Convergence measure and some parallel aspects of Markov-chain Monte Carlo algorithms

We examine methods to assess the convergence of Markov chain Monte Carlo (MCMC) algorithms and to accelerate their execution via parallel computing. We propose a convergence measure based on the deviations between simultaneously running MCMC algorithms. We also examine the acceleration of MCMC algorithms when independent parallel sampler are used and report on some experiments with coupled samplers. As applications we use small Ising model simulations and a larger medical image processing algorithm.