{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/uncertainty-aware-bayes-rule-and-its","title":"Uncertainty-Aware Bayes' Rule and Its Applications","arxiv_id":"2311.05532","date":"2023-11-09","proceeding":null,"authors":["Shixiong Wang"],"abstract":"Bayes' rule has enabled innumerable powerful algorithms of statistical signal processing and statistical machine learning. However, when model misspecifications exist in prior and/or data distributions, the direct application of Bayes' rule is questionable. Philosophically, the key is to balance the relative importance between prior and data distributions when calculating posterior distributions: if prior distributions are overly conservative (i.e., exceedingly spread), we upweight the prior belief; if prior distributions are overly opportunistic (i.e., exceedingly concentrated), we downweight the prior belief. The same operation also applies to data distributions. This paper studies a generalized Bayes' rule, called uncertainty-aware Bayes' rule, to technically realize the above philosophy, thus combating the model uncertainties in prior and/or data distributions. Applications of the uncertainty-aware Bayes' rule on classification and estimation are discussed: In particular, the uncertainty-aware Bayes classifier, the uncertainty-aware Kalman filter, the uncertainty-aware particle filter, and the uncertainty-aware interactive-multiple-model filter are suggested and experimentally validated.","url_abs":"https://arxiv.org/abs/2311.05532v3","url_pdf":"https://arxiv.org/pdf/2311.05532v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"uncertainty-aware-bayes-rule-and-its","repo_url":"https://github.com/spratm-asleaf/bayes-rule","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"philosophy","task_name":"Philosophy"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}