A random cluster algorithm for some continuous Markov random fields

Abstract

Based on a random cluster representation, the Swendsen–Wang algorithm for the Ising and Potts distributions is extended to a class of continuous Markov random fields. The algorithm can be described briefly as follows. A given configuration is decomposed into clusters. Probabilities for flipping the values of the random variables in each cluster are calculated. According to these probabilities, values of all the random variables in each cluster will be either updated or kept unchanged and this is done independently across the clusters. A new configuration is then obtained. We will show through a simulation study that, like the Swendsen–Wang algorithm in the case of Ising and Potts distributions, the cluster algorithm here also outperforms the Gibbs sampler in beating the critical slowing down for some strongly correlated Markov random fields.