{
  "abstract": "Sparse count forecasting arises when events are rare, exposure varies across observational units, and short histories contain many zeros. Using thin-market airline demand as a motivating application, this paper develops a hierarchical exposure-adjusted Poisson-Gamma (HEPG) framework for probabilistic forecasting. Conditional counts follow a Poisson model with an exposure offset and pooled calendar effects, while unit specific baseline intensities receive a Gamma prior whose hyperparameters are estimated empirically across the population. The resulting posterior is Gamma and the posterior predictive distribution is negative binomial, providing closed-form partial pooling and explicit propagation of parameter uncertainty. This is especially useful for zero-history or low-exposure units, where independent maximum-likelihood estimates are unstable or collapse to zero. An adaptive extension, A-HEPG, adds a moment-matched negative-binomial variance correction when residual extra-Poisson variation remains. In synthetic experiments with 400 heterogeneous markets, HEPG improves average negative log predictive probability relative to complete pooling and independent route-level Poisson estimation. At a mean latent rate of 0.15 requests per exposure unit, the score is 0.525 for HEPG, compared with 0.585 for pooled Poisson and 0.731 for route-level Poisson maximum likelihood. Under strong overdispersion, A-HEPG reduces the score from 0.552 to 0.529. A downstream cabin-capacity example links the predictive distribution to a seat-protection rule based on predictive survival probabilities and fare ratios. The study emphasizes coherent probabilistic inference, partial pooling, and diagnostic model escalation for sparse applied count data.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.14530",
  "author_total": 1,
  "authors": [
    {
      "name": "Irakli Gudavadze"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6fsmdfphh1hzz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.14530",
  "fulltext_url": null,
  "id": "6fsmdfphh1hzz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.14530",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "stat.AP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.14530",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6fsmdfphh1hzz.ris",
  "sources": [
    {
      "first_seen": "2026-11-13T06:21:06Z",
      "native_id": "2611.14530",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.14530"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.AP",
      "subfield": "statistics"
    }
  ],
  "title": "Hierarchical Empirical-Bayes Forecasting of Sparse Counts with Exposure: An Application to Airline Demand and Premium-Cabin Capacity Sharing",
  "title_text": "Hierarchical Empirical-Bayes Forecasting of Sparse Counts with Exposure: An Application to Airline Demand and Premium-Cabin Capacity Sharing",
  "type": "preprint",
  "updated_at": "2026-11-13T06:21:06Z",
  "url": "https://research.draconitic.com/paper/6fsmdfphh1hzz",
  "venue": "arXiv",
  "versions": []
}