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May 2021 Comment: On Focusing, Soft and Strong Revision of Choquet Capacities and Their Role in Statistics
Thomas Augustin, Georg Schollmeyer
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Statist. Sci. 36(2): 205-209 (May 2021). DOI: 10.1214/21-STS765D

Abstract

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.

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Thomas Augustin. Georg Schollmeyer. "Comment: On Focusing, Soft and Strong Revision of Choquet Capacities and Their Role in Statistics." Statist. Sci. 36 (2) 205 - 209, May 2021. https://doi.org/10.1214/21-STS765D

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Published: May 2021
First available in Project Euclid: 19 April 2021

Digital Object Identifier: 10.1214/21-STS765D

Rights: Copyright © 2021 Institute of Mathematical Statistics

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Vol.36 • No. 2 • May 2021
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