University of Bristol - Department of Mathematics
Propp and Wilson (Random structures and Algorithms, 1996) described a protocol, called coupling from the past, that allows us to organise a Markov chain Monte Carlo simulation so that it yields EXACTLY a sample from its limiting distribution (after a random but finite time). Current applications of this idea are to large but discrete physical systems: what possibilities does this idea open up for Bayesian computation? I will present methods for extending coupling from the past to various MCMC samplers on a continuous state space; rather than following the monotone sampling device of Propp and Wilson, our approach uses methods related to gamma-coupling and rejection sampling to simulate the chain, and direct accounting of sample paths. I will touch on the possibilities for automating the process to avoid the cumbersome algebra currently needed.
This is joint work with Duncan Murdoch (Queens University, Canada).