{"ID":6267819,"CreatedAt":"2026-07-10T01:11:38.759438437Z","UpdatedAt":"2026-07-12T00:46:20.476453333Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.08019","arxiv_id":"2607.08019","title":"From Bayes' Rule to Bayes Rules: Optimal Information Processing and Axiomatic Foundations Beyond Probability","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.","short_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-c...","url_abs":"https://arxiv.org/abs/2607.08019","url_pdf":"https://arxiv.org/pdf/2607.08019v1","authors":"[\"Jeremie Houssineau\",\"Badr-Eddine Chérief-Abdellatif\"]","published":"2026-07-09T00:53:41Z","proceeding":"math.ST","tasks":"[\"math.ST\",\"cs.IT\"]","methods":"[]","has_code":false}