Hierarchical Bayesian Approach to a Multi-Site Hidden Markov Model

Abstract

Multivariate data with a sequential or temporal structure occur in various fields of study. The hidden Markov model (HMM) provides an attractive framework for modeling long-term persistence in areas of pattern recognition through the extension of independent and identically distributed mixture models. Unlike in typical mixture models, the heterogeneity of data is represented by hidden Markov states. This article extends the HMM to a multi-site or multivariate case by taking a hierarchical Bayesian approach. This extension has many advantages over a single-site HMM. For example, it can provide more information for identifying the structure of the HMM than a single-site analysis. We evaluate the proposed approach by exploiting a spatial correlation that depends on the distance between sites.

Keywords:

• Bayesian analysis
• Hierarchical modeling
• Multi-site hidden Markov model

Mathematics Subject Classification:

• Primary 62F15
• Secondary 62H99

Acknowledgments

The research of Dal Ho Kim was supported by Kyungpook National University Research Fund, 2012. The research of Yongku Kim was supported by Basic Science Research Program through the National Research Foundation of (NRF) funded by the Ministry of Education, Science and Technology (No. 2012R1A1011113).