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Bayesian hypothesis testing for equality of high-dimensional means using cluster subspaces

Author

Listed:
  • Fang Chen

    (Center for Biologics Evaluation and Research (CBER), Food and Drug Administration)

  • Qiuchen Hai

    (Texas A&M University-San Antonio)

  • Min Wang

    (The University of Texas at San Antonio)

Abstract

The classical Hotelling’s $$T^2$$ T 2 test and Bayesian hypothesis tests breakdown for the problem of comparing two high-dimensional population means due to the singularity of the pooled sample covariance matrices when the model dimension p exceeds the sample size n. In this paper, we develop a simple closed-form Bayesian testing procedure based on a split-and-merge technique. Specifically, we adopt the subspace clustering technique to split the high-dimensional data into lower-dimensional random spaces so that the Bayes factor can be implemented. Then we utilize the geometric mean to merge the results of the Bayesian test to obtain a novel test statistic. We carry out simulation studies to compare the performance of the proposed test with several existing ones in the literature. Finally, two real-data applications are provided for illustrative purposes.

Suggested Citation

  • Fang Chen & Qiuchen Hai & Min Wang, 2024. "Bayesian hypothesis testing for equality of high-dimensional means using cluster subspaces," Computational Statistics, Springer, vol. 39(3), pages 1301-1320, May.
    • Handle: RePEc:spr:compst:v:39:y:2024:i:3:d:10.1007_s00180-023-01366-0
    DOI: 10.1007/s00180-023-01366-0
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