Constriction for Sets of Probabilities
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
Text
Caprio and Seidenfeld. "Constriction for Sets of Probabilities." Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications, 2023.Markdown
[Caprio and Seidenfeld. "Constriction for Sets of Probabilities." Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications, 2023.](https://mlanthology.org/isipta/2023/caprio2023isipta-constriction/)BibTeX
@inproceedings{caprio2023isipta-constriction,
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},
year = {2023},
pages = {84-95},
volume = {215},
url = {https://mlanthology.org/isipta/2023/caprio2023isipta-constriction/}
}