{
  "abstract": "The learning rate of a generalized posterior governs posterior uncertainty but typically has no canonical value. Generalized posterior calibration (GPC) selects this rate by matching bootstrap-estimated credible-interval coverage to its nominal level, often requiring repeated posterior simulation. We propose GPC via importance reweighting (GPC-IRW), which reuses draws from a reference posterior fitted to the original data across bootstrap resamples and candidate learning rates. For quantile-based intervals of a scalar functional, we express the coverage criterion in terms of bootstrap posterior cumulative distribution functions, avoiding computation of individual bootstrap credible intervals. Safeguards based on importance-weight effective sample size and proximity to coverage-decision boundaries invoke reweighting from cached bootstrap-specific draws or direct posterior simulation when necessary. Under the stated regularity conditions, with numerical error tending to zero, we show that median-centered calibration preserves the first-order learning-rate target and achieves asymptotically nominal coverage. The approach extends to independent clusters through cluster-level resampling. Simulations yield coverage and interval lengths comparable to those of existing GPC algorithms at substantially lower computational cost. In an exoplanet mass-radius analysis, GPC-IRW achieves 6.7- and 9.6-fold speedups over MCMC-based calibration in the single-planet and full-sample analyses, respectively, while illustrating the effects of within-host dependence.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37232",
  "author_total": 1,
  "authors": [
    {
      "name": "Masahiro Tanaka"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bwneeyzqjwvm3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37232",
  "fulltext_url": null,
  "id": "bwneeyzqjwvm3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37232",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "stat.CO"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "openalex",
      "2613|Markov Chains and Monte Carlo Methods"
    ]
  ],
  "openalex": "W7224109801",
  "pdf_url": "https://arxiv.org/pdf/2610.37232",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bwneeyzqjwvm3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:59Z",
      "native_id": "2610.37232",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37232"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.CO",
      "subfield": "statistics"
    }
  ],
  "title": "Efficient Bootstrap Calibration of Generalized Posteriors with Importance Reweighting",
  "title_text": "Efficient Bootstrap Calibration of Generalized Posteriors with Importance Reweighting",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:59Z",
  "url": "https://research.draconitic.com/paper/bwneeyzqjwvm3",
  "venue": "arXiv",
  "versions": []
}