Bayesian parameter and order estimation in profile hidden Markov models

Hidden Markov models are used as tools for pattern recognition in a number of areas, ranging from speech processing to biological sequence analysis. Profile hidden Markov models represent a class of so-called "left-right" models that have an architecture that is specifically relevant to classification of proteins into structural families based on their amino acid sequences. Standard learning methods for such models employ a variety of heuristics applied to the expectation-maximization implementation of the maximum likelihood estimation procedure in order to find the global maximum of the likelihood function.; In this thesis, maximum likelihood estimation is compared to fully Bayesian estimation of parameters for profile hidden Markov models with a small number of parameters. Bayesian methods are found to assign higher scores to data sequences that are distantly related to the pattern consensus, show better performance in classifying these sequences correctly, and continue to perform robustly with regard to misspecification of the number of model parameters, relative to maximum likelihood methods. Though the study is limited in scope, the results are expected to remain relevant for models with a large number of parameters and other types of left-right hidden Markov models.; Further, higher order hidden Markov models are investigated and the standard method of discerning Markov order, the Bayesian Information Criterion (BIC). The results show that the overlap in emission distributions from different hidden states is a dominant factor governing the BICs ability to correctly discern model order.