Explaining the perfect sampler

In 1996, Propp and Wilson introduced coupling from the past (CFTP), an algorithm for generating a sample from the exact stationary distribution of a Markov chain. In 1998, Fill proposed another so-called perfect sampling algorithm. These algorithms have enormous potential in Markov Chain Monte Carlo (MCMC) problems because they eliminate the need to monitor convergence and mixing of the chain. This article provides a brief introduction to the algorithms, with an emphasis on understanding rather than technical detail.