IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v31y2022i4d10.1007_s11749-022-00819-w.html
   My bibliography  Save this article

Bayes factors for peri-null hypotheses

Author

Listed:
  • Alexander Ly

    (University of Amsterdam
    Machine Learning Group, Centrum Wiskunde & Informatica)

  • Eric-Jan Wagenmakers

    (University of Amsterdam)

Abstract

A perennial objection against Bayes factor point-null hypothesis tests is that the point-null hypothesis is known to be false from the outset. We examine the consequences of approximating the sharp point-null hypothesis by a hazy ‘peri-null’ hypothesis instantiated as a narrow prior distribution centered on the point of interest. The peri-null Bayes factor then equals the point-null Bayes factor multiplied by a correction term which is itself a Bayes factor. For moderate sample sizes, the correction term is relatively inconsequential; however, for large sample sizes, the correction term becomes influential and causes the peri-null Bayes factor to be inconsistent and approach a limit that depends on the ratio of prior ordinates evaluated at the maximum likelihood estimate. We characterize the asymptotic behavior of the peri-null Bayes factor and briefly discuss suggestions on how to construct peri-null Bayes factor hypothesis tests that are also consistent.

Suggested Citation

  • Alexander Ly & Eric-Jan Wagenmakers, 2022. "Bayes factors for peri-null hypotheses," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 1121-1142, December.
    • Handle: RePEc:spr:testjl:v:31:y:2022:i:4:d:10.1007_s11749-022-00819-w
    DOI: 10.1007/s11749-022-00819-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11749-022-00819-w
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11749-022-00819-w?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Valen E. Johnson & David Rossell, 2010. "On the use of non‐local prior densities in Bayesian hypothesis tests," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(2), pages 143-170, March.
    Full references (including those not matched with items on IDEAS)

    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. Fetene B. Tekle & Dereje W. Gudicha & Jeroen K. Vermunt, 2016. "Power analysis for the bootstrap likelihood ratio test for the number of classes in latent class models," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 10(2), pages 209-224, June.
    2. Riccardo (Jack) Lucchetti & Luca Pedini, 2020. "ParMA: Parallelised Bayesian Model Averaging for Generalised Linear Models," Working Papers 2020:28, Department of Economics, University of Venice "Ca' Foscari".
    3. Mark F. J. Steel, 2020. "Model Averaging and Its Use in Economics," Journal of Economic Literature, American Economic Association, vol. 58(3), pages 644-719, September.
    4. Kelter, Riko, 2022. "Power analysis and type I and type II error rates of Bayesian nonparametric two-sample tests for location-shifts based on the Bayes factor under Cauchy priors," Computational Statistics & Data Analysis, Elsevier, vol. 165(C).
    5. Christine Peterson & Francesco C. Stingo & Marina Vannucci, 2015. "Bayesian Inference of Multiple Gaussian Graphical Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 159-174, March.
    6. D. Fouskakis, 2019. "Priors via imaginary training samples of sufficient statistics for objective Bayesian hypothesis testing," METRON, Springer;Sapienza Università di Roma, vol. 77(3), pages 179-199, December.
    7. Nilotpal Sanyal & Marco A. R. Ferreira, 2017. "Bayesian Wavelet Analysis Using Nonlocal Priors with an Application to fMRI Analysis," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(2), pages 361-388, November.
    8. Byron Botha & Rulof Burger & Kevin Kotzé & Neil Rankin & Daan Steenkamp, 2023. "Big data forecasting of South African inflation," Empirical Economics, Springer, vol. 65(1), pages 149-188, July.
    9. Christian P. Robert, 2013. "On the jeffreys-Lindley's Paradox," Working Papers 2013-46, Center for Research in Economics and Statistics.
    10. Francesco Denti & Michele Guindani & Fabrizio Leisen & Antonio Lijoi & William Duncan Wadsworth & Marina Vannucci, 2021. "Two‐group Poisson‐Dirichlet mixtures for multiple testing," Biometrics, The International Biometric Society, vol. 77(2), pages 622-633, June.
    11. Davide Altomare & Guido Consonni & Luca La Rocca, 2013. "Objective Bayesian Search of Gaussian Directed Acyclic Graphical Models for Ordered Variables with Non-Local Priors," Biometrics, The International Biometric Society, vol. 69(2), pages 478-487, June.
    12. Shi, Guiling & Lim, Chae Young & Maiti, Tapabrata, 2019. "Model selection using mass-nonlocal prior," Statistics & Probability Letters, Elsevier, vol. 147(C), pages 36-44.
    13. Dimitris Korobilis & Kenichi Shimizu, 2022. "Bayesian Approaches to Shrinkage and Sparse Estimation," Foundations and Trends(R) in Econometrics, now publishers, vol. 11(4), pages 230-354, June.
    14. Scott D. Goddard & Valen E. Johnson, 2016. "Restricted most powerful Bayesian tests for linear models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(4), pages 1162-1177, December.
    15. Weibing Li & Thierry Chekouo, 2022. "Bayesian group selection with non-local priors," Computational Statistics, Springer, vol. 37(1), pages 287-302, March.
    16. Guido Consonni & Luca La Rocca, 2010. "Moment Priors for Bayesian Model Choice with Applications to Directed Acyclic Graphs," Quaderni di Dipartimento 115, University of Pavia, Department of Economics and Quantitative Methods.
    17. Ho-Hsiang Wu & Marco A. R. Ferreira & Mohamed Elkhouly & Tieming Ji, 2020. "Hyper Nonlocal Priors for Variable Selection in Generalized Linear Models," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(1), pages 147-185, February.
    18. Arnab Kumar Maity & Sanjib Basu & Santu Ghosh, 2021. "Bayesian criterion‐based variable selection," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(4), pages 835-857, August.
    19. Christoph Semken & David Rossell, 2022. "Specification analysis for technology use and teenager well‐being: Statistical validity and a Bayesian proposal," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1330-1355, November.
    20. Gelman Andrew & Robert Christian P. & Rousseau Judith, 2013. "Inherent difficulties of non-Bayesian likelihood-based inference, as revealed by an examination of a recent book by Aitkin," Statistics & Risk Modeling, De Gruyter, vol. 30(2), pages 105-120, June.

    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:spr:testjl:v:31:y:2022:i:4:d:10.1007_s11749-022-00819-w. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.