Nonparametric Bayesian Approaches to Non-homogeneous Hidden Markov Models

Abstract: In this article a flexible Bayesian non-parametric model is proposed for non-homogeneous hidden Markov models. The model is developed through the amalgamation of the ideas of hidden Markov models and predictor dependent stick-breaking processes. Computation is carried out using auxiliary variable representation of the model which enable us to perform exact MCMC sampling from the posterior. Furthermore, the model is extended to the situation when the predictors can simultaneously in influence the transition dynamics of the hidden states as well as the emission distribution. Estimates of few steps ahead conditional predictive distributions of the response have been used as performance diagnostics for these models. The proposed methodology is illustrated through simulation experiments as well as analysis of a real data set concerned with the prediction of rainfall induced malaria epidemics.