An MCMC sampling approach to estimation of nonstationary hidden Markov models

Hidden Markov models (HMMs) represent a very important tool for analysis of signals and systems. In the past two decades, HMMs have attracted the attention of various research communities, including the ones in statistics, engineering, and mathematics. Their extensive use in signal processing and, in particular, speech processing is well documented. A major weakness of conventional HMMs is their inflexibility in modeling state durations. This weakness can be avoided by adopting a more complicated class of HMMs known as nonstationary HMMs. In this paper, we analyze nonstationary HMMs whose state transition probabilities are functions of time that indirectly model state durations by a given probability mass function and whose observation spaces are discrete. The objective of our work is to estimate all the unknowns of a nonstationary HMM, which include its parameters and the state sequence. To that end, we construct a Markov chain Monte Carlo (MCMC) sampling scheme, where sampling from all the posterior probability distributions is very easy. The proposed MCMC sampling scheme has been tested in extensive computer simulations on finite discrete-valued observed data, and some of the simulation results are presented in the paper.