Bayesian Multiple Change-Point for Small Data Cheon, Soo-Young; Yu, Wenxing;
Bayesian methods have been recently used to identify multiple change-points. However, the studies for small data are limited. This paper suggests the Bayesian noncentral t distribution change-point model for small data, and applies the Metropolis-Hastings-within-Gibbs Sampling algorithm to the proposed model. Numerical results of simulation and real data show the performance of the new model in terms of the quality of the resulting estimation of the numbers and positions of change-points for small data.
Small data;change-point;noncentral t distribution;Metropolis-Hastings-within-Gibbs sampling;Typhoon-frequency;
Barry, D. and Hartigan, J. A. (1993). A Bayesian analysis for change-point problems, Journal of the American Statistical Association, 88, 309-319.
Carlin, B. P., Gelfand, A. E. and Smith, A. F. M. (1992). Hierarchical Bayesian analysis of change point problem, Applied statistics, 41, 389-405.
Chen, M. H. and Schmeiser, B. W. (1998). Towards black-box sampling, Journal of Computational and Graphical Statistics, 7, 1-22.
Cheon, S. and Kim, J. (2010). Multiple change-point detection of multivariate mean vectors with the Bayesian approach, Computational Statistics & Data Analysis, 54, 406-415.
Chib, S. (1998). Estimation and comparison of multiple change-point models, Journal of Econometrics, 86, 221-241.
Geman, S. and Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images, IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721-741.
Hastings, W. K. (1970). Monte Carlo Sampling Methods using Markov Chains and their applications, Biometrika, 57, 97-109.
Hinkley, D. V. (1970). Inference about the change-point in a sequence of random variables, Biometrika, 57, 1-17.
Kim, J. and Cheon, S. (2010). Bayesian multiple change-point estimation with annealing stochastic approximation Monte Carlo, Computational Statistics, 25, 215-239.
Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H. and Teller, E. (1953). Equations of state calculations by fast computing machines, Journal of Chemical Physics, 21, 1087-1091.
Muller, P. (1991). A generic approach to posterior integration and Gibbs sampling, Technical Report, Purdue University, West Lafayette IN.
Muller, P. (1992). Alternatives to the Gibbs Sampling Scheme, Duke University.
Smith, A. F. M. (1975). A Bayesian approach to inference about a change-point in a sequence of random variables, Biometrika, 62, 407-416.
Sugi, M., Noda, A. and Sato, N. (2002). Influence of the global warming on tropical cyclone climatology: An experiment with the JMA global model, Journal of the Meteorological Society of Japan, 80, 249-272.
Venter, J. H. and Steel, S. J. (1996). Finding multiple abrupt change points, Computational Statistics & Data Analysis, 22, 481-504.