Abstract
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.
Citation
A. Philip Dawid. Monica Musio. "Bayesian Model Selection Based on Proper Scoring Rules." Bayesian Anal. 10 (2) 479 - 499, June 2015. https://doi.org/10.1214/15-BA942
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