{"paper":{"title":"Some developments of exchangeable measure-valued P\\'{o}lya sequences","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Exchangeable measure-valued Pólya sequences have Dirichlet process mixture priors indexed by a latent parameter on the atoms of an emergent conditioning sigma-algebra.","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hristo Sariev, Mladen Savov, Yoana R. Chorbadzhiyska","submitted_at":"2025-05-02T21:29:32Z","abstract_excerpt":"Measure-valued P\\'{o}lya sequences (MVPS) are processes whose dynamics are governed by generalized P\\'{o}lya urn schemes with infinitely many colors. Assuming a general reinforcement rule, exchangeable MVPSs can be viewed as extensions of Blackwell and MacQueen's P\\'{o}lya sequence, which characterizes an exchangeable sequence whose directing random measure has a Dirichlet process prior distribution. Here, we show that the prior distribution of any exchangeable MVPS is a Dirichlet process mixture with respect to a latent parameter that is associated with the atoms of an emergent conditioning $"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The prior distribution of any exchangeable MVPS is a Dirichlet process mixture with respect to a latent parameter that is associated with the atoms of an emergent conditioning σ-algebra. As the mixing components have disjoint supports, the directing random measure can be interpreted as a random histogram with bins randomly located on these same atoms.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The analysis assumes a general reinforcement rule for the MVPS and relies on the emergence of a conditioning σ-algebra whose atoms support the latent parameter in the mixture representation (abstract, paragraph on exchangeable MVPS priors).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Exchangeable MVPS have Dirichlet process mixture priors tied to emergent conditioning sigma-algebras, with null-component extensions and c.i.d. equivalence for balanced cases.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Exchangeable measure-valued Pólya sequences have Dirichlet process mixture priors indexed by a latent parameter on the atoms of an emergent conditioning sigma-algebra.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"82d83268e8afbcb7d3cd11db39ebaf5bb20325029ca1d56ea25f1d8b64283ca3"},"source":{"id":"2505.01594","kind":"arxiv","version":3},"verdict":{"id":"3d7d3b03-89d8-4858-aafe-a5a047d8bc40","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-22T16:31:48.609116Z","strongest_claim":"The prior distribution of any exchangeable MVPS is a Dirichlet process mixture with respect to a latent parameter that is associated with the atoms of an emergent conditioning σ-algebra. As the mixing components have disjoint supports, the directing random measure can be interpreted as a random histogram with bins randomly located on these same atoms.","one_line_summary":"Exchangeable MVPS have Dirichlet process mixture priors tied to emergent conditioning sigma-algebras, with null-component extensions and c.i.d. equivalence for balanced cases.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The analysis assumes a general reinforcement rule for the MVPS and relies on the emergence of a conditioning σ-algebra whose atoms support the latent parameter in the mixture representation (abstract, paragraph on exchangeable MVPS priors).","pith_extraction_headline":"Exchangeable measure-valued Pólya sequences have Dirichlet process mixture priors indexed by a latent parameter on the atoms of an emergent conditioning sigma-algebra."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.01594/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":54,"sample":[{"doi":"","year":1985,"title":"D. J. Aldous. Exchangeability and related topics.Lecture Notes in Math., 1117:1–198, 1985","work_id":"835a3f44-955f-44a9-8064-4967f73fe457","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2022,"title":"A. Bandyopadhyay and D. Thacker. A new approach to P´ olya urn schemes and its infinite color generalization.Ann. Appl. Probab., 32(1):46–79, 2022","work_id":"cd890dc3-1f20-4595-95da-c1b086a213f2","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2020,"title":"A. Bandyopadhyay, S. Janson, and D. Thacker. Strong convergence of infinite color balanced urns under uniform ergodicity.J. Appl. Probab., 57(3):853–865, 2020","work_id":"2c0d263c-8eb5-48ea-8400-84cb89cb9971","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2010,"title":"F. Bassetti, I. Crimaldi, and F. Leisen. Conditionally identically distributed species sampling sequences. Adv. Appl. Probab., 42(2):433–459, 2010","work_id":"59153bf5-65d4-4c96-b452-e75428a9b130","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"Bayesian predictive inference beyond martingales","work_id":"4315e8a7-959a-4638-8eb5-2c1b59a0c3d5","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":54,"snapshot_sha256":"bffe333affef8f884bc49a6d40822f0e55a7e4fc239795765bf066a965ddbc7b","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"789826d39bb69331e80fbd4b0f007b9bd5b9c1744adc5bd619485e0a8fde93dd"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}