| Title:
|
Application of MCMC to change point detection (English) |
| Author:
|
Antoch, Jaromír |
| Author:
|
Legát, David |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
53 |
| Issue:
|
4 |
| Year:
|
2008 |
| Pages:
|
281-296 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A nonstandard approach to change point estimation is presented in this paper. Three models with random coefficients and Bayesian approach are used for modelling the year average temperatures measured in Prague Klementinum. The posterior distribution of the change point and other parameters are estimated from the random samples generated by the combination of the Metropolis-Hastings algorithm and the Gibbs sampler. (English) |
| Keyword:
|
change point estimation |
| Keyword:
|
Markov chain Monte Carlo (MCMC) |
| Keyword:
|
Metropolis-Hastings algorithm |
| Keyword:
|
Gibbs sampler |
| Keyword:
|
Bayesian statistics |
| Keyword:
|
Klementinum temperature series |
| MSC:
|
62F40 |
| MSC:
|
62P12 |
| MSC:
|
65C05 |
| MSC:
|
65C40 |
| MSC:
|
65C60 |
| MSC:
|
86A10 |
| idZBL:
|
Zbl 1199.65016 |
| idMR:
|
MR2433722 |
| DOI:
|
10.1007/s10492-008-0026-9 |
| . |
| Date available:
|
2010-07-20T12:24:18Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140321 |
| . |
| Reference:
|
[1] Antoch, J., Hušková, M., Jarušková, D.: Off-line statistical process control.In: Multivariate Total Quality Control, Chapter 1 Physica-Verlag/Springer Heidelberg (2002), 1-86. Zbl 1039.62110, MR 1886416 |
| Reference:
|
[2] Antoch, J., Hušková, M.: Estimators of changes.Asymptotics, Nonparametrics, and Time Series Marcel Dekker Basel (1999), 533-577. MR 1724708 |
| Reference:
|
[3] Barry, D., Hartigan, J.: A Bayesian analysis for change-point problems.J. Am. Stat. Assoc. 88 (1993), 309-319. Zbl 0775.62065, MR 1212493 |
| Reference:
|
[4] Carlin, B. P., Gelfand, A. E., Smith, A. F. M.: Hierarchical Bayesian analysis of change point problems.Appl. Stat. 41 (1992), 389-405. 10.2307/2347570 |
| Reference:
|
[5] Csörgő, M., Horváth, L.: Limit Theorems in Change-Point Analysis.J. Wiley & Sons New York (1997). MR 2743035 |
| Reference:
|
[6] Gilks, W. R., Richardson, S., (eds.), D. J. Spiegelhalter: Markov Chain Monte Carlo in Practice.Chapman & Hall/CRC London (1995). MR 1397966 |
| Reference:
|
[7] Hastings, W. K.: Monte Carlo sampling methods using Markov chains and their applications.Biometrika 57 (1970), 97-109. Zbl 0219.65008, 10.1093/biomet/57.1.97 |
| Reference:
|
[8] Hinkley, D. V.: Inference about the intersection in two-phase regression.Biometrika 56 (1969), 495-504. Zbl 0183.48505, 10.1093/biomet/56.3.495 |
| Reference:
|
[9] Janžura, M., Nielsen, J.: Segmentation method and change-point problem.ROBUST'02 J. Antoch, G. Dohnal, J. Klaschka JČMF Praha 163-177 Czech. |
| Reference:
|
[10] Jarušková, D.: Some problems with application of change point detection methods to enviromental data.Environmetrics 8 (1997), 469-483. 10.1002/(SICI)1099-095X(199709/10)8:5<469::AID-ENV265>3.0.CO;2-J |
| Reference:
|
[11] Legát, D.: MCMC methods.Master thesis Charles University Praha (2004), Czech. |
| Reference:
|
[12] Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., Teller, E.: Equations of state calculations by fast computing machines.J. Chem. Phys. 21 (1953), 1087-1092. 10.1063/1.1699114 |
| Reference:
|
[13] O'Hogan, A., Foster, J.: Kendall's Advanced Theory of Statistics, Bayesian Inference.Arnold London (1999). |
| Reference:
|
[14] Robert, Ch. P., Casella, G.: Monte Carlo Statistical Methods, 2nd ed.Springer Heidelberg (2005). MR 2080278 |
| . |
