IDEAS home Printed from https://ideas.repec.org/a/bla/jorssb/v71y2009i5p905-925.html
   My bibliography  Save this article

A Bayesian discovery procedure

Author

Listed:
  • Michele Guindani
  • Peter Müller
  • Song Zhang

Abstract

Summary. We discuss a Bayesian discovery procedure for multiple‐comparison problems. We show that, under a coherent decision theoretic framework, a loss function combining true positive and false positive counts leads to a decision rule that is based on a threshold of the posterior probability of the alternative. Under a semiparametric model for the data, we show that the Bayes rule can be approximated by the optimal discovery procedure, which was recently introduced by Storey. Improving the approximation leads us to a Bayesian discovery procedure, which exploits the multiple shrinkage in clusters that are implied by the assumed non‐parametric model. We compare the Bayesian discovery procedure and the optimal discovery procedure estimates in a simple simulation study and in an assessment of differential gene expression based on microarray data from tumour samples. We extend the setting of the optimal discovery procedure by discussing modifications of the loss function that lead to different single‐thresholding statistics. Finally, we provide an application of the previous arguments to dependent (spatial) data.

Suggested Citation

  • Michele Guindani & Peter Müller & Song Zhang, 2009. "A Bayesian discovery procedure," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(5), pages 905-925, November.
    • Handle: RePEc:bla:jorssb:v:71:y:2009:i:5:p:905-925
    DOI: 10.1111/j.1467-9868.2009.00714.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9868.2009.00714.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9868.2009.00714.x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Gelfand, Alan E. & Kottas, Athanasios & MacEachern, Steven N., 2005. "Bayesian Nonparametric Spatial Modeling With Dirichlet Process Mixing," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1021-1035, September.
    2. Dahl, David B. & Newton, Michael A., 2007. "Multiple Hypothesis Testing by Clustering Treatment Effects," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 517-526, June.
    3. Sonia Petrone & Michele Guindani & Alan E. Gelfand, 2009. "Hybrid Dirichlet mixture models for functional data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(4), pages 755-782, September.
    4. John D. Storey, 2007. "The optimal discovery procedure: a new approach to simultaneous significance testing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 347-368, June.
    5. Cohen, Arthur & Sackrowitz, Harold B., 2007. "More on the inadmissibility of step-up," Journal of Multivariate Analysis, Elsevier, vol. 98(3), pages 481-492, March.
    6. M. Perone Pacifico & C. Genovese & I. Verdinelli & L. Wasserman, 2004. "False Discovery Control for Random Fields," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1002-1014, December.
    7. 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, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jules Ellis, 2014. "An Inequality for Correlations in Unidimensional Monotone Latent Variable Models for Binary Variables," Psychometrika, Springer;The Psychometric Society, vol. 79(2), pages 303-316, April.
    2. Wang, Xia & Shojaie, Ali & Zou, Jian, 2019. "Bayesian hidden Markov models for dependent large-scale multiple testing," Computational Statistics & Data Analysis, Elsevier, vol. 136(C), pages 123-136.
    3. Edsel Peña & Joshua Habiger & Wensong Wu, 2015. "Classes of multiple decision functions strongly controlling FWER and FDR," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(5), pages 563-595, July.
    4. Michele Guindani & Wesley O. Johnson, 2018. "More nonparametric Bayesian inference in applications," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(2), pages 239-251, June.
    5. Luis G. León-Novelo & Peter Müller & Wadih Arap & Mikhail Kolonin & Jessica Sun & Renata Pasqualini & Kim-Anh Do, 2013. "Semiparametric Bayesian Inference for Phage Display Data," Biometrics, The International Biometric Society, vol. 69(1), pages 174-183, March.
    6. Barrientos, Andrés F. & Canale, Antonio, 2021. "A Bayesian goodness-of-fit test for regression," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    7. Sean Chang & James O. Berger, 2020. "Frequentist Properties of Bayesian Multiplicity Control for Multiple Testing of Normal Means," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(2), pages 310-329, August.
