A Bayesian significance test of change for correlated observations

Abdeldjalil Slama

Discussiones Mathematicae Probability and Statistics (2014)

  • Volume: 34, Issue: 1-2, page 51-62
  • ISSN: 1509-9423

Abstract

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This paper presents a Bayesian significance test for a change in mean when observations are not independent. Using a noninformative prior, a unconditional test based on the highest posterior density credible set is determined. From a Gibbs sampler simulation study the effect of correlation on the performance of the Bayesian significance test derived under the assumption of no correlation is examined. This paper is a generalization of earlier studies by KIM (1991) to not independent observations.

How to cite

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Abdeldjalil Slama. "A Bayesian significance test of change for correlated observations." Discussiones Mathematicae Probability and Statistics 34.1-2 (2014): 51-62. <http://eudml.org/doc/270900>.

@article{AbdeldjalilSlama2014,
abstract = {This paper presents a Bayesian significance test for a change in mean when observations are not independent. Using a noninformative prior, a unconditional test based on the highest posterior density credible set is determined. From a Gibbs sampler simulation study the effect of correlation on the performance of the Bayesian significance test derived under the assumption of no correlation is examined. This paper is a generalization of earlier studies by KIM (1991) to not independent observations.},
author = {Abdeldjalil Slama},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {autoregressive model; change point; HPD region sets; p-value; Gibbs sampler; -value},
language = {eng},
number = {1-2},
pages = {51-62},
title = {A Bayesian significance test of change for correlated observations},
url = {http://eudml.org/doc/270900},
volume = {34},
year = {2014},
}

TY - JOUR
AU - Abdeldjalil Slama
TI - A Bayesian significance test of change for correlated observations
JO - Discussiones Mathematicae Probability and Statistics
PY - 2014
VL - 34
IS - 1-2
SP - 51
EP - 62
AB - This paper presents a Bayesian significance test for a change in mean when observations are not independent. Using a noninformative prior, a unconditional test based on the highest posterior density credible set is determined. From a Gibbs sampler simulation study the effect of correlation on the performance of the Bayesian significance test derived under the assumption of no correlation is examined. This paper is a generalization of earlier studies by KIM (1991) to not independent observations.
LA - eng
KW - autoregressive model; change point; HPD region sets; p-value; Gibbs sampler; -value
UR - http://eudml.org/doc/270900
ER -

References

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  1. [1] M.M. Barbieri and C. Conigliani, Bayesian analysis of autoregressive time series with change points, J. Italian Stat. Soc. 7 (1998) 243-255. doi: 10.1007/BF03178933 
  2. [2] R.L. Brown, J. Durbin and J.M. Evans, Techniques for testing the constancy of regression relationships over time (with discussion), J.R. Statist. Soc. A 138 (1975) 149-63. Zbl0321.62063
  3. [3] H. Chernoff and S. Zacks, Estimating the current mean distribution which is subjected to change in time, Ann. Math. Statist. 35 (1964) 999-1018. doi: 10.1214/aoms/1177700517 Zbl0218.62033
  4. [4] D. Ghorbanzadeh and R. Lounes, Bayesian analysis for detecting a change in exponential family, Appl. Math. Comp. 124 (2001) 1-15. doi: 10.1016/S0096-3003(00)00029-1 Zbl1022.62028
  5. [5] H.-J. Kim, Change-point detection for correlated observations, Statistica Sinica 6 (1996) 275-287. Zbl0839.62014
  6. [6] A. Kander and S. Zacks, Test procedure for possible change in parameters of statistical distributions occuring at unknown time point, Ann. Math. Statist. 37 (1966) 1196-1210. doi: 10.1214/aoms/1177699265 Zbl0143.41002
  7. [7] D. Kim, A Bayesian significance test of the stationarity of regression parametres, Biometrika 78 (1991) 667-675. doi: 10.2307/2337036 Zbl0737.62059
  8. [8] D.V. Hinkley, Inference about the change-point in a sequence of random variables, Biometrika 57 (1970) 1-17. doi: 10.2307/2334932 Zbl0198.51501
  9. [9] E.S. Page, Continuous inspection schemes, Biometrika 41 (1954) 100-115. Zbl0056.38002
  10. [10] E.S. Page, A test for change in a parameter occurring at an unknown point, Biometrika 42 (1955) 523-527. doi: 10.2307/2333009 Zbl0067.11602
  11. [11] A. Sen and M.S. Srivastava, Some one-sided tests for change in level, Technometrics 17 (1975) 61-64. doi: 10.2307/1268001 Zbl0294.62023
  12. [12] D. Siegmund, Boundary Crossing probabilities and statistical applications, Ann. Statist. 14 (1986) 361-404. doi: 10.1214/aos/1176349928 Zbl0632.62077
  13. [13] D. Siegmund, Confidence sets in change point problem, Int. Statist. Rev. 56 (1988) 31-48. doi: 10.2307/1403360 Zbl0684.62028
  14. [14] K.J. Worsley, The power of likelihood ratio and cumulative sum tests for a change in a binomial probability, Biometrika 70 (1983) 455-464. doi: 10.2307/2335560 Zbl0529.62025
  15. [15] K.J. Worsley, Confidence regions and tests for a change-point in a sequence of exponential family random variables, Biometrika 73 (1986) 91-104. doi: 10.2307/2336275 Zbl0589.62016

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