Properization: constructing proper scoring rules via Bayes acts

Scoring rules serve to quantify predictive performance. A scoring rule is proper if truth telling is an optimal strategy in expectation. Subject to customary regularity conditions, every scoring rule can be made proper, by applying a special case of the Bayes act construction studied by Grünwald and...

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Bibliographic Details
Published inAnnals of the Institute of Statistical Mathematics Vol. 72; no. 3; pp. 659 - 673
Main Authors Brehmer, Jonas R., Gneiting, Tilmann
Format Journal Article
LanguageEnglish
Published Tokyo Springer Japan 01.06.2020
Springer Nature B.V
Subjects
Bayesian analysis
Economic models
Economics
Finance
Insurance
Management
Mathematics
Mathematics and Statistics
Performance prediction
Statistics
Statistics for Business
Forecast evaluation
Misclassification error
Consistent scoring function
Proper scoring rule
Bayes act
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Summary:Scoring rules serve to quantify predictive performance. A scoring rule is proper if truth telling is an optimal strategy in expectation. Subject to customary regularity conditions, every scoring rule can be made proper, by applying a special case of the Bayes act construction studied by Grünwald and Dawid (Ann Stat 32:1367–1433, 2004 ) and Dawid (Ann Inst Stat Math 59:77–93, 2007 ), to which we refer as properization. We discuss examples from the recent literature and apply the construction to create new types, and reinterpret existing forms, of proper scoring rules and consistent scoring functions. In an abstract setting, we formulate sufficient conditions under which Bayes acts exist and scoring rules can be made proper.
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ISSN:0020-3157
1572-9052
DOI:10.1007/s10463-019-00705-7