When Belief Functions and Lower Probabilities are Indistinguishable

Esther Anna Corsi, Tommaso Flaminio, Hykel Hosni
Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications, PMLR 147:83-89, 2021.

Abstract

This paper reports on a geometrical investigation of de Finetti’s Dutch Book method as an operational foundation for a wide range of generalisations of probability measures, including lower probabilities, necessity measures and belief functions. Our main result identifies a number of non-limiting circumstances under which de Finetti’s coherence fails to lift from less to more general models. In particular our result shows that rich enough sets of events exist such that the coherence criteria for belief functions and lower probability collapse.

Cite this Paper

BibTeX
@InProceedings{pmlr-v147-corsi21a, title = {When Belief Functions and Lower Probabilities are Indistinguishable}, author = {Corsi, Esther Anna and Flaminio, Tommaso and Hosni, Hykel}, booktitle = {Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications}, pages = {83--89}, year = {2021}, editor = {Cano, Andrés and De Bock, Jasper and Miranda, Enrique and Moral, Serafı́n}, volume = {147}, series = {Proceedings of Machine Learning Research}, month = {06--09 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v147/corsi21a/corsi21a.pdf}, url = {https://proceedings.mlr.press/v147/corsi21a.html}, abstract = {This paper reports on a geometrical investigation of de Finetti’s Dutch Book method as an operational foundation for a wide range of generalisations of probability measures, including lower probabilities, necessity measures and belief functions. Our main result identifies a number of non-limiting circumstances under which de Finetti’s coherence fails to lift from less to more general models. In particular our result shows that rich enough sets of events exist such that the coherence criteria for belief functions and lower probability collapse.} }
Endnote
%0 Conference Paper %T When Belief Functions and Lower Probabilities are Indistinguishable %A Esther Anna Corsi %A Tommaso Flaminio %A Hykel Hosni %B Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications %C Proceedings of Machine Learning Research %D 2021 %E Andrés Cano %E Jasper De Bock %E Enrique Miranda %E Serafı́n Moral %F pmlr-v147-corsi21a %I PMLR %P 83--89 %U https://proceedings.mlr.press/v147/corsi21a.html %V 147 %X This paper reports on a geometrical investigation of de Finetti’s Dutch Book method as an operational foundation for a wide range of generalisations of probability measures, including lower probabilities, necessity measures and belief functions. Our main result identifies a number of non-limiting circumstances under which de Finetti’s coherence fails to lift from less to more general models. In particular our result shows that rich enough sets of events exist such that the coherence criteria for belief functions and lower probability collapse.
APA
Corsi, E.A., Flaminio, T. & Hosni, H.. (2021). When Belief Functions and Lower Probabilities are Indistinguishable. Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications, in Proceedings of Machine Learning Research 147:83-89 Available from https://proceedings.mlr.press/v147/corsi21a.html.

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