A pointfree approach to measurability and statistical models

Antonio Di Nola, Serafina Lapenta, Giacomo Lenzi
Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications, PMLR 215:189-199, 2023.

Abstract

In this work we approach the problem of finding the most natural algebraic structure of the set of all possible random variables on a measurable space, inspired by Nelson’s point of view. We build our work on previous papers by the same authors and set our investigation in the framework of MV-algebras and algebraic logic. We approach the problem from the perspective of pointfree topology, in order to take the notion of random variable as the primitive one. In the final part of the paper we approach statistical models from the point of view of algebra and category theory, providing a different and perhaps more insightful justification for our logico-algebraic approach to the notion.

Cite this Paper

BibTeX
@InProceedings{pmlr-v215-di-nola23a, title = {A pointfree approach to measurability and statistical models}, author = {Di Nola, Antonio and Lapenta, Serafina and Lenzi, Giacomo}, booktitle = {Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications}, pages = {189--199}, 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/di-nola23a/di-nola23a.pdf}, url = {https://proceedings.mlr.press/v215/di-nola23a.html}, abstract = {In this work we approach the problem of finding the most natural algebraic structure of the set of all possible random variables on a measurable space, inspired by Nelson’s point of view. We build our work on previous papers by the same authors and set our investigation in the framework of MV-algebras and algebraic logic. We approach the problem from the perspective of pointfree topology, in order to take the notion of random variable as the primitive one. In the final part of the paper we approach statistical models from the point of view of algebra and category theory, providing a different and perhaps more insightful justification for our logico-algebraic approach to the notion.} }
Endnote
%0 Conference Paper %T A pointfree approach to measurability and statistical models %A Antonio Di Nola %A Serafina Lapenta %A Giacomo Lenzi %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-di-nola23a %I PMLR %P 189--199 %U https://proceedings.mlr.press/v215/di-nola23a.html %V 215 %X In this work we approach the problem of finding the most natural algebraic structure of the set of all possible random variables on a measurable space, inspired by Nelson’s point of view. We build our work on previous papers by the same authors and set our investigation in the framework of MV-algebras and algebraic logic. We approach the problem from the perspective of pointfree topology, in order to take the notion of random variable as the primitive one. In the final part of the paper we approach statistical models from the point of view of algebra and category theory, providing a different and perhaps more insightful justification for our logico-algebraic approach to the notion.
APA
Di Nola, A., Lapenta, S. & Lenzi, G.. (2023). A pointfree approach to measurability and statistical models. Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications, in Proceedings of Machine Learning Research 215:189-199 Available from https://proceedings.mlr.press/v215/di-nola23a.html.

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