Exact Simulation and Error-Controlled Sampling via Regeneration and a Bernoulli Factory

Methods using regeneration have been used to draw approximations to the stationary distribution of Markov Chain Monte Carlo processes. We introduce an algorithm that allows exact sampling of the stationary distribution through the use of a regeneration method and a Bernoulli Factory to select samples within each regeneration cycle that are shown to be from the desired density. We demonstrate the algorithm on a probit model Markov Chain using a known data set for comparison to other approximate methods.