Index: The Book of Statistical ProofsGeneral Theorems ▷ Machine learning ▷ Scoring rules ▷ Strictly proper scoring rule

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 $Q \in \mathcal{Q}$.


Metadata: ID: D194 | shortcut: spsr | author: KarahanS | date: 2024-02-28, 20:50.