Bayesian model selection based on proper scoring rules

Philip Dawid, A.;MUSIO, MONICA

2015-01-01

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Abstract

Bayesian model selection with improper priors is not well-defined becauseof the dependence of the marginal likelihood on the arbitrary scaling constantsof the within-model prior densities. We show how this problem can beevaded by replacing marginal log-likelihood by a homogeneous proper scoring rule,which is insensitive to the scaling constants. Suitably applied, this will typicallyenable consistent selection of the true model.