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The two-sample problem via relative belief ratio

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  • Luai Al-Labadi

    (University of Toronto Mississauga)

Abstract

This paper deals with a new Bayesian approach to the two-sample problem. For two independent samples, the interest is to determine whether the two samples are generated from the same population. At first, two Dirichlet processes are considered as priors for the true distributions generated the data. Then the concentration of the posterior distribution of the distance between the two processes is compared to the concentration of the prior distribution of the distance between the two processes through the relative belief ratio. Many theoretical properties of the procedure have been developed. Several examples have been discussed to illustrate the approach.

Suggested Citation

  • Luai Al-Labadi, 2021. "The two-sample problem via relative belief ratio," Computational Statistics, Springer, vol. 36(3), pages 1791-1808, September.
    • Handle: RePEc:spr:compst:v:36:y:2021:i:3:d:10.1007_s00180-020-00988-y
    DOI: 10.1007/s00180-020-00988-y
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    References listed on IDEAS

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    1. Luai Al-Labadi & Zeynep Baskurt & Michael Evans, 2017. "Goodness of fit for the logistic regression model using relative belief," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-12, December.
    2. Luai Al Labadi & Ibrahim Abdelrazeq, 2017. "On functional central limit theorems of Bayesian nonparametric priors," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(2), pages 215-229, June.
    3. ROSS McVINISH & JUDITH ROUSSEAU & KERRIE MENGERSEN, 2009. "Bayesian Goodness of Fit Testing with Mixtures of Triangular Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 337-354, June.
    4. Evans, Michael & Jang, Gun Ho, 2011. "A limit result for the prior predictive applied to checking for prior-data conflict," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1034-1038, August.
    5. Chen, Yuhui & Hanson, Timothy E., 2014. "Bayesian nonparametric k-sample tests for censored and uncensored data," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 335-346.
    6. Florens, J-P & Richard, J-F & Rolin, J-M, 1996. "Bayesian Encompassing Specification Tests of a Parametric Model Against a Non Parametric Alternative," Papers 9608, Catholique de Louvain - Institut de statistique.
    7. Kan Shang & Cavan Reilly, 2017. "Non parametric Bayesian analysis of the two-sample problem with censoring," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(24), pages 12008-12022, December.
    8. repec:dau:papers:123456789/369 is not listed on IDEAS
    9. Berger J. O & Guglielmi A., 2001. "Bayesian and Conditional Frequentist Testing of a Parametric Model Versus Nonparametric Alternatives," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 174-184, March.
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    Cited by:

    1. Luai Al-Labadi & Petru Ciur & Milutin Dimovic & Kyuson Lim, 2023. "Assessing Multinomial Distributions with a Bayesian Approach," Mathematics, MDPI, vol. 11(13), pages 1-16, July.
    2. Luai Al-Labadi & Yifan Cheng & Forough Fazeli-Asl & Kyuson Lim & Yanqing Weng, 2022. "A Bayesian One-Sample Test for Proportion," Stats, MDPI, vol. 5(4), pages 1-12, December.

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