In contrast to a posterior analysis given a particular sampling model, post
erior model probabilities in the context of model uncertainty are typically
rather sensitive to the specification of the prior. In particular, 'diffus
e' priors on model-specific parameters can lead to quite unexpected consequ
ences. Here we focus on the practically relevant situation where we need to
entertain a (large) number of sampling models and we have (or wish to use)
little or no subjective prior information. We aim at providing an 'automat
ic' or 'benchmark' prior structure that can be used in such cases. We focus
on the normal linear regression model with uncertainty in the choice of re
gressors. We propose a partly non-informative prior structure related to a
natural conjugate g-prior specification, where the amount of subjective inf
ormation requested from the user is limited to the choice of a single scala
r hyperparameter g(0j). The consequences of different choices for g(0j) are
examined, We investigate theoretical properties, such as consistency of th
e implied Bayesian procedure. Links with classical information criteria are
provided. More importantly, we examine the finite sample implications of s
everal choices of g(0j) in a simulation study. The use of the MC3 algorithm
of Madigan and York (Int. Stat. Rev. 63 (1995) 215), combined with efficie
nt coding in Fortran, makes it feasible to conduct large simulations. In ad
dition to posterior criteria, we shall also compare the predictive performa
nce of different priors. A classic example concerning the economics of crim
e will also be provided and contrasted with results in the literature. The
main findings of the paper will lead us to propose a 'benchmark' prior spec
ification in a linear regression context with model uncertainty. (C) 2001 E
lsevier Science S.A. All rights reserved. JEL classification: C11; C15.