Bayesian Detection of Changepoints in Finite-State Markov Chains for Multiple Sequences

Abstract

We consider the analysis of sets of categorical sequences consisting of piecewise homogenous Markov segments. The sequences are assumed to be governed by a common underlying process with segments occurring in the same order for each sequence. Segments are defined by a set of unobserved changepoints where the positions and number of changepoints can vary from sequence to sequence. We propose a Bayesian framework for analyzing such data, placing priors on the locations of the changepoints and on the transition matrices and using Markov chain Monte Carlo (MCMC) techniques to obtain posterior samples given the data. Experimental results using simulated data illustrate how the methodology can be used for inference of posterior distributions for parameters and changepoints, as well as the ability to handle considerable variability in the locations of the changepoints across different sequences. We also investigate the application of the approach to sequential data from an application involving monsoonal rainfall patterns. Supplementary materials for this article are available online.

• Changepoint model
• Cross-validation
• Hidden Markov model
• Multiple sequences

Acknowledgments

This work was supported in part by U.S. Department of Energy award DOE-SC0006619 (TH and PS), U.S. Office of Naval Research under MURI grant N00014-08-1-1015 (TH and PS), and U.S. National Science Foundation award IIS-1320527 and a Google Faculty Award (PS).