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pith:B5DEKBVN

pith:2025:B5DEKBVNMYUPY5DVF7HM6UB7WG

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Some developments of exchangeable measure-valued P\'{o}lya sequences

Hristo Sariev, Mladen Savov, Yoana R. Chorbadzhiyska

Exchangeable measure-valued Pólya sequences have Dirichlet process mixture priors indexed by a latent parameter on the atoms of an emergent conditioning sigma-algebra.

arxiv:2505.01594 v3 · 2025-05-02 · math.PR

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Claims

C1strongest 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.

C2weakest 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).

C3one 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.

References

54 extracted · 54 resolved · 0 Pith anchors

[1] D. J. Aldous. Exchangeability and related topics.Lecture Notes in Math., 1117:1–198, 1985 1985

[2] 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 2022

[3] 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 2020

[4] F. Bassetti, I. Crimaldi, and F. Leisen. Conditionally identically distributed species sampling sequences. Adv. Appl. Probab., 42(2):433–459, 2010 2010

[5] Bayesian predictive inference beyond martingales 2025

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Cited by

1 paper in Pith

Predictive Inference via Kernel Density Estimates

Receipt and verification

First computed	2026-05-27T01:04:48.222034Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0f464506ad6628fc74752fcecf503fb1b3e44cac15b22cbd6d796c41ee9f6a9c

Aliases

arxiv: 2505.01594 · arxiv_version: 2505.01594v3 · doi: 10.48550/arxiv.2505.01594 · pith_short_12: B5DEKBVNMYUP · pith_short_16: B5DEKBVNMYUPY5DV · pith_short_8: B5DEKBVN

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/B5DEKBVNMYUPY5DVF7HM6UB7WG \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 0f464506ad6628fc74752fcecf503fb1b3e44cac15b22cbd6d796c41ee9f6a9c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8a324d3a9aa0c8bf5e7863fc568d1c550e09cc34a5126ad83997c5e3f64edde8",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-05-02T21:29:32Z",
    "title_canon_sha256": "384ec1f909282be0af91cd484655a80edaf55bc5ddae951c1335a064874e9fa5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.01594",
    "kind": "arxiv",
    "version": 3
  }
}