IDEAS home Printed from https://ideas.repec.org/a/bla/scjsta/v34y2007i4p816-828.html
   My bibliography  Save this article

A Robust Conflict Measure of Inconsistencies in Bayesian Hierarchical Models

Author

Listed:
  • FREDRIK A. DAHL
  • JØRUND GÅSEMYR
  • BENT NATVIG

Abstract

. O'Hagan (Highly Structured Stochastic Systems, Oxford University Press, Oxford, 2003) introduces some tools for criticism of Bayesian hierarchical models that can be applied at each node of the model, with a view to diagnosing problems of model fit at any point in the model structure. His method relies on computing the posterior median of a conflict index, typically through Markov chain Monte Carlo simulations. We investigate a Gaussian model of one‐way analysis of variance, and show that O'Hagan's approach gives unreliable false warning probabilities. We extend and refine the method, especially avoiding double use of data by a data‐splitting approach, accompanied by theoretical justifications from a non‐trivial special case. Through extensive numerical experiments we show that our method detects model mis‐specification about as well as the method of O'Hagan, while retaining the desired false warning probability for data generated from the assumed model. This also holds for Student's‐t and uniform distribution versions of the model.

Suggested Citation

  • Fredrik A. Dahl & Jørund Gåsemyr & Bent Natvig, 2007. "A Robust Conflict Measure of Inconsistencies in Bayesian Hierarchical Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(4), pages 816-828, December.
    • Handle: RePEc:bla:scjsta:v:34:y:2007:i:4:p:816-828
    DOI: 10.1111/j.1467-9469.2007.00560.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9469.2007.00560.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9469.2007.00560.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
    ---><---

    Citations

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


    Cited by:

    1. Jørund Gåsemyr & Bent Natvig, 2009. "Extensions of a Conflict Measure of Inconsistencies in Bayesian Hierarchical Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(4), pages 822-838, December.
    2. Jørund Gåsemyr, 2016. "Uniformity of Node Level Conflict Measures in Bayesian Hierarchical Models Based on Directed Acyclic Graphs," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 20-34, March.
    3. Gunnhildur Högnadóttir Steinbakk & Geir Olve Storvik, 2009. "Posterior Predictive p‐values in Bayesian Hierarchical Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 320-336, June.
    4. Ying Yuan & Valen E. Johnson, 2012. "Goodness-of-Fit Diagnostics for Bayesian Hierarchical Models," Biometrics, The International Biometric Society, vol. 68(1), pages 156-164, 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:scjsta:v:34:y:2007:i:4:p:816-828. 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.

    We have no bibliographic 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.

    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: http://www.blackwellpublishing.com/journal.asp?ref=0303-6898 .

    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.