Estimation of nonstationary hidden Markov models by MCMC sampling

Abstract

Hidden Markov models are very important for analysis of signals and systems. They have been attracting the attention of the speech processing community, and they have become the favorite models of biologists. A major weakness of conventional hidden Markov models is their inflexibility in modeling state duration. In this paper, we analyze nonstationary hidden Markov models whose state transition probabilities are functions of time, thereby indirectly modeling state durations by a given probability mass function. The objective of our work is to estimate all the unknowns of the nonstationary hidden Markov model, its parameters and state sequence. To this end, we construct a Markov chain Monte Carlo sampling scheme in which all the posterior probability distributions of the unknowns are easy to sample from. Extensive simulation results show that the estimation procedure yields excellent results.