  We propose that Bayesian variable selection for linear parametrisations with
Gaussian iid likelihoods be based on the spherical symmetry of the diagonalised
parameter space. Our r-prior results in closed forms for the evidence for four
examples, including the hyper-g prior and the Zellner-Siow prior, which are
shown to be special cases. Scenarios of a single variable dispersion parameter
and of fixed dispersion are studied, and asymptotic forms comparable to the
traditional information criteria are derived. A simulation exercise shows that
model comparison based on our r-prior gives good results comparable to or
better than current model comparison schemes.
