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

Definition: A scoring rule $\mathbf{S}$ is called a proper scoring rule, if and only if

\[\label{eq:psr} \max_{Q \in \mathcal{Q}} \mathbb{E}_{Y \sim P}[\mathbf{S}(Q, Y)] = \mathbb{E}_{Y \sim P}[\mathbf{S}(P, Y)] \; .\]

In other words, score function $\mathbf{S}$ is a proper scoring rule, if it is maximized when the forecaster gives exactly the ground truth distribution $P(Y)$ as its probabilistic forecast $Q \in \mathcal{Q}$.


Metadata: ID: D193 | shortcut: psr | author: KarahanS | date: 2024-02-28, 20:50.