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.
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