{
  "abstract": "In exact Bayes rules for change-points, the penalty of a change-point decomposes into a localisation cost of 2 log n, for specifying its position among n candidates, and a dimension cost of order log n per changing coefficient. We show that, for small jumps, the localisation cost is determined by the loss. We introduce losses that tolerate an error of w positions on each change-point, bridging the exact 0–1 loss and a counting loss whose Bayes rule is the posterior mode of the number of change-points. For one small change in a Gaussian mean, the counting rule sums the Bayes factors over all positions; the effective number of positions has a limit law involving a functional of a Brownian motion with drift, and the detection threshold on the squared standardised jump falls from 3 log n to log n. In exchange, the false alarm rate, which still vanishes, is bounded by n^(-1/2) rather than n^(-1), up to logarithmic factors. For several change-points, we prove a band, stated with joint energies, between the thresholds of the two rules. In regression with q changing coefficients, the exact rule needs (2+q) log n, and we conjecture that the counting rule relaxes this to q log n. Simulations compare the rules with other criteria.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Faouzi Lyazrhi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ap41jvhcgn6ge.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "ap41jvhcgn6ge",
  "issns": [],
  "landing_url": "https://hal.science/hal-05792398v2",
  "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",
      "0.stat"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05792398/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ap41jvhcgn6ge.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:02Z",
      "native_id": "hal-05792398",
      "source": "hal",
      "url": "https://hal.science/hal-05792398v2"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:0.stat",
      "subfield": "statistics"
    }
  ],
  "title": "The cost of an exact position: tolerant losses, integrated positions and detection thresholds for change-points",
  "title_text": "The cost of an exact position: tolerant losses, integrated positions and detection thresholds for change-points",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:02Z",
  "url": "https://research.draconitic.com/paper/ap41jvhcgn6ge",
  "venue": "HAL",
  "versions": []
}