From Bayes’ Rule to Bayes Rules: Information Processing, Bayes’ Theorem, and Imprecise Probabilities

Jeremie Houssineau, Badr-Eddine Chérief-Abdellatif
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:2179-2195, 2026.

Abstract

This paper develops principled updating rules for possibilistic inference, where uncertainty about a fixed parameter is represented by a possibility function, the maxitive analogue of a probability distribution, and comparisons are made pointwise via a partial order. From two complementary foundations, an information-conservation viewpoint and an axiomatic viewpoint, we derive the same canonical update: the posterior is the prior-likelihood product followed by supremum normalisation. The two derivations agree for an arbitrary loss, differing only in where the learning-rate parameter enters. This parameter controls epistemic strength and is not identifiable from the normalising evidence alone, clarifying the role of analogous learning-rate parameters in generalised {Bayesian} updating.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-houssineau26a, title = {From {Bayes}’ Rule to {Bayes} Rules: Information Processing, {Bayes}’ Theorem, and Imprecise Probabilities}, author = {Houssineau, Jeremie and Ch\'{e}rief-Abdellatif, Badr-Eddine}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {2179--2195}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/houssineau26a/houssineau26a.pdf}, url = {https://proceedings.mlr.press/v337/houssineau26a.html}, abstract = {This paper develops principled updating rules for possibilistic inference, where uncertainty about a fixed parameter is represented by a possibility function, the maxitive analogue of a probability distribution, and comparisons are made pointwise via a partial order. From two complementary foundations, an information-conservation viewpoint and an axiomatic viewpoint, we derive the same canonical update: the posterior is the prior-likelihood product followed by supremum normalisation. The two derivations agree for an arbitrary loss, differing only in where the learning-rate parameter enters. This parameter controls epistemic strength and is not identifiable from the normalising evidence alone, clarifying the role of analogous learning-rate parameters in generalised {Bayesian} updating.} }
Endnote
%0 Conference Paper %T From Bayes’ Rule to Bayes Rules: Information Processing, Bayes’ Theorem, and Imprecise Probabilities %A Jeremie Houssineau %A Badr-Eddine Chérief-Abdellatif %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-houssineau26a %I PMLR %P 2179--2195 %U https://proceedings.mlr.press/v337/houssineau26a.html %V 337 %X This paper develops principled updating rules for possibilistic inference, where uncertainty about a fixed parameter is represented by a possibility function, the maxitive analogue of a probability distribution, and comparisons are made pointwise via a partial order. From two complementary foundations, an information-conservation viewpoint and an axiomatic viewpoint, we derive the same canonical update: the posterior is the prior-likelihood product followed by supremum normalisation. The two derivations agree for an arbitrary loss, differing only in where the learning-rate parameter enters. This parameter controls epistemic strength and is not identifiable from the normalising evidence alone, clarifying the role of analogous learning-rate parameters in generalised {Bayesian} updating.
APA
Houssineau, J. & Chérief-Abdellatif, B.. (2026). From Bayes’ Rule to Bayes Rules: Information Processing, Bayes’ Theorem, and Imprecise Probabilities. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:2179-2195 Available from https://proceedings.mlr.press/v337/houssineau26a.html.

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