ON SOME PROPERTIES OF POSTERIOR PREDICTIVE DISTRIBUTIONS
DOI:
https://doi.org/10.68302/std2026.vol3.37Keywords:
Posterior predictive distributions, Markov chain Monte Carlo (MCMC), Metropolis–Hastings algorithm, Data fitting methodsAbstract
This article considers the method of posterior predictive distributions as the one of the specific tools for checking the correspondence between data and the statistical model. The generated examples demonstrate that in the role of posterior predictive testing statistics (as a discrepancy measure), dispersion measures should be taken, because the central tendency measures do not give the expected results.
Supporting Agencies
The authors are very grateful to the department colleagues for the support of this work, which was partially developed in the framework with the national project BG05M2OP001-2.016-0003 "Modernization of the National Military University "Vasil Levski" and Sofia University "St. Kliment Ohridski".Downloads
References
[1] M. Aitkin, Statistical Inference: An Integrated Bayesian/Likelihood Approach (1st ed.). Chapman and Hall/CRC.
https://doi.org/10.1201/EBK1420093438
[2] I. Ntzoufras, Bayesian modeling using WinBUGS, Hoboken, N. J: Wiley, 2009.
[3] P. Congdon, Bayesian Models for Categorical Data, New York: Wiley, 2005.
[4] J. Albert, Bayesian Computation with R, 2nd ed., New York: Springer, 2009. https://doi.org/10.1007/978-0-387-92298-0
[5] N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller and E. Teller, "Equations of state calculations by fast computing machines," J. Chem. Phys., vol. 21, pp. 1087-1091, 1953. https://doi.org/10.1063/1.1699114
[6] C. P. Robert and G. Casella, Monte Carlo statistical methods, New York: Springer, 2004.
[7] C. P. Robert and G. Casella, Introducing Monte Carlo methods with R, New York: Springer, 2010.
[8] R. Angelova-Slavova, Convergence and Applications of the Metropolis-Hasting algorithm, Plovdiv: Astarta, 2020.
[9] W. Link and M. Eaton, M. "On thinning of chains in MCMC," Methods in Ecology and Evolution, vol. 3, pp. 112–115, 2012. https://doi.org/10.1111/j.2041-210X.2011.00131.x
[10] A. Gelman, X.-L. Meng and H. Stern, "Posterior Predictive Assessment of Model Fitness via Realized Discrepancies," Statistica Sinica, vol. 6(4), pp. 733-807, 1996. [Online]. Oxford Reference Online,
https://sites.stat.columbia.edu/gelman/research/published/A6n41.pdf, [Accessed December 06, 2025].
[11] M. A. Tanner and W. H. Wong, "The Calculation of Posterior Distributions by Data Augmentation," Journal of the American Statistical Association, vol. 82(398), pp. 528-540, 1987.
[12] M. M. Barbieri and J. O. Berger, "Optimal predictive model selection," Ann. Statist., vol. 32(3), pp. 870-897, 2004.
https://doi.org/10.1214/009053604000000238
[13] X.-L. Meng, "Posterior predictive p-values", The Annals of Statistics, vol. 22(3), pp. 1142-1160, 1994.
[14] T. Ando, Bayesian Model Selection and Statistical Modeling, Taylor and Francis Group, 2010.
[15] J.-P. Fox, Bayesian Item Response Modeling. Theory and Applications, New-York: Springer, 2010.
https://doi.org/10.1007/978-1-4419-0742-4
[16] C. A. Stone and Z. Xiaowen, Bayesian Analysis of Item Response Theory Models Using SAS, Cary, NC: SAS Institute Inc., 2015.
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Copyright (c) 2026 Ralitsa Angelova-Slavova, Dimiter Tsvetkov
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