{
  "abstract": "Searches for new physics in low-background experiments infer a non-negative signal strength from few events and often report an upper limit. Nominal frequentist coverage requires both a valid interval construction and an adequate data model. We study how controlled model departures affect lower- and upper-endpoint coverage for six interval procedures in an exact Poisson counting experiment, dark-matter recoil spectra, and a neutrinoless-double-beta-decay peak search. We introduce the Poisson--Fisher degeneracy index $\\mathcal I_{\\mathrm{PF}}(δν;\\vartheta_0)=(β,γ)$, which maps a specified expected-count deformation, after projection onto the complete fitted tangent space, to $β$, the signed fitted signal shift in profiled standard-error units, and $γ$, the Poisson--Fisher norm of the unabsorbed residual. Locally, the sign of $β$ identifies the threatened endpoint, while larger $γ$ implies greater detectability by the saturated-Poisson goodness-of-fit test used here at a fixed $5\\%$ type-I error rate. Across the studied deformations, positive signal-like bias degrades discovery-side coverage while making upper limits conservative; negative signal bias from overestimated signal efficiency can make the upper endpoint undercover. Calibration under the nominal simulator does not protect against misspecification of that simulator relative to the data-generating process. A plausible deformation with large $|β|$ and small $γ$ may therefore evade diagnosis and should be represented by a nuisance constrained with auxiliary information or included in a defensible envelope. In the exactly collinear constrained-nuisance benchmark, modelling the deformation restores coverage at the evaluated grid points, at a quantifiable cost in interval sensitivity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.09203",
  "author_total": 1,
  "authors": [
    {
      "name": "Davide Pagano"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1h7j4b97sn2d2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.09203",
  "fulltext_url": null,
  "id": "1h7j4b97sn2d2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.09203",
  "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",
      "hep-ex"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "openalex",
      "3106|Neutrino Physics Research"
    ]
  ],
  "openalex": "W7202213144",
  "pdf_url": "https://arxiv.org/pdf/2608.09203",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1h7j4b97sn2d2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2608.09203",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.09203"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-ex",
      "subfield": "high-energy"
    }
  ],
  "title": "Silent coverage failures in rare-event searches and a degeneracy index that predicts them",
  "title_text": "Silent coverage failures in rare-event searches and a degeneracy index that predicts them",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:26Z",
  "url": "https://research.draconitic.com/paper/1h7j4b97sn2d2",
  "venue": "arXiv",
  "versions": []
}