{
  "abstract": "The Brier risk summarizes probability-prediction error but does not explain why two prediction rules differ. We develop Brier-UDAM, a framework for paired binary prediction-rule comparisons that separates the Brier-risk difference into mean-bias, dispersion, and Brier-scale alignment contributions. Although the observable contrast identity follows algebraically from Yates-type moment decompositions, the framework gives these terms a latent-risk interpretation and shows that paired contrasts can be identified from observed outcomes and paired predictions without estimating the conditional event-risk function. For two rules evaluated in the same target population, the exact identity $ΔR = ΔM + ΔD + ΔL$ holds, and the corresponding plug-in estimators reproduce the empirical paired Brier-risk difference exactly in finite samples. We derive influence-function-based inference for first-order regular contrasts and a projection-based confidence procedure for the mean-bias contrast when first-order inference degenerates. Simulations confirmed interpretable component behavior, recovery of the target contrasts, and generally satisfactory inference in regular settings; projection intervals retained coverage near degeneracy but were conservative. In a large public-data analysis of 30-day hospital readmission, models with similar held-out Brier risks showed substantially larger and opposing dispersion and alignment contributions, revealing cancellation that was hidden in the aggregate score. Brier-UDAM therefore provides a diagnostic account of paired Brier-risk differences, while calibration, discrimination, and information-based assessments continue to address their distinct performance questions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06945",
  "author_total": 2,
  "authors": [
    {
      "name": "Eiji Nakatani"
    },
    {
      "name": "Hiroya Hashimoto"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dm2rm05tskqsy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06945",
  "fulltext_url": null,
  "id": "dm2rm05tskqsy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06945",
  "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 Methods in Epidemiology"
    ]
  ],
  "openalex": "W7212040634",
  "pdf_url": "https://arxiv.org/pdf/2609.06945",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dm2rm05tskqsy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:07Z",
      "native_id": "2609.06945",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06945"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Brier-UDAM for Paired Prediction-Rule Comparisons: Latent-Risk Interpretation, Observable Contrasts, and Inference",
  "title_text": "Brier-UDAM for Paired Prediction-Rule Comparisons: Latent-Risk Interpretation, Observable Contrasts, and Inference",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:07Z",
  "url": "https://research.draconitic.com/paper/dm2rm05tskqsy",
  "venue": "arXiv",
  "versions": []
}