Distorting lower probabilities using common distortion models

David Nieto-Barba, Ignacio Montes, Enrique Miranda
Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications, PMLR 290:207-217, 2025.

Abstract

Distortion or neighbourhood models are useful tools in the imprecise probability theory allowing to robustify a probabilistic model by considering a neighbourhood around a given probability measure. In this work, we tackle the more general problem of distorting a lower probability. This problem can be interesting when we believe that a given lower probability is too precise, or in coalitional game theory when the set of solutions is empty. Our main purpose is to investigate how the linear vacuous and pari mutuel models can be defined for the distortion of lower probabilities, and for this aim we address the problem in a more general manner: we extend the vertical barrier models, which include the linear vacuous and pari mutuel models, and investigate the properties they satisfy.

Cite this Paper

BibTeX
@InProceedings{pmlr-v290-nieto-barba25a, title = {Distorting lower probabilities using common distortion models}, author = {Nieto-Barba, David and Montes, Ignacio and Miranda, Enrique}, booktitle = {Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications}, pages = {207--217}, year = {2025}, editor = {Destercke, Sébastien and Erreygers, Alexander and Nendel, Max and Riedel, Frank and Troffaes, Matthias C. M.}, volume = {290}, series = {Proceedings of Machine Learning Research}, month = {15--18 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v290/main/assets/nieto-barba25a/nieto-barba25a.pdf}, url = {https://proceedings.mlr.press/v290/nieto-barba25a.html}, abstract = {Distortion or neighbourhood models are useful tools in the imprecise probability theory allowing to robustify a probabilistic model by considering a neighbourhood around a given probability measure. In this work, we tackle the more general problem of distorting a lower probability. This problem can be interesting when we believe that a given lower probability is too precise, or in coalitional game theory when the set of solutions is empty. Our main purpose is to investigate how the linear vacuous and pari mutuel models can be defined for the distortion of lower probabilities, and for this aim we address the problem in a more general manner: we extend the vertical barrier models, which include the linear vacuous and pari mutuel models, and investigate the properties they satisfy.} }
Endnote
%0 Conference Paper %T Distorting lower probabilities using common distortion models %A David Nieto-Barba %A Ignacio Montes %A Enrique Miranda %B Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications %C Proceedings of Machine Learning Research %D 2025 %E Sébastien Destercke %E Alexander Erreygers %E Max Nendel %E Frank Riedel %E Matthias C. M. Troffaes %F pmlr-v290-nieto-barba25a %I PMLR %P 207--217 %U https://proceedings.mlr.press/v290/nieto-barba25a.html %V 290 %X Distortion or neighbourhood models are useful tools in the imprecise probability theory allowing to robustify a probabilistic model by considering a neighbourhood around a given probability measure. In this work, we tackle the more general problem of distorting a lower probability. This problem can be interesting when we believe that a given lower probability is too precise, or in coalitional game theory when the set of solutions is empty. Our main purpose is to investigate how the linear vacuous and pari mutuel models can be defined for the distortion of lower probabilities, and for this aim we address the problem in a more general manner: we extend the vertical barrier models, which include the linear vacuous and pari mutuel models, and investigate the properties they satisfy.
APA
Nieto-Barba, D., Montes, I. & Miranda, E.. (2025). Distorting lower probabilities using common distortion models. Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications, in Proceedings of Machine Learning Research 290:207-217 Available from https://proceedings.mlr.press/v290/nieto-barba25a.html.

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