Perfect sampling from independent Metropolis-Hastings chains

Abstract

“Perfect sampling” enables exact draws from the invariant measure of a Markov chain. We show that the independent Metropolis-Hastings chain has certain stochastic monotonicity properties that enable a perfect sampling algorithm to be implemented, at least when the candidate is overdispersed with respect to the target distribution. We prove that the algorithm has an optimal geometric convergence rate, and applications show that it may converge extreme rapidly.