Parameter and Mixture Component Estimation in Spatial Hidden Markov Models: A Comparative Analysis of Computational Methods

Hidden Markov models incorporating the Potts model for the labelling process are an important class of mixture models in spatial statistics. These models have been applied to problems in statistical mechanics, image analysis and disease mapping, among other areas. Jointly estimating the model parameters, the discrete state variables and the number of states (number of mixture components) is recognized as a difficult combinatorial optimization problem. We make comparisons between iterated conditional modes (ICM), simulated annealing (SA) and hybrid ICM with ant colony system (ACS-ICM) optimization for pixel labelling, parameter estimation and mixture component estimation. These comparisons are made for different levels of spatial dependence in the underlying true image. Our studies demonstrate that estimation based on ACS-ICM when carefully tuned exhibits performance that is uniformly superior to both ICM as well as a carefully tuned SA algorithm.