{"paper":{"title":"Finite-horizon quantile martingale posteriors: raw-urn laws and matrix-gain regression","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Nam Anh Le","submitted_at":"2026-07-22T07:21:59Z","abstract_excerpt":"Martingale posteriors quantify uncertainty by forward-imputing observations from one-step-ahead predictive distributions, but implementations stop after finitely many imputations. For the empirical P\\'olya-urn posterior of a quantile the law of the stopped state is derived. The quantile of the stopped urn measure keeps the familiar martingale tail-sum variance fraction; the deployed stochastic-approximation tracker with frozen gain $c$ does not. Its variance carries an explicit factor $G_a$ with $a=cf_0(q_\\tau)$, which may fall below or exceed the tail fraction, and a density-adapted gain rest"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.19839","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/2607.19839/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"}