    8. Cipolli III, William & Hanson, Timothy & McLain, Alexander C., 2016. "Bayesian nonparametric multiple testing," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 64-79.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lianming Wang & David B. Dunson, 2010. "Semiparametric Bayes Multiple Testing: Applications to Tumor Data," Biometrics, The International Biometric Society, vol. 66(2), pages 493-501, June.
    2. Ebrahimi, Nader, 2008. "Simultaneous control of false positives and false negatives in multiple hypotheses testing," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 437-450, March.
    3. Huixia Wang & Xuming He, 2008. "An Enhanced Quantile Approach for Assessing Differential Gene Expressions," Biometrics, The International Biometric Society, vol. 64(2), pages 449-457, June.
    4. Xiaoquan Wen, 2017. "Robust Bayesian FDR Control Using Bayes Factors, with Applications to Multi-tissue eQTL Discovery," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 9(1), pages 28-49, June.
    5. Qingyun Cai & Hock Peng Chan, 2017. "A Double Application of the Benjamini-Hochberg Procedure for Testing Batched Hypotheses," Methodology and Computing in Applied Probability, Springer, vol. 19(2), pages 429-443, June.
    6. Xiao Li & Michele Guindani & Chaan S. Ng & Brian P. Hobbs, 2021. "A Bayesian nonparametric model for textural pattern heterogeneity," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(2), pages 459-480, March.
    7. Chen, Xiongzhi, 2019. "Uniformly consistently estimating the proportion of false null hypotheses via Lebesgue–Stieltjes integral equations," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 724-744.
    8. Christoph Hellmayr & Alan E. Gelfand, 2021. "A Partition Dirichlet Process Model for Functional Data Analysis," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 30-65, May.
    9. Leek Jeffrey T & Storey John D., 2011. "The Joint Null Criterion for Multiple Hypothesis Tests," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 10(1), pages 1-22, June.
    10. Zahra Barzegar & Firoozeh Rivaz, 2020. "A scalable Bayesian nonparametric model for large spatio-temporal data," Computational Statistics, Springer, vol. 35(1), pages 153-173, March.
    11. Hwang J.T. Gene & Liu Peng, 2010. "Optimal Tests Shrinking Both Means and Variances Applicable to Microarray Data Analysis," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 9(1), pages 1-35, October.
    12. Wenguang Sun & T. Tony Cai, 2009. "Large‐scale multiple testing under dependence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 393-424, April.
    13. Alessio Farcomeni, 2009. "Generalized Augmentation to Control the False Discovery Exceedance in Multiple Testing," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 501-517, September.
    14. Youngjo Lee & Jan F. Bjørnstad, 2013. "Extended likelihood approach to large-scale multiple testing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(3), pages 553-575, June.
    15. Peter Müeller & Fernando A. Quintana & Garritt Page, 2018. "Nonparametric Bayesian inference in applications," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(2), pages 175-206, June.
    16. Habiger, Joshua D. & Peña, Edsel A., 2014. "Compound p-value statistics for multiple testing procedures," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 153-166.
    17. Shiyun Chen & Ery Arias-Castro, 2021. "On the power of some sequential multiple testing procedures," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(2), pages 311-336, April.
    18. Wang, Xia & Shojaie, Ali & Zou, Jian, 2019. "Bayesian hidden Markov models for dependent large-scale multiple testing," Computational Statistics & Data Analysis, Elsevier, vol. 136(C), pages 123-136.
    19. Youngchao Ge & Sandrine Dudoit & Terence Speed, 2003. "Resampling-based multiple testing for microarray data analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 12(1), pages 1-77, June.
    20. Shonosuke Sugasawa & Hisashi Noma, 2021. "Efficient screening of predictive biomarkers for individual treatment selection," Biometrics, The International Biometric Society, vol. 77(1), pages 249-257, March.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:jorssb:v:71:y:2009:i:5:p:905-925. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/rssssea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.