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 Gr\"unw...

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Bibliographic Details
Published inarXiv.org
Main Authors Brehmer, Jonas, Gneiting, Tilmann
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 16.08.2018
Subjects
Bayesian analysis
Economic models
Mathematics - Statistics Theory
Performance prediction
Statistics - Theory
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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 Gr\"unwald and Dawid (2004) and Dawid (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.
Bibliography:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
ISSN:2331-8422
DOI:10.48550/arxiv.1806.07144