<title>Convergence measure and some parallel aspects of Markov-chain Monte Carlo algorithms</title>

Abstract

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 samplers 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.

Convergence of concurrent Markov chain Monte-Carlo algorithms

“…For Boltzmann probabilities, the sum of prior and conditional potentials thus forms the posterior potential. [7,8].…”

A review of parallel processing for statistical computation

“…Brick and Hoffmeister (1994), discuss the use of parallel processing in their introduction to genetic algorithms. Parallel aspects of Markov chain Monte Carlo methods are discussed in Malfait et al (1993). The successful use of SIMD hardware for image processing is described by Grenander and Miller (1994).…”