Jopseph B. Kadane, CMU, USA

Title: Identification of Regeneration Times in MCMC Simulation, with Application to Adaptive Schemes

Abstract: Regeneration is a useful tool in Markov chain Monte Carlo simulation, since it can be used to side-step the burn-in problem and to construct better estimates of the variance of parameter estimates themselves. It also provides a simple way to introduce adaptive behaviour into a Markov chain, and to use parallel processors to build a single chain. Regeneration is often di cult to take advantage of, since for most chains, no recurrent proper atom exists, and it is not always easy to use Nummelin s splitting method to identify regeneration times. This paper describes a constructive method for generating a Markov chain with a speci ed target distribution and identifying regeneration times. As a special case of the method, an algorithm which can be  wrapped  around an existing Markov transition kernel is given. In addition, a speci c rule for adapting the transition kernel at regeneration times is introduced, which gradually replaces the original transition kernel with an independence-sampling Metropolis-Hastings kernel using a mixture normal approximation to the target density as its proposal density. Computational gains for the regenerative adaptive algorithm are demonstrated in examples.

Joint work with Anthony Brockwell.