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A Bayesian decision theoretic approach to directional multiple hypotheses problems

Author

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  • Bansal, Naveen K.
  • Miescke, Klaus J.

Abstract

A multiple hypothesis problem with directional alternatives is considered in a decision theoretic framework. Skewness in the alternatives is considered, and it is shown that this skewness permits the Bayes rules to possess certain advantages when one direction of the alternatives is more important or more probable than the other direction. Bayes rules subject to constraints on certain directional false discovery rates are obtained, and their performances are compared with a traditional FDR rule through simulation. We also analyzed a gene expression data using our methodology, and compare the results to that of a FDR method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:120:y:2013:i:c:p:205-215
    DOI: 10.1016/j.jmva.2013.05.012
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    Cited by:

    1. 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.
    2. Kachiashvili KJ, 2019. "Modern State of Statistical Hypotheses Testing and Perspectives of its Development," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 9(2), pages 41-44, March.
    3. 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.

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