Consistency of Bayes factors for intrinsic priors in normal linear models

Abstract

The Jeffreys–Lindley paradox refers to the well-known fact that a sharp null hypothesis on the normal mean parameter is always accepted when the variance of the conjugate prior goes to infinity, thus implying that the resulting Bayesian procedure is not consistent, and that some limiting forms of proper prior distributions are not necessarily suitable for testing problems. Intrinsic priors, which are limits of proper priors, have been proved to be extremely useful for testing problems, and, in particular, for testing hypothesis on the regression coefficients of normal linear models. This Note shows the consistency of the Bayes factors when using intrinsic priors for normal linear models under very mild conditions on the design matrix. To cite this article: E. Moreno, F.J. Girón, C. R. Acad. Sci. Paris, Ser. I 340 (2005).