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Constrained Bayesian Methods for Testing Directional Hypotheses Restricted False Discovery Rates

Author

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  • K. J. Kachiashvili
  • I.A. Prangishvili

    (Faculty of Informatics and Control Systems, Georgian Technical University, Georgia)

  • J. K. Kachiashvili

    (I. Vekua Institute of Applied Mathematics)

Abstract

Constrained Bayesian method (CBM) and the concept of false discovery rates (FDR) for testing directional hypotheses is considered in the paper. Here is shown that the direct application of CBM allows us to control FDR on the desired level. Theoretically it is proved that mixed directional false discovery rates (mdFDR) are restricted on the desired levels at the suitable choice of restriction levels at different statements of CBM. The correctness of the obtained theoretical results is confirmed by computation results of concrete examples.

Suggested Citation

  • K. J. Kachiashvili & I.A. Prangishvili & J. K. Kachiashvili, 2019. "Constrained Bayesian Methods for Testing Directional Hypotheses Restricted False Discovery Rates," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 9(3), pages 47-56, March.
    • Handle: RePEc:adp:jbboaj:v:9:y:2019:i:3:p:47-56
    DOI: 10.19080/BBOAJ.2019.09.555761
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    References listed on IDEAS

    as
    1. Bansal, Naveen K. & Miescke, Klaus J., 2013. "A Bayesian decision theoretic approach to directional multiple hypotheses problems," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 205-215.
    2. KJ Kachiashvili, 2018. "On One Aspect of Constrained Bayesian Method for Testing Directional Hypotheses," Biomedical Journal of Scientific & Technical Research, Biomedical Research Network+, LLC, vol. 2(5), pages 2901-2903, March.
    3. Naveen K. Bansal & Gholamhossein G. Hamedani & Mehdi Maadooliat, 2016. "Testing multiple hypotheses with skewed alternatives," Biometrics, The International Biometric Society, vol. 72(2), pages 494-502, June.
    4. Yoav Benjamini & Daniel Yekutieli, 2005. "False Discovery Rate-Adjusted Multiple Confidence Intervals for Selected Parameters," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 71-81, March.
    5. Efron, Bradley, 2007. "Correlation and Large-Scale Simultaneous Significance Testing," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 93-103, March.
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