Comment: On Focusing, Soft and Strong Revision of Choquet Capacities and Their Role in Statistics

We congratulate Ruobin Gong and Xiao-Li Meng on their thought-provoking paper demonstrating the power of imprecise probabilities in statistics. In particular, Gong and Meng clarify important statistical paradoxes by discussing them in the framework of generalized uncertainty quantification and different conditioning rules used for updating. In this note, we characterize all three conditioning rules as envelopes of certain sets of conditional probabilities. This view also suggests some generalizations that can be seen as compromise rules. Similar to Gong and Meng, our derivations mainly focus on Choquet capacities of order 2, and so we also briefly discuss in general their role as statistical models. We conclude with some general remarks on the potential of imprecise probabilities to cope with the multidimensional nature of uncertainty.

Automated summary

The paper illustrates the power of imprecise probabilities in statistics by clarifying important statistical paradoxes and discussing different conditioning rules. The authors characterize conditioning rules as envelopes of certain sets of conditional probabilities, suggesting generalizations that can be seen as compromise rules. The discussion also touches on the role of Choquet capacities of order 2 as statistical models and the potential of imprecise probabilities to cope with the multidimensional nature of uncertainty.