Definition: Strictly proper scoring rule
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The Book of Statistical Proofs ▷
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Strictly proper scoring rule
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Metadata: ID: D194  shortcut: spsr  author: KarahanS  date: 20240228, 20:50.
Definition: A scoring rule $\mathbf{S}$ is called a strictly proper scoring rule, if and only if

$\mathbf{S}$ is a proper scoring rule, and

$\operatorname*{arg\,max}_{Q \in \mathcal{Q}} \mathbb{E}_{Y \sim P}[\mathbf{S}(Q, Y)] = P$ is the unique maximizer of $\mathbf{S}$ in $Q$.
In other words, a strictly proper scoring rule is maximized only when the the forecaster gives exactly the ground truth distribution $P(Y)$ as its probabilistic forecast $Q \in \mathcal{Q}$.
 Bálint Mucsányi, Michael Kirchhof, Elisa Nguyen, Alexander Rubinstein, Seong Joon Oh (2023): "Proper/Strictly Proper Scoring Rule"; in: Trustworthy Machine Learning; URL: https://trustworthyml.io/; DOI: 10.48550/arXiv.2310.08215.
Metadata: ID: D194  shortcut: spsr  author: KarahanS  date: 20240228, 20:50.