Strategies for speeding Markov chain Monte.pdfVIP

Strategies for speeding Markov chain MonteCarlo algorithms by Antonietta MIRA1 and Daniel J. SARGENT2University of Insubria, Varese, Italy1; Mayo Clinic, Rochester, MN2AbstractMarkov chain Monte Carlo (MCMC) methods have become popular as a basisfor drawing inference from complex statistical models. Two common dicultieswith MCMC algorithms are slow convergence and long run-times, which are of-ten closely related. Algorithm convergence can often be aided by careful tuningof the chains transition kernel. In order to preserve the algorithms stationarydistribution, however, care must be taken when updating a chains transitionkernel based on that same chains history. In this paper we introduce a tech-nique that allows the transition kernel to be updated at user speci ed intervals,while preserving the chains stationary distribution. This technique may bebene cial in aiding both the rate of convergence (by allowing adaptation of thetransition kernel) and the speed of computing. The approach is particularlyhelpful when calculation of the full conditional (for a Gibbs algorithm) or of thecandidate distribution (for a Metropolis-Hastings algorithm) is computationallyexpensive. 1 1 IntroductionMarkov chain Monte Carlo (MCMC) methods have become popular as a basisfor drawing inference from complex statistical models. Two common dicultieswith MCMC algorithms are slow convergence and long run-times, which areoften closely related. Inference based on the output of a slowly convergingalgorithm may require many iterations (thousands, tens of thousands, or more)to be valid, which can be problematic due to the length of time required torun such an algorithm and the storage space needed for the output. Long run-times are also common in high dimensional problems, where the sheer number ofrequired calculations manifests itself in excessive computing time. These issueshave important implications for the use of these methods in everyday practice.Multiple authors have suggested approaches