of Warwick,
Coventry, CV4 7AL, UK