{"paper":{"title":"A categorical foundation for Bayesian probability","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CT","authors_text":"Jared Culbertson, Kirk Sturtz","submitted_at":"2012-05-07T19:35:39Z","abstract_excerpt":"Given two measurable spaces $H$ and $D$ with countably generated $\\sigma$-algebras, a perfect prior probability measure $P_H$ on $H$ and a sampling distribution $S: H \\rightarrow D$, there is a corresponding inference map $I: D \\rightarrow H$ which is unique up to a set of measure zero. Thus, given a data measurement $\\mu: 1 \\rightarrow D$, a posterior probability $\\widehat{P_H}= I \\circ \\mu$ can be computed. This procedure is iterative: with each updated probability $P_H$, we obtain a new joint distribution which in turn yields a new inference map $I$ and the process repeats with each additio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1488","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}