DOI QR코드

DOI QR Code

Bayesian Changepoints Detection for the Power Law Process with Binary Segmentation Procedures

  • Kim Hyunsoo (School of Information and Communications Engineering, Sungkyunkwan University) ;
  • Kim Seong W. (Division of Applied Mathematics, Hanyang University) ;
  • Jang Hakjin (Division of Applied Mathematics, Hanyang University)
  • Published : 2005.08.01

Abstract

We consider the power law process which is assumed to have multiple changepoints. We propose a binary segmentation procedure for locating all existing changepoints. We select one model between the no-changepoints model and the single changepoint model by the Bayes factor. We repeat this procedure until no more changepoints are found. Then we carry out a multiple test based on the Bayes factor through the intrinsic priors of Berger and Pericchi (1996) to investigate the system behaviour of failure times. We demonstrate our procedure with a real dataset and some simulated datasets.

Keywords

References

  1. Ascher, H. and Feingold, H. (1984). Repairable Systems Reliability: Modeling, Inference, Misconceptions and Their Causes, Marcel Dekker, New York
  2. Berger, J. O. and Pericchi, L. (1996). The intrinsic Bayes factor for model selection and prediction, Journal of the American Statistical Association, Vol. 91, 109-122 https://doi.org/10.2307/2291387
  3. Carlin, B. P., Gelfand A. E., and Smith, A. F. M. (1992), Hierarchical Bayesian analysis of change point problems, Journal of the Royal Statistical Society C, Vol. 41, 389-405
  4. Chen, J. and Gupta, A. K. (1997). Testing and locating variance changepoints with application to stock prices, Journal of the American Statistical Association, Vol. 92, 739-747 https://doi.org/10.2307/2965722
  5. Chib, S. (1998). Estimation and comparison of multiple change-point models, Journal of Econometrics, Vol. 86, 221-241 https://doi.org/10.1016/S0304-4076(97)00115-2
  6. Crow, L. H. (1974). Reliability Analysis of Complex Repairable Systems, Reliability and Biometry, F. Proschan and R. J. Serfling , (Eds.) , 379-410, SIAM, Philadelphia
  7. Duane, J. T. (1964). Learning curve approach to reliability monitoring, IEEE Transactions on Aerospace, Vol. 2, 563-566
  8. Green, P, J. (1995). Revisible Jump Markov Chanin Monte Carlo Computation and Bayesian Model Determination, Biometrika, Vol. 82, 711-732 https://doi.org/10.1093/biomet/82.4.711
  9. Jarrett, R.G. (1979). A note on the Intervals Between Coal-Mining Disasters, Biometrika, 66, 191-193 https://doi.org/10.1093/biomet/66.1.191
  10. Kim, S. W. and Sun, D. (2000). Intrinsic priors for model selection using an encompassing model with applications to censored failure time data, Lifetime Data Analysis, Vol. 6, 251-269 https://doi.org/10.1023/A:1009641709382
  11. Lingham, R. T. and Sivaganesan, S. (1997). Testing hypotheses about the power law process under failure truncation using intrinsic Bayes factors, Annals of the Institute of Statistical Mathematics, Vol. 49, 693-710 https://doi.org/10.1023/A:1003218410136
  12. Raftery, A. E. (1994). Change point and change curve modeling in stocastic processes and spatial statistics, Journal of Applied Statistical Science, Vol. 1, 403-424
  13. Raftery, A. E. and Akman, V. E. (1986). Bayesian analysis of a Poisson process with a changepoint, Biometrika, Vol. 73, 85-89 https://doi.org/10.1093/biomet/73.1.85
  14. Yang, T. Y. and Lynn, Kuo (2001). Bayesian Binary Segmentation Procedure for a Poisson Process with Multiple Changepoints, Journal of Computational and Graphical Statistics, Vol. 10, 772-785 https://doi.org/10.1198/106186001317243449
  15. Vostrikova, L.J, (1981). Detecting disorder in multidimensional random processes, Soviet Mathematics Doklady, Vol. 24, 55-59