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The false discovery rate: a variable selection perspective

Author

Listed:
  • Debashis Ghosh

    (University of Michigan)

  • Wei Chen

    (University of Michigan Biostatistics)

  • Trivellore Raghuanthan

    (University of Michigan)

Abstract

In many scientific and medical settings, large-scale experiments are generating large quantities of data that lead to inferential problems involving multiple hypotheses. This has led to recent tremendous interest in statistical methods regarding the false discovery rate (FDR). Several authors have studied the properties involving FDR in a univariate mixture model setting. In this article, we turn the problem on its side; in this manuscript, we show that FDR is a by-product of Bayesian analysis of variable selection problem for a hierarchical linear regression model. This equivalence gives many Bayesian insights as to why FDR is a natural quantity to consider. In addition, we relate the risk properties of FDR-controlling procedures to those from variable selection procedures from a decision theoretic framework different from that considered by other authors.

Suggested Citation

  • Debashis Ghosh & Wei Chen & Trivellore Raghuanthan, 2004. "The false discovery rate: a variable selection perspective," The University of Michigan Department of Biostatistics Working Paper Series 1040, Berkeley Electronic Press.
  • Handle: RePEc:bep:mchbio:1040
    Note: oai:bepress.com:umichbiostat-1040
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    File URL: http://www.bepress.com/cgi/viewcontent.cgi?article=1040&context=umichbiostat
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    References listed on IDEAS

    as
    1. Smith, Michael & Kohn, Robert, 1996. "Nonparametric regression using Bayesian variable selection," Journal of Econometrics, Elsevier, vol. 75(2), pages 317-343, December.
    2. Efron B. & Tibshirani R. & Storey J.D. & Tusher V., 2001. "Empirical Bayes Analysis of a Microarray Experiment," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1151-1160, December.
    3. Christopher Genovese & Larry Wasserman, 2002. "Operating characteristics and extensions of the false discovery rate procedure," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 499-517.
    4. John D. Storey, 2002. "A direct approach to false discovery rates," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 479-498.
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