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A note on Bayesian model selection for discrete data using proper scoring rules. (English) Zbl 1379.62022
Summary: We consider homogeneous scoring rules for selecting between Bayesian models for discrete data with possibly improper priors. Simulations indicate that, applied prequentially, the method will consistently select the true model.

MSC:
62F15 Bayesian inference
62A01 Foundations and philosophical topics in statistics
62C99 Statistical decision theory
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References:
[1] Dawid, A. P., Posterior model probabilities, (Bandyopadhyay, P. S.; Forster, M., Philosophy of Statistics, (2011), Elsevier New York), 607-630
[2] Dawid, A. P.; Lauritzen, S. L.; Parry, M., Proper local scoring rules on discrete sample spaces, Ann. Statist., 40, 593-608, (2012) · Zbl 1246.62010
[3] Dawid, A. P.; Musio, M., Bayesian model selection based on proper scoring rules (with discussion), Bayesian Anal., 10, 479-521, (2015) · Zbl 1335.62016
[4] Hyv√§rinen, A., Estimation of non-normalized statistical models by score matching, J. Mach. Learn. Res., 6, 695-709, (2005) · Zbl 1222.62051
[5] Parry, M. F.; Dawid, A. P.; Lauritzen, S. L., Proper local scoring rules, Ann. Statist., 40, 561-592, (2012) · Zbl 1246.62011
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