Simulated annealing for maximum a Posteriori parameter estimation of hidden Markov models

Hidden Markov models are mixture models in which the populations from one observation to the next are selected according to an unobserved finite state-space Markov chain. Given a realization of the observation process, our aim is to estimate both the parameters of the Markov chain and of the mixture model in a Bayesian framework. In this paper, we present an original simulated annealing algorithm which, in the same way as the EM (Expectation–Maximization) algorithm, relies on data augmentation, and is based on stochastic simulation of the hidden Markov chain. This algorithm is shown to converge toward the set of Maximum A Posteriori (MAP) parameters under suitable regularity conditions.