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

TL;DR

This paper introduces a Bayesian method using MCMC for detecting changepoints in multiple categorical sequences modeled as finite-state Markov chains, accommodating variability across sequences.

Contribution

It develops a novel Bayesian framework for changepoint detection in multiple Markov sequences, allowing for variable changepoint locations and sequence-specific transition matrices.

Findings

Effective in identifying changepoints in simulated data

Handles variability in changepoint locations across sequences

Successfully applied to rainfall and tree branching data

Abstract

We consider the analysis of sets of categorical sequences consisting of piecewise homogeneous 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 illustrates 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 two applications involving monsoonal rainfall patterns and branching patterns in trees.