IDEAS home Printed from https://ideas.repec.org/a/oup/biomet/v103y2016i4p993-999..html
   My bibliography  Save this article

A conditional Lindley paradox in Bayesian linear models

Author

Listed:
  • Agniva Som
  • Christopher M Hans
  • Steven N MacEachern

Abstract

The development of prior distributions for Bayesian regression has traditionally been driven by the goal of achieving sensible model selection and parameter estimation. The formalization of properties that characterize good performance has led to the development and popularization of thick-tailed mixtures of g priors such as the Zellner–Siow and hyper-g priors. In this paper we introduce a conditional information asymptotic regime that is motivated by the common data analysis setting where at least one regression coefficient is much larger than the others. We analyse existing mixtures of g priors under this limit and reveal two new phenomena, essentially least-squares estimation and the conditional Lindley paradox, and argue that these are, in general, undesirable. The driver behind both is the use of a single, latent scale parameter common to all coefficients.

Suggested Citation

  • Agniva Som & Christopher M Hans & Steven N MacEachern, 2016. "A conditional Lindley paradox in Bayesian linear models," Biometrika, Biometrika Trust, vol. 103(4), pages 993-999.
  • Handle: RePEc:oup:biomet:v:103:y:2016:i:4:p:993-999.
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1093/biomet/asw037
    Download Restriction: Access to full text is restricted to subscribers.

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

    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:oup:biomet:v:103:y:2016:i:4:p:993-999.. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Oxford University Press) or (Christopher F. Baum). General contact details of provider: https://academic.oup.com/biomet .

    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.

    We have no references for this item. You can help adding them by using 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.