{
  "abstract": "Consider a sample of size $N$ from a two-layer hierarchical Pitman--Yor model, and let $ξ(N)$ denote the random number of clusters generated at the first layer of the hierarchy. We study moderate deviation principles for partition statistics evaluated at the random sample size $ξ(N)$. In particular, we establish moderate deviation principles for the total number of clusters $K_{ξ(N)}$ and for the frequency count $M_{l,ξ(N)}$, the number of upper-level clusters represented by exactly $l$ first-level clusters. Our analysis combines fixed-sample-size small-tilt asymptotics with a moderate deviation principle for the random index $ξ(N)$. A uniform small-tilt argument, together with exponentially weighted tail estimates, allows us to pass from deterministic sample sizes to the hierarchical random-index setting. We obtain explicit deviation speeds and good rate functions on a family of intermediate scales between the typical growth order $N^{α_1α_2}$ and the linear scale $N$. The resulting rate functions exhibit a common power-law structure governed by the product $α_1α_2$, revealing a multiplicative effect of the two levels of the hierarchy.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05328",
  "author_total": 1,
  "authors": [
    {
      "name": "Nian Yao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dswy3p4fmawgj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05328",
  "fulltext_url": null,
  "id": "dswy3p4fmawgj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05328",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "1702|Bayesian Methods and Mixture Models"
    ]
  ],
  "openalex": "W7220686526",
  "pdf_url": "https://arxiv.org/pdf/2610.05328",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dswy3p4fmawgj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05328",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05328"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Moderate Deviations for Random-Indexed Cluster Counts in Hierarchical Pitman-Yor Models",
  "title_text": "Moderate Deviations for Random-Indexed Cluster Counts in Hierarchical Pitman-Yor Models",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/dswy3p4fmawgj",
  "venue": "arXiv",
  "versions": []
}