Bayesian Multiple Change-Point Estimation of Multivariate Mean Vectors for Small Data

Title & Authors
Bayesian Multiple Change-Point Estimation of Multivariate Mean Vectors for Small Data
Cheon, Sooyoung; Yu, Wenxing;

Abstract
A Bayesian multiple change-point model for small data is proposed for multivariate means and is an extension of the univariate case of Cheon and Yu (2012). The proposed model requires data from a multivariate noncentral $\small{t}$-distribution and conjugate priors for the distributional parameters. We apply the Metropolis-Hastings-within-Gibbs Sampling algorithm to the proposed model to detecte multiple change-points. The performance of our proposed algorithm has been investigated on simulated and real dataset, Hanwoo fat content bivariate data.
Keywords
Small data;change-point;noncentral t-distribution;Metropolis-Hastings-Within-Gibbs sampling;Hanwoo fat content;
Language
Korean
Cited by
References
1.
Barry, D. and Hartigan, J. A. (1993). A Bayesian analysis for change-point problems, Journal of the American Statistical Association, 88, 309-319.

2.
Carlin, B. P., Gelfand, A. E. and Smith, A. F. M. (1992). Hierarchical Bayesian analysis of change point problem, Applied Statistics, 41, 389-405.

3.
Chen, M. H. and Schmeiser, B. W. (1998). Towards black-box sampling, Journal of Computational and Graphical Statistics, 8, 1-22.

4.
Cheon, S. and Kim, J. (2010). Multiple change-point detection of multivariate mean vectors with the Bayesian approach, Computational Statistics and Data Analysis, 54, 406-415.

5.
Cheon, S. and Yu, W. (2012). Bayesian Multiple change-point for small data, Communications of the Korean Statistical Society, 19, 237-246.

6.
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, 35, 999-1018.

7.
Forrest, R. J. (1975). Effects of castration, sire and hormone treatments on the quality of rib roasts from Holstein-Friesian males, Canadian Journal of Animal Science, 55, 287-290.

8.
Geman, S. and Geman, D. (1984). Stochastic Relaxation, Gibbs Distributions, and Bayesian Restoration of images, IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721-741.

9.
Hastings, W. K. (1970). Monte Carlo sampling methods using Markov Chains and their applications, Biometrika, 57, 97-109.

10.
Indurain, G., Carr, T. R., Gonim, M. V., Insausti, K. and Beriain, M. J. (2009). The relationship of carcass measurements to carcass composition and intramuscular fat in Spanish beef, Meat Science, 82, 155-161.

11.
Jennings, T. G., Berry, B. W. and Joseph, A. L. (1978). Influence of fat thickness, marbling and length of aging on beef palatability and shelf-life characteristics, Journal of Animal Science, 46, 658-665.

12.
Kim, J. and Cheon, S. (2010). Bayesian multiple change-point estimation with annealing stochastic approximation Monte Carlo, Computational Statistics, 25, 215-239.

13.
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.

14.
Muller, P. (1991). A Bayesian analysis for change-point problems, A generic approach to posterior integration and Gibbs sampling. Technical Report, Purdue University, West Lafayette IN.

15.
Muller, P. (1993). Alternatives to the Gibbs sampling scheme,Technical, Report, Institute of Statistics and Decision Sciences, Duke University.

16.
Smith, A. F. M. (1975). A Bayesian approach to inference about a change-point in a sequence of random variables, Biometrika, 62, 407-416.

17.
Wheeler, T. L., Cundiff, L. V. and Koch, R. M. (1994). Effect of marbling degree on beef palatability in Bos Taurus and Bos Inbdicus cattle, Journal of Animal Science, 72, 3145-3151.