Extending conventional priors for testing general hypotheses in linear models

M.J. Bayarri and Gonzalo García-Donato

Biometrika, 2007, vol. 94, issue 1, 135-152

Abstract: We consider that observations come from a general normal linear model and that it is desirable to test a simplifying null hypothesis about the parameters. We approach this problem from an objective Bayesian, model-selection perspective. Crucial ingredients for this approach are 'proper objective priors' to be used for deriving the Bayes factors. Jeffreys-Zellner-Siow priors have good properties for testing null hypotheses defined by specific values of the parameters in full-rank linear models. We extend these priors to deal with general hypotheses in general linear models, not necessarily of full rank. The resulting priors, which we call 'conventional priors', are expressed as a generalization of recently introduced 'partially informative distributions'. The corresponding Bayes factors are fully automatic, easily computed and very reasonable. The methodology is illustrated for the change-point problem and the equality of treatments effects problem. We compare the conventional priors derived for these problems with other objective Bayesian proposals like the intrinsic priors. It is concluded that both priors behave similarly although interesting subtle differences arise. We adapt the conventional priors to deal with nonnested model selection as well as multiple-model comparison. Finally, we briefly address a generalization of conventional priors to nonnormal scenarios. Copyright 2007, Oxford University Press.

Date: 2007
References: Add references at CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://hdl.handle.net/10.1093/biomet/asm014 (application/pdf)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:oup:biomet:v:94:y:2007:i:1:p:135-152

Ordering information: This journal article can be ordered from
https://academic.oup.com/journals

Access Statistics for this article

Biometrika is currently edited by Paul Fearnhead

More articles in Biometrika from Biometrika Trust Oxford University Press, Great Clarendon Street, Oxford OX2 6DP, UK.
Bibliographic data for series maintained by Oxford University Press ().