This note gives an easily verified necessary and sufficient condition for one probability forecaster to empirically outperform another one in terms of all strictly proper scoring rules.

The paper explores the relationship between various orderings among probability forecasts that have been suggested in the literature. It is shown that well calibrated forecasters are in general not comparable according to the domination ordering suggested by Vardeman and Meeden (1983), that the...

The paper explores the relationship between various orderings among probability forecasts that have been suggested in the literature. It is shown that well calibrated forecasters are in general not comparable according to the domination ordering suggested by Vardeman and Meeden (1983), that the...

Proper scoring rules are over evaluation measures that reward accurate probabilities Specific rules encountered in the literature and used in practice are invariably symmetric in the sense that the expected score for a perfectly-calibrated probability assessor (or model generating probabilities)...

Probability forecasters who are rewarded via a proper scoring rule may care not only about the score, but also about their performance relative to other forecasters. We model this type of preference and show that a competitive forecaster who wants to do better than another forecaster typically...

We consider 1927 borrowers from 54 countries who had a credit rating by both Moody's and S&P as of the end of 1998, and their subsequent default history up to the end of 2002. Viewing bond ratings as predicted probabilities of default, we show that it is unlikely that both agencies are well...