Summary: Resampling from the past to improve on MCMC
Yves F. Atchad´e
(Dec. 2007, First version May 2006)
Abstract: We explore two strategies that resample from previously sampled observations
in a Markov Chain Monte Carlo algorithm. In one strategy the MCMC sampler reuses its
own past. We show that in general this strategy generates a sampler with slower mixing. We
propose another strategy based on multiple chains where some of the chains reuse past sam-
ples generated by other chains. This latter algorithm is related to the Equi-Energy sampler
of . We show by examples that this strategy yields a viable Monte Carlo methods with
mixing properties similar to those of the Equi-Energy sampler.
AMS 2000 subject classifications: Primary 60C05, 60J27, 60J35, 65C40.
Keywords and phrases: Monte Carlo methods, Adaptive MCMC, Importance resampling,
Stochastic volatility models.
Markov Chain Monte Carlo (MCMC) methods have become the standard computational tool for
bayesian inference. But the great flexibility of the method comes with a price. Namely, it is very
difficult to determine whether a given MCMC sampler can mix or has mixed in a given computing
time. Given this limitation, there is a lot of interest in developing new algorithms with improved
mixing and convergence properties.