Estimation and comparison of multiple change-point models

Abstract

This paper provides a new Bayesian approach for models with multiple change points. The centerpiece of the approach is a formulation of the change-point model in terms of a latent discrete state variable that indicates the regime from which a particular observation has been drawn. This state variable is specified to evolve according to a discrete-time discrete-state Markov process with the transition probabilities constrained so that the state variable can either stay at the current value or jump to the next higher value. This parameterization exactly reproduces the change point model. The model is estimated by Markov chain Monte Carlo methods using an approach that is based on Chib (1996). This methodology is quite valuable since it allows for the fitting of more complex change point models than was possible before. Methods for the computation of Bayes factors are also developed. All the techniques are illustrated using simulated and real data sets.