{
  "abstract": "Bridge sampling estimates of marginal likelihoods are routinely reported with a delta-method Monte Carlo standard error (MCSE). Existing theory is asymptotic and cannot say whether a given run is long enough to trust the estimate or its MCSE. We give finite-sample answers. The optimal bridge estimator fits a logistic regression that separates posterior from proposal draws, and its accuracy is governed by their overlap, within a factor of two of the classification's Bayes error. Because the estimating function is a sum of bounded terms, no moment conditions are needed, and all bounds hold uniformly over targets, proposals and dimensions. A number of draws inversely proportional to the overlap suffices and is necessary in the worst case, paralleling the exponential-in-Kullback--Leibler requirement of importance sampling. A Berry--Esseen bound with an explicit constant holds at the optimal rate, and the MCSE is accurate once the effective overlap is large; it is estimated at no cost. For Markov chain draws, the required sample size grows in proportion to the sampler's relaxation time, unavoidably in the worst case. The estimated bridge, the fixed-point iteration and the fitted proposal matter only at second order, and we give free diagnostics for sampler failure and misestimated autocorrelation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17403",
  "author_total": 1,
  "authors": [
    {
      "name": "Giorgio Micaletto"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fsgaf5jxgz456.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17403",
  "fulltext_url": null,
  "id": "fsgaf5jxgz456",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17403",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.CO"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Markov Chains and Monte Carlo Methods"
    ]
  ],
  "openalex": "W7221780229",
  "pdf_url": "https://arxiv.org/pdf/2610.17403",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fsgaf5jxgz456.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.17403",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17403"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Overlap, Not Moments: Finite-Sample Theory for Bridge Sampling",
  "title_text": "Overlap, Not Moments: Finite-Sample Theory for Bridge Sampling",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:26Z",
  "url": "https://research.draconitic.com/paper/fsgaf5jxgz456",
  "venue": "arXiv",
  "versions": []
}