Strategies for Speeding Markov Chain Monte Carlo Algorithms

Markov chain Monte Carlo (MCMC) methods have become popular as a basis for drawing inference from complex statistical models. Two common diiculties with MCMC algorithms are slow convergence and long run-times, which are often closely related. Algorithm convergence can often be aided by careful tuning of the chain's transition kernel. In order to preserve the algorithm's stationary distribution, however, care must be taken when updating a chain's transition kernel based on that same chain's history. In this paper we introduce a technique that allows the transition kernel to be updated at user speciied intervals, while preserving the chain's stationary distribution. This technique may be beneecial in aiding both the rate of convergence (by allowing adaptation of the transition kernel) and the speed of computing. The approach is particularly helpful when calculation of the full conditional (for a Gibbs algorithm) or of the candidate distribution (for a Metropolis-Hastings algorithm) is computationally expensive.