Nonparametric Bayesian Approaches to Non-homogeneous Hidden Markov Models

TL;DR

This paper introduces a flexible Bayesian non-parametric model for non-homogeneous hidden Markov models, combining predictor-dependent stick-breaking processes with exact MCMC sampling, and extends it to include multiple predictor influences.

Contribution

It develops a novel non-parametric Bayesian framework for non-homogeneous HMMs that accounts for multiple predictor influences on transition and emission dynamics.

Findings

Effective in simulation experiments

Successfully applied to rainfall-induced malaria data

Provides accurate predictive distributions

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.