Convergence of MCEM and Related Algorithms for Hidden Markov Random Field

Abstract : The Monte Carlo EM (MCEM) algorithm is a stochastic version of the EM algorithm using MCMC methods to approximate the conditional distribution of the hidden data. In the context of hidden Markov field model-based image segmentation, the behavior of this algorithm has been illustrated in experimental studies but little theoretical results have been established. In this paper new results on MCEM for parameter estimation of the observed data model are presented, showing that under suitable regularity conditions the sequence of MCEM estimates converges to a maximizer of the likelihood of the model. A variant of the Monte Carlo step in the MCEM algorithm is proposed, leading to the Generalized Simulated Field (GSF) algorithm, and it is shown that the two procedures have similar properties.