{
  "abstract": "We study the multi-modal Laplace approximation, given by a weighted Gaussian mixture centred at the local minima of the negative log-density, for sampling from probability measures that concentrate around finitely many modes as an inverse-temperature parameter $n$ grows. Such distributions occur in Bayesian inference in the small noise or large data regime. We derive explicit, non-asymptotic bounds on the Hellinger distance between the multi-modal Laplace approximation and the concentrating posterior. The bound decays like $n^{-1/2}$ with $n$ and the constants depend only polynomially on the dimension $d$. Moreover, we analyse the Laplace mixture as a proposal distribution for self-normalised importance sampling and independent Metropolis--Hastings (IMH) targeting concentration multimodal distributions. We derive asymptotic results, as $n\\to\\infty$, on the effective sample size in case of importance sampling as well as on the average acceptance probability, lag-one autocorrelation, and spectral gap in case of IMH. Numerical experiments illustrate and verify our theoretical findings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03773",
  "author_total": 4,
  "authors": [
    {
      "name": "Maxime Egéa"
    },
    {
      "name": "Hanyue Gu"
    },
    {
      "name": "Daniel Rudolf"
    },
    {
      "name": "Björn Sprungk"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cs6n279t26ac7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03773",
  "fulltext_url": null,
  "id": "cs6n279t26ac7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03773",
  "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",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.CO"
    ],
    [
      "arxiv",
      "stat.TH"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03773",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cs6n279t26ac7.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.03773",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03773"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Multi-modal Laplace-based sampling",
  "title_text": "Multi-modal Laplace-based sampling",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:44Z",
  "url": "https://research.draconitic.com/paper/cs6n279t26ac7",
  "venue": "arXiv",
  "versions": []
}