Probabilistic coherence and proper scoring rules

TL;DR

This paper proves a new theorem linking probabilistic coherence of forecasts to their optimality under proper scoring rules, enhancing understanding of forecast evaluation.

Contribution

It provides a self-contained proof of a novel theorem connecting probabilistic coherence with non-domination under proper scoring rules.

Findings

The theorem establishes a fundamental link between coherence and scoring rule optimality.

It clarifies the theoretical foundations of forecast evaluation.

The proof is self-contained and relates to existing results in the literature.

Abstract

We provide self-contained proof of a theorem relating probabilistic coherence of forecasts to their non-domination by rival forecasts with respect to any proper scoring rule. The theorem appears to be new but is closely related to results achieved by other investigators.