Bayesian Analysis

Dirichlet Process Hidden Markov Multiple Change-point Model

Stanley I. M. Ko, Terence T. L. Chong, and Pulak Ghosh

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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.

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Bayesian Anal., Volume 10, Number 2 (2015), 275-296.

First available in Project Euclid: 2 February 2015

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Change-point Dirichlet process Hidden Markov model Markov chain Monte Carlo Nonparametric Bayesian


Ko, Stanley I. M.; Chong, Terence T. L.; Ghosh, Pulak. Dirichlet Process Hidden Markov Multiple Change-point Model. Bayesian Anal. 10 (2015), no. 2, 275--296. doi:10.1214/14-BA910.

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  • Beal, M. J., Ghahramani, Z., and Rasmussen, C. E. (2002). “The Infinite Hidden Markov Model.” In Dietterich, T. G., Becker, S., and Ghahramani, Z. (eds.), Advances in Neural Information Processing Systems, 577–584. MIT Press.
  • Blackwell, D. and MacQueen, J. B. (1973). “Ferguson Distributions Via Polya Urn Schemes.” The Annals of Statistics, 1(2): 353–355.
  • Carlin, P. B., Gelfand, A. E., and Smith, A. F. M. (1992). “Hierarchical Bayesian Analysis of Changepoint Problems.” Journal of the Royal Statistical Society. Series C (Applied Statistics), 41(2): 389–405.
  • Chernoff, H. and Zacks, S. (1964). “Estimating the Current Mean of a Normal Distribution which is Subjected to Changes in Time.” The Annals of Mathematical Statistics, 35(3): pp. 999–1018.
  • Chib, S. (1998). “Estimation and comparison of multiple change-point models.” Journal of Econometrics, 86(2): 221 – 241.
  • Chong, T. T.-L. (2001). “Structural Change in AR(1) Models.” Econometric Theory, 17(1): 87–155.
  • Connor, R. J. and Mosimann, J. E. (1969). “Concepts of Independence for Proportions with a Generalization of the Dirichlet Distribution.” Journal of the American Statistical Association, 64(325): pp. 194–206.
  • Ferguson, T. S. (1973). “A Bayesian analysis of some nonparametric problems.” Annals of Statistics, 1: 209–230.
  • Geweke, J. and Yu, J. (2011). “Inference and prediction in a multiple-structural-break model.” Journal of Econometrics, 163(2): 172–185.
  • Giordani, P. and Kohn, R. (2008). “Efficient Bayesian Inference for Multiple Change-Point and Mixture Innovation Models.” Journal of Business and Economic Statistics, 26(1): 66–77.
  • Jarrett, R. G. (1979). “A Note on the Intervals Between Coal-Mining Disasters.” Biometrika, 66(1): 191–193.
  • Koop, G. and Potter, S. M. (2007). “Estimation and Forecasting in Models with Multiple Breaks.” The Review of Economic Studies, 74(3): pp. 763–789.
  • Kozumi, H. and Hasegawa, H. (2000). “A Bayesian analysis of structural changes with an application to the displacement effect.” The Manchester School, 68(4): 476–490.
  • Maheu, J. M. and Gordon, S. (2008). “Learning, forecasting and structural breaks.” Journal of Applied Econometrics, 23(5): 553–583.
  • Neal, R. M. (1992). “The Infinite Hidden Markov Model.” In Smith, C. R., Erickson, G. J., and Neudorfer, P. O. (eds.), Proceedings of the Workshop on Maximum Entropy and Bayesian Methods of Statistical Analysis, 197–211. Kluwer Academic Publishers.
  • — (2000). “Markov Sampling Methods for Dirichlet Process Mixture Models.” Journal of Computational and Graphical Statistics, 9(2): 249–265.
  • Pesaran, M. H., Pettenuzzo, D., and Timmermann, A. (2006). “Forecasting Time Series Subject to Multiple Structural Breaks.” Review of Economic Studies, 73(4): 1057–1084.
  • Sethuraman, J. (1994). “A Constructive Definition of Dirichlet Priors.” Statistica Sinica, 4(2): 639–650.
  • Smith, A. F. M. (1975). “A Bayesian approach to inference about a change-point in a sequence of random variables.” Biometrika, 62: 407–416.
  • Stephens, D. A. (1994). “Bayesian Retrospective Multiple-Changepoint Identification.” Journal of the Royal Statistical Society. Series C (Applied Statistics), 43(1): 159–178.
  • Wang, J. and Zivot, E. (2000). “A Bayesian Time Series Model of Multiple Structural Changes in Level, Trend, and Variance.” Journal of Business & Economic Statistics, 18(3): 374–386.
  • Wong, T. (1998). “Generalized Dirichlet distribution in Bayesian analysis.” Applied Mathematics and Computation, 97(2-3): 165–181.