Proper Scores for Probability Forecasters

Abstract

A probability forecaster is asked to give a density p of a randomvariable ω. In return he gets a reward (or score) depending on pand on a subsequently observed value of ω. A scoring rule is calledproper if the expected score is maximized when the true density ischosen. The present paper uses convex analysis to generalize McCarthy'scharacterization of proper scoring rules.