Bayesian model selection with improper priors is not well-defined because of
the dependence of the marginal likelihood on the arbitrary scaling constants of
the within-model prior densities. We show how this problem can be evaded by
replacing marginal log-likelihood by a homogeneous proper scoring rule, which
is insensitive to the scaling constants. Suitably applied, this will typically
enable consistent selection of the true model.Comment: Published at http://dx.doi.org/10.1214/15-BA942 in the Bayesian
Analysis (http://projecteuclid.org/euclid.ba) by the International Society of
Bayesian Analysis (http://bayesian.org/
