{
  "abstract": "Examination capacity is fixed, so a supervisor screening firms must decide which files to open rather than which firms are deficient. A movement in the class prior rescales the posterior monotonically, leaving the ranking untouched and with it, the area under the receiver operating characteristic curve; that much is classical. This paper takes up the two quantities such a supervisor actually feels, neither of them a functional of the ranking. Hold the cut-off fixed: the detection rate does not move, the flagged share moves by the prevalence change times the Youden index—the adjusted-count identity of the quantification literature, read here as a workload forecast—and an exact algebraic split separates the deployment precision gap into a prior term, which recalibration reaches, and a residual, which it does not. Sorting the usual summaries by prior-invariance and by dependence on the operating region shows that both properties belong to quantities indexed by a fixed cut-off alone; the area under the curve carries only one, and precision and lift at a fixed budget only the other. The same indexing settles the decision problem: under a pure prior movement, carrying a cut-off across the deployment gap weakly dominates carrying a selection rate whichever way the prior moves, with an exact shortfall and a characterised equality case. That dominance is the paper’s one new analytical statement; the remaining apparatus is classical or a specialisation of existing methods, and a dedicated subsection of this paper says which is which, result by result. An exact binomial tolerance bound calibrates the budget—an order-statistic construction borrowed from Neyman–Pearson classification—and its certified level inflates by the distance between the positive-class score laws, a distance to which a prior movement contributes nothing. Two panels supply the evidence, and are the substance of the contribution: 122,335 United States firm-years under enforcement-based misstatement labels, and 172,566 bank-years over which the prior moves by a factor of 45 in both directions. Precision at the five per cent operating budget tracks the base rate there with an elasticity of 0.986, while chance-adjusted discrimination moves at −0.005, and a transported cut-off captures 71.4 and 93.1 per cent of the attainable audit surplus—the share of the value an oracle policy could realise at the same budget—against 2.8 and 33.2 for a standing fixed-share policy. Two negative findings follow: recalibration reaches only the smaller part of the deployment precision gap on the enforcement panel, and distribution-free certificates fall short of their certified coverage once deployed.",
  "abstract_shown": true,
  "affiliations": [
    "China-ASEAN Institute of Statistics, Guangxi University of Finance and Economics, Nanning 530003, China",
    "Graduate School of Technology and Management, Kyung Hee University, Seoul 02447, Republic of Korea"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Songbao Li"
    },
    {
      "affs": [
        0
      ],
      "name": "Dongxu Mo"
    },
    {
      "affs": [
        1
      ],
      "name": "Chao He"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/atd4f45b35wdy.bib",
  "cited_by": 0,
  "doi": "10.3390/math14193571",
  "fulltext_url": null,
  "id": "atd4f45b35wdy",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/19/3571",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "1702|Imbalanced Data Classification Techniques"
    ]
  ],
  "openalex": "W7216050324",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/atd4f45b35wdy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14193571",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/19/3571"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:2227-7390",
      "subfield": "general"
    }
  ],
  "title": "Prior-Shift-Invariant Threshold Transport in Budget-Constrained Supervisory Screening: Workload Identity, Prior–Drift Decomposition, and Distribution-Free Risk Control",
  "title_text": "Prior-Shift-Invariant Threshold Transport in Budget-Constrained Supervisory Screening: Workload Identity, Prior–Drift Decomposition, and Distribution-Free Risk Control",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/atd4f45b35wdy",
  "venue": "Mathematics",
  "versions": []
}