On the segmentation of switching autoregressive processes by nonparametric Bayesian methods

We demonstrate the use of a variant of the nonparametric Bayesian (NPB) forward-backward (FB) method for sampling state sequences of hidden Markov models (HMMs), when the continuous-valued observations follow autoregressive (AR) processes. The goal is to get an accurate representation of the posterior probability of the state-sequence configuration. The advantage of using NPB samplers towards this end is well-known; one need not specify (or heuristically estimate) the number of states present in the model. Instead one uses hierarchical Dirichlet processes (HDPs) as priors for the state-transition probabilities to account for a potentially infinite number of states. The FB algorithm is known to increase the mixing rate of such samplers (compared to direct Gibbs), but can still yield significant spread in segmentation error. We show that by approximately integrating out some parameters of the model, one can alleviate this problem considerably.