{
  "abstract": "Finite discrete count data are ubiquitous in fields such as biomedicine and social sciences and these data frequently exhibit over-dispersion, rendering the binomial distribution inadequate for modeling. Although the beta-binomial distribution mitigates this by assigning a subjective beta prior to the success probability, its reliance on a pre-specified parametric shape may result in biased representations of prior information, failing to capture the complex and heterogeneous characteristics of real-world data. To address these limitations, this paper proposes a novel Bernstein-binomial model. By leveraging the uniform approximation properties of Bernstein distribution, we construct a highly flexible and general prior framework for the success probability in binomial distribition, which dynamically adapts to complex data structures, avoiding the subjectivity and restrictions associated with conventional unimodal priors. A comprehensive theoretical framework for both frequentist and Bayesian inferences is established. Furthermore, the model is extended to a regression setting to account for covariate effects. Extensive simulation studies and real-world data applications confirm that the proposed Bernstein-binomial model significantly outperforms existing models. It offers superior fitting accuracy, robustness, and out-of-sample predictive performance when modeling over-dispersed counts with complex latent prior structures.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04964",
  "author_total": 5,
  "authors": [
    {
      "name": "Yuan-Fan ZHAO"
    },
    {
      "name": "Yikai GUO"
    },
    {
      "name": "Xun-Jian LI"
    },
    {
      "name": "Man-Lai TANG"
    },
    {
      "name": "Guo-Liang TIAN"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6tbgxs04aj78r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04964",
  "fulltext_url": null,
  "id": "6tbgxs04aj78r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04964",
  "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",
      "stat.ME"
    ],
    [
      "openalex",
      "2613|Statistical Distribution Estimation and Applications"
    ]
  ],
  "openalex": "W7220688936",
  "pdf_url": "https://arxiv.org/pdf/2610.04964",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6tbgxs04aj78r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:16Z",
      "native_id": "2610.04964",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04964"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "A new Bernstein-binomial model for fitting finite discrete data with over-dispersion: Likelihood-based and Bayesian approaches",
  "title_text": "A new Bernstein-binomial model for fitting finite discrete data with over-dispersion: Likelihood-based and Bayesian approaches",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:16Z",
  "url": "https://research.draconitic.com/paper/6tbgxs04aj78r",
  "venue": "arXiv",
  "versions": []
}