Dirichlet Process Hidden Markov Multiple Change-point Model

TL;DR

This paper introduces a Bayesian hidden Markov model based on Dirichlet processes for multiple change-point detection that automatically determines the number of change-points, demonstrated through simulations and real data applications.

Contribution

It presents a nonparametric Bayesian approach that does not require pre-specifying the number of change-points, improving robustness over traditional models.

Findings

Successfully detects change-points in simulated data

Identifies change-points consistent with existing methods in real data

Provides a flexible, model-agnostic framework for change-point analysis

Abstract

This paper proposes a new Bayesian multiple change-point model which is based on the hidden Markov approach. The Dirichlet process hidden Markov model does not require the specification of the number of change-points a priori. Hence our model is robust to model specification in contrast to the fully parametric Bayesian model. We propose a general Markov chain Monte Carlo algorithm which only needs to sample the states around change-points. Simulations for a normal mean-shift model with known and unknown variance demonstrate advantages of our approach. Two applications, namely the coal-mining disaster data and the real United States Gross Domestic Product growth, are provided. We detect a single change-point for both the disaster data and US GDP growth. All the change-point locations and posterior inferences of the two applications are in line with existing methods.