Based on a reparametrization of the Gaussian density and a natural prior for the parameters, a Bayesian model selection criterion is derived, which differs from Schwarz' (1978) criterion by a term which does not vanish as the sample size increases.

It is shown that in the linear normal regression model asymptotically the expected value of the penalty term implied by the Akaike-BIC can, under certain circumstances, be smaller than that implied by the AIC. Consequences for consistency are discussed.