Constriction for sets of probabilities

Michele Caprio, Teddy Seidenfeld
Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications, PMLR 215:84-95, 2023.

Abstract

Given a set of probability measures $\mathcal{P}$ representing an agent’s knowledge on the elements of a sigma-algebra $\mathcal{F}$, we can compute upper and lower bounds for the probability of any event $A\in\mathcal{F}$ of interest. A procedure generating a new assessment of beliefs is said to constrict $A$ if the bounds on the probability of $A$ after the procedure are contained in those before the procedure. It is well documented that (generalized) Bayes’ updating does not allow for constriction, for all $A\in\mathcal{F}$. In this work, we show that constriction can take place with and without evidence being observed, and we characterize these possibilities.

Cite this Paper

BibTeX
@InProceedings{pmlr-v215-caprio23b, title = {Constriction for sets of probabilities}, author = {Caprio, Michele and Seidenfeld, Teddy}, booktitle = {Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications}, pages = {84--95}, year = {2023}, editor = {Miranda, Enrique and Montes, Ignacio and Quaeghebeur, Erik and Vantaggi, Barbara}, volume = {215}, series = {Proceedings of Machine Learning Research}, month = {11--14 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v215/caprio23b/caprio23b.pdf}, url = {https://proceedings.mlr.press/v215/caprio23b.html}, abstract = {Given a set of probability measures $\mathcal{P}$ representing an agent’s knowledge on the elements of a sigma-algebra $\mathcal{F}$, we can compute upper and lower bounds for the probability of any event $A\in\mathcal{F}$ of interest. A procedure generating a new assessment of beliefs is said to constrict $A$ if the bounds on the probability of $A$ after the procedure are contained in those before the procedure. It is well documented that (generalized) Bayes’ updating does not allow for constriction, for all $A\in\mathcal{F}$. In this work, we show that constriction can take place with and without evidence being observed, and we characterize these possibilities.} }
Endnote
%0 Conference Paper %T Constriction for sets of probabilities %A Michele Caprio %A Teddy Seidenfeld %B Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications %C Proceedings of Machine Learning Research %D 2023 %E Enrique Miranda %E Ignacio Montes %E Erik Quaeghebeur %E Barbara Vantaggi %F pmlr-v215-caprio23b %I PMLR %P 84--95 %U https://proceedings.mlr.press/v215/caprio23b.html %V 215 %X Given a set of probability measures $\mathcal{P}$ representing an agent’s knowledge on the elements of a sigma-algebra $\mathcal{F}$, we can compute upper and lower bounds for the probability of any event $A\in\mathcal{F}$ of interest. A procedure generating a new assessment of beliefs is said to constrict $A$ if the bounds on the probability of $A$ after the procedure are contained in those before the procedure. It is well documented that (generalized) Bayes’ updating does not allow for constriction, for all $A\in\mathcal{F}$. In this work, we show that constriction can take place with and without evidence being observed, and we characterize these possibilities.
APA
Caprio, M. & Seidenfeld, T.. (2023). Constriction for sets of probabilities. Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications, in Proceedings of Machine Learning Research 215:84-95 Available from https://proceedings.mlr.press/v215/caprio23b.html.

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