Application of MCMC to change point detection

Jaromír Antoch; David Legát

Applications of Mathematics (2008)

  • Volume: 53, Issue: 4, page 281-296
  • ISSN: 0862-7940

Abstract

top
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.

How to cite

top

Antoch, Jaromír, and Legát, David. "Application of MCMC to change point detection." Applications of Mathematics 53.4 (2008): 281-296. <http://eudml.org/doc/37784>.

@article{Antoch2008,
abstract = {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.},
author = {Antoch, Jaromír, Legát, David},
journal = {Applications of Mathematics},
keywords = {change point estimation; Markov chain Monte Carlo (MCMC); Metropolis-Hastings algorithm; Gibbs sampler; Bayesian statistics; Klementinum temperature series; change point estimation; Markov chain Monte Carlo method; Metropolis-Hastings algorithm; Gibbs sampler; year average temperatures; Prague Klementinum},
language = {eng},
number = {4},
pages = {281-296},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Application of MCMC to change point detection},
url = {http://eudml.org/doc/37784},
volume = {53},
year = {2008},
}

TY - JOUR
AU - Antoch, Jaromír
AU - Legát, David
TI - Application of MCMC to change point detection
JO - Applications of Mathematics
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 4
SP - 281
EP - 296
AB - 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.
LA - eng
KW - change point estimation; Markov chain Monte Carlo (MCMC); Metropolis-Hastings algorithm; Gibbs sampler; Bayesian statistics; Klementinum temperature series; change point estimation; Markov chain Monte Carlo method; Metropolis-Hastings algorithm; Gibbs sampler; year average temperatures; Prague Klementinum
UR - http://eudml.org/doc/37784
ER -

References

top
  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. (2002) Zbl1039.62110MR1886416
  2. Antoch, J., Hušková, M., Estimators of changes, Asymptotics, Nonparametrics, and Time Series Marcel Dekker Basel (1999), 533-577. (1999) MR1724708
  3. Barry, D., Hartigan, J., A Bayesian analysis for change-point problems, J. Am. Stat. Assoc. 88 (1993), 309-319. (1993) Zbl0775.62065MR1212493
  4. Carlin, B. P., Gelfand, A. E., Smith, A. F. M., 10.2307/2347570, Appl. Stat. 41 (1992), 389-405. (1992) DOI10.2307/2347570
  5. Csörgő, M., Horváth, L., Limit Theorems in Change-Point Analysis, J. Wiley &amp; Sons New York (1997). (1997) MR2743035
  6. Gilks, W. R., Richardson, S., (eds.), D. J. Spiegelhalter, Markov Chain Monte Carlo in Practice, Chapman &amp; Hall/CRC London (1995). (1995) MR1397966
  7. Hastings, W. K., 10.1093/biomet/57.1.97, Biometrika 57 (1970), 97-109. (1970) Zbl0219.65008DOI10.1093/biomet/57.1.97
  8. Hinkley, D. V., 10.1093/biomet/56.3.495, Biometrika 56 (1969), 495-504. (1969) Zbl0183.48505DOI10.1093/biomet/56.3.495
  9. Janžura, M., Nielsen, J., Segmentation method and change-point problem, ROBUST'02 J. Antoch, G. Dohnal, J. Klaschka JČMF Praha 163-177 Czech. 
  10. Jarušková, D., 10.1002/(SICI)1099-095X(199709/10)8:5<469::AID-ENV265>3.0.CO;2-J, Environmetrics 8 (1997), 469-483. (1997) DOI10.1002/(SICI)1099-095X(199709/10)8:5<469::AID-ENV265>3.0.CO;2-J
  11. Legát, D., MCMC methods, Master thesis Charles University Praha (2004), Czech. (2004) 
  12. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., Teller, E., 10.1063/1.1699114, J. Chem. Phys. 21 (1953), 1087-1092. (1953) DOI10.1063/1.1699114
  13. O'Hogan, A., Foster, J., Kendall's Advanced Theory of Statistics, Bayesian Inference, Arnold London (1999). (1999) 
  14. Robert, Ch. P., Casella, G., Monte Carlo Statistical Methods, 2nd ed, Springer Heidelberg (2005). (2005) MR2080278

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.