Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Bayesian Multiple Change-point Estimation in Normal with EMC

  • Kim, Jae-Hee (Department of Statistics, Duksung Women's University) ;
  • Cheon, Soo-Young (Department of Statistics, Texas A&M University, College Station)
  • Published : 2006.12.31
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Abstract

In this paper, we estimate multiple change-points when the data follow the normal distributions in the Bayesian way. Evolutionary Monte Carlo (EMC) algorithm is applied into general Bayesian model with variable-dimension parameters and shows its usefulness and efficiency as a promising tool especially for computational issues. The method is applied to the humidity data of Seoul and the final model is determined based on BIC.

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References

  1. Barry, D. and Hartigan, J.A. (1993). A Bayesian Analysis for Change Point Problems. Journal of the American Statistical Association, Vol. 88, 309 -319 https://doi.org/10.2307/2290726
  2. Brown, P.J. and Vannucci, M. (1998). Multivariate Bayesian Variable Selection and Prediction. Journal of Royal. Statistics Society B, Vol. 60, 627-641 https://doi.org/10.1111/1467-9868.00144
  3. Chernoff, H. and Zacks, S. (1964). Estimating the Current Mean of a Normal Distribution which is subject to Changes in Time. Annals of Mathematical Statistics, Vol. 35, 999-1018 https://doi.org/10.1214/aoms/1177700517
  4. Chen, J. and Gupta, A.K. (2000). Parametric Statistical Change Point Analysis, Birkhauser. New York
  5. George, E.I. and McCulloch, R.E. (1993). Variable Selection via Gibbs Sampling. Journal of the American Statistical Association, Vol. 88, 881-889 https://doi.org/10.2307/2290777
  6. Geyer, C.J. (1991). Markov chain Monte Carlo Maximum Likelihood. In Com -puting Science and Statistics: Proceedings of the 23rd Symposium on the Interface (Edited by E.M. Keramigas), 156-163. Interface Foundations. Fairfax
  7. Green, P.J. (1995). Reversible Jump Markov Chain Monte Carlo Computation and Bayesian Model Determination. Biometrika, Vol. 82, 711-732 https://doi.org/10.1093/biomet/82.4.711
  8. Holland, J.H. (1975). Adaptation In Natural and Artificial Systems. University of Michigan Press, Ann Arbor
  9. Hukushima, K. and Nemoto, K. (1996). Exchange Monte Carlo Method and Application to Spin Glass Simulations. Journal. Physics. Society. in Japan. Vol. 65, 1604-1608 https://doi.org/10.1143/JPSJ.65.1604
  10. Liang, F. and Wong, W.H. (1999). Real Parameter Evolutionary Monte Carlo with Applications in Bayesian Neural Networks. Technical Report, Department of Statistics and Applied Probability, NUS
  11. Liang, F. and Wong, W.H. (2000) Evolutionary Monte Carlo Applications to Cp Model Sampling and Change Point Problem. Statistica Sinica, Vol. 10, 317-342
  12. Liang, F. and Liu, C. (2005). Efficient MCMC Estimation of Discrete Distri -butions. Computational Statistics & Data Analysis, Vol. 49, 1039-1052 https://doi.org/10.1016/j.csda.2004.07.022
  13. Marinari, E. and Parisi, G. (1992). Simulated Tempering: a New Monte Carlo Scheme. Europhyics. Letters, Vol. 19, 451-458 https://doi.org/10.1209/0295-5075/19/6/002
  14. Spears, W.M. (1992). Crossover or mutation? In Foundations of Genetic Algorithms 2 (Edited by L. D. Whitley). Morgan Kaufmann, San Mateo
  15. Tierney, L. (1994). Markov Chains for Exploring Posterior Distributions (with discussion). Annals of Statistics, Vol. 22, 1701-1762 https://doi.org/10.1214/aos/1176325750
  16. Yao, Y.C. (1984). Estimation of a Noisy Discrete-time Step Function: Bayes and Empirical Bayes Approaches. Annals of Statistics, Vol. 12, 1434-144 https://doi.org/10.1214/aos/1176346802