Perfect sampling without a lifetime commitment

Generating perfect samples from distributions using Markov chains has a wide range of applications , from statistical physics to approximation algorithms. In perfect sampling algorithms, a sample is drawn exactly from the stationary distribution of a chain, as opposed to methods that run the chain \for a long time" and create samples drawn from a distribution that is close to the stationary distribution. One of the primary methods for creating perfect samples, the coupling from the past protocol of Propp and Wilson, suuers from the fact that the user must be willing to commit to running the algorithm in its entirety in order to obtain unbiased, perfect samples. By using another method, the acceptance rejection method of Fill, Murdoch, and Rosenthal (FMR), the user may abort the procedure in the middle of a run without introducing bias. In this paper, we give the rst general analysis of the running time of FMR compared to the running time of of CFTP. Furthermore, we show that FMR can be used to generate a strong stationary stopping time of a Markov chain. We show how to use FMR to generate perfect sampling algorithms for two real world examples, the hard core gas model and the Widom-Rowlinson mixture model. These two examples illustrate the techniques needed to apply FMR to a wide range of discrete and innnite state space chains.