Graphically explain comparative premium-rule performance

Determine how to use graphical diagnostics to identify the respective weaknesses of two competing insurance premium rules when one rule is preferred over the other according to the Bregman-score preference order.

Background

The paper compares competing unit-premium rules using expected or empirical Bregman losses and scores. A numerical score establishes an overall preference, but it does not by itself reveal which premium ranges, risk groups, calibration defects, or ranking failures generate that preference.

The author asks for a graphical interpretation that can localize and explain the sources of comparative predictive performance. Subsequent paired iterative Bregman-score aggregation graphs provide a partial approach, but the question is explicitly posed before that discussion and is not presented as fully resolved in general.

References

Table \ref{gamma deviance example table} gives a clear preference to one of the two premium rules in terms of preference order 1. Can we understand this numerical result graphically, e.g., identifying the weaknesses of the premium rules?

— A Practical Guide on Graphical Model Validation  (2609.26445 - Wüthrich, 22 Sep 2026) in Section 6, immediately after Example “Gamma deviance scoring” and before subsection “Graphical illustration of the Bregman score”