{
  "abstract": "Cooke's Classical Model scores the statistical accuracy of experts by the $p$-value of a likelihood ratio test that compares the bin frequencies of realized seed variables with nominal probabilities, using a $χ^2$ reference. This calibration score drives performance-based weights and implicitly assumes independent seed variables, although seeds often share a common driver, such as the same indicator in several regions or periods. Under dependence the statistic converges to a weighted sum of $χ^2_1$ variables, and positive dependence makes the classical score anti-conservative. Under a Gaussian-copula working model, a Mehler-Hermite expansion gives the long-run covariance of the bin indicators in closed form, defines a design effect and an effective number of seed variables, and shows that the first-order correction coincides with the ad hoc calibration power of existing software. Rao-Scott-type and parametric-bootstrap corrected scores are proposed, together with a restricted maximum likelihood estimator of the nuisance dependence, computed from rank normal scores and invariant to location-scale miscalibration, and a prepivoted bootstrap that propagates its uncertainty. In simulations the classical score rejects up to 68\\% of calibrated experts at a nominal 5\\% level, whereas the corrected scores remove most of the excess rejection. In 45 published studies, design effects of 1.25-2 shift more than 5\\% of the optimized weight in 29-44\\% of studies. In three social-science studies with structured seeds, the baseline estimates imply that 18-21 seed variables carry the information of only 11-13 independent ones, although conclusions about individual experts depend on how the dependence is specified.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28831",
  "author_total": 1,
  "authors": [
    {
      "name": "Yuri Calleo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aymbxy8xq4z21.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28831",
  "fulltext_url": null,
  "id": "aymbxy8xq4z21",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28831",
  "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.AP"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "openalex",
      "1803|Forecasting Techniques and Applications"
    ]
  ],
  "openalex": "W7223230054",
  "pdf_url": "https://arxiv.org/pdf/2610.28831",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aymbxy8xq4z21.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:29Z",
      "native_id": "2610.28831",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28831"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.AP",
      "subfield": "statistics"
    }
  ],
  "title": "Calibration scoring under dependent seed variables in Cooke's Classical Model: a Mehler-Hermite design-effect correction",
  "title_text": "Calibration scoring under dependent seed variables in Cooke's Classical Model: a Mehler-Hermite design-effect correction",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:29Z",
  "url": "https://research.draconitic.com/paper/aymbxy8xq4z21",
  "venue": "arXiv",
  "versions": []
}