Exact sampling with highly uniform point sets

In 1996, Propp and Wilson came up with a remarkably clever method for generating exact samples from the stationary distribution of a Markov chain [17]. Their method, called “perfect sampling” or “exact sampling” avoids the inherent bias of samples that are generated by running the chain for a large but fixed number of steps. It does so by using a strategy called “coupling from the past”. Although the sampling mechanism used in their method is typically driven by independent random points, more structured sampling can also be used. Recently, Craiu and Meng [4, 5] suggested to use different forms of antithetic coupling for that purpose. In this paper, we consider the use of highly-uniform point sets to drive the exact sampling in Propp and Wilson’s method, and illustrate the effectiveness of the proposed method with a few numerical examples. ∗Corresponding author