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.

Bayesian model selection based on proper scoring rules

MUSIO, MONICA
2015-01-01

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.
2015
Consistent model selection; Homogeneous score; Hyvárinen score; Prequential; Applied mathematics; Statistics and probability
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11584/186178
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