{
  "abstract": "This paper establishes the theoretical validity of the use of adaptive templates in the context of simultaneous control of the False Discovery Proportion (FDP). Previous work, Blain et al. (2022), has shown that combining data-driven templates with the inference framework of Blanchard et al. (2020) improves the quality of the resulting post-hoc bounds, however the validity guarantees provided relied on datasplitting. In this work we demonstrate that using data-driven templates, learnt on the same dataset via resampling, provides asymptotically valid inference. We prove that these templates converge as the sample size increases, and use this to establish asymptotic control of the joint error rate and provide valid simultaneous lower bounds for the FDP as a consequence. We show that using a single round of bootstraps to learn the templates is sufficient for validity, allowing for a speed up in the inference procedure. We provide experiments validating the approach, showing that using the same dataset to learn the templates and perform inference is valid in practice and increases power relative to data-splitting.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "name": "Samuel Davenport"
    },
    {
      "name": "Bertrand Thirion"
    },
    {
      "name": "Pierre Neuvial"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2tz99a73gmw7r.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "2tz99a73gmw7r",
  "issns": [],
  "landing_url": "https://hal.science/hal-05778262v1",
  "language": "en",
  "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": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-st"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05778262/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-06-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2tz99a73gmw7r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:47Z",
      "native_id": "hal-05778262",
      "source": "hal",
      "url": "https://hal.science/hal-05778262v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-st",
      "subfield": "statistics"
    }
  ],
  "title": "Post Hoc Confidence Bounds On False Positives Using Learned Templates",
  "title_text": "Post Hoc Confidence Bounds On False Positives Using Learned Templates",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:47Z",
  "url": "https://research.draconitic.com/paper/2tz99a73gmw7r",
  "venue": "HAL",
  "versions": []
}