{"paper":{"title":"Weak convergence of predictive distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.ME","stat.TH"],"primary_cat":"math.PR","authors_text":"Fabrizio Leisen, Luca Pratelli, Pietro Rigo","submitted_at":"2025-07-25T11:15:19Z","abstract_excerpt":"Let $(X_n)$ be a sequence of random variables with values in a standard Borel space $S$. We investigate the condition \\begin{gather}\\label{x56w1q} E\\bigl\\{f(X_{n+1})\\mid X_1,\\ldots,X_n\\bigr\\}\\,\\quad\\text{converges in probability,}\\tag{*} \\\\\\text{as }n\\rightarrow\\infty,\\text{ for each bounded Borel function }f:S\\rightarrow\\mathbb{R}.\\notag \\end{gather} Some consequences of \\eqref{x56w1q} are highlighted and various sufficient conditions for it are obtained. In particular, \\eqref{x56w1q} is characterized in terms of stable convergence. Since \\eqref{x56w1q} holds whenever $(X_n)$ is conditionally"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.19169","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/2507.19169/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"}