{"paper":{"title":"Embedding martingale diffusions as binary posteriors in sequential inference","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Karl Kristian Engelund, Steven Campbell","submitted_at":"2026-07-22T17:02:57Z","abstract_excerpt":"Posterior probabilities are bounded martingales, but this fact alone does not identify the experiment that generates them. We show that every time-homogeneous martingale diffusion on $[0,1]$ with strictly positive $C^1$ volatility on the interior and absorbing endpoints, which we call an autonomous win-martingale, can be realized as the Bayesian posterior of an explicit binary sequential experiment observed through a scalar diffusion. Conversely, in a general binary diffusion experiment, the current time and observation are jointly sufficient for the hidden state precisely when the difference "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.20373","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.20373/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}