Convergence of concurrent Markov chain Monte-Carlo algorithms

We examine the parallel execution of a class of stochastic algorithms called Markov chain Monte-Carlo (MCMC) algorithms, We focus on MCMC algorithms in the context of image processing, using Markov random field models, Our parallelisation approach is based on several, concurrently running, instances of the same stochastic algorithm that deal with the whole data set, Firstly we show that the speed-up of the parallel algorithm is limited because of the statistical properties of the MCMC algorithm, We examine coupled MCMC as a remedy for this problem, Secondly, we exploit the parallel execution to monitor the convergence of the stochastic algorithms in a statistically reliable manner, This new convergence measure for MCMC algorithms performs well, and is an improvement on known convergence measures. We also link our findings with recent work in the statistical theory of MCMC.