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A Bayesian nonparametric multi-sample test in any dimension

Author

Listed:
  • Luai Al-Labadi

    (University of Toronto Mississauga)

  • Forough Fazeli Asl

    (Isfahan University of Technology)

  • Zahra Saberi

    (Isfahan University of Technology)

Abstract

This paper considers a general Bayesian test for the multi-sample problem. Specifically, for M independent samples, the interest is to determine whether the M samples are generated from the same multivariate population. First, M Dirichlet processes are considered as priors for the true distributions generated the data. Then, the concentration of the distribution of the total distance between the M posterior processes is compared to the concentration of the distribution of the total distance between the M prior processes through the relative belief ratio. The total distance between processes is established based on the energy distance. Various interesting theoretical results of the approach are derived. Several examples covering the high dimensional case are considered to illustrate the approach.

Suggested Citation

  • Luai Al-Labadi & Forough Fazeli Asl & Zahra Saberi, 2022. "A Bayesian nonparametric multi-sample test in any dimension," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(2), pages 217-242, June.
    • Handle: RePEc:spr:alstar:v:106:y:2022:i:2:d:10.1007_s10182-021-00419-3
    DOI: 10.1007/s10182-021-00419-3
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    References listed on IDEAS

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    1. Subhadeep Mukhopadhyay & Kaijun Wang, 2020. "A nonparametric approach to high-dimensional k-sample comparison problems," Biometrika, Biometrika Trust, vol. 107(3), pages 555-572.
    2. Biswas, Munmun & Ghosh, Anil K., 2014. "A nonparametric two-sample test applicable to high dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 160-171.
    3. 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.
    4. Paul R. Rosenbaum, 2005. "An exact distribution‐free test comparing two multivariate distributions based on adjacency," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(4), pages 515-530, September.
    5. Petrie, Adam, 2016. "Graph-theoretic multisample tests of equality in distribution for high dimensional data," Computational Statistics & Data Analysis, Elsevier, vol. 96(C), pages 145-158.
    6. Heller, Ruth & Jensen, Shane T. & Rosenbaum, Paul R. & Small, Dylan S., 2010. "Sensitivity Analysis for the Cross-Match Test, With Applications in Genomics," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1005-1013.
    7. Shin-ichi Tsukada, 2019. "High dimensional two-sample test based on the inter-point distance," Computational Statistics, Springer, vol. 34(2), pages 599-615, June.
    8. 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.
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