{
  "abstract": "In many practical applications of Bayesian inference, it is difficult or undesirable to compute the gradient of the negative log-posterior, motivating the study of derivative-free samplers, also called zeroth-order samplers. The aim of this paper is to generalize and rigorously analyze a multiscale derivative-free sampler recently proposed in the literature by Pavliotis, Stuart and Vaes (2022). In the discrete-time setting, the multiscale sampler we study bears a strong resemblance to other recently proposed methods, such as the so-called zeroth-order perturbed stochastic gradient descent algorithm (Jin et al., 2018) and the zeroth-order Langevin Monte Carlo algorithm by Roy et al. (2022). We present error estimates with respect to all the parameters of the problem, both in the continuous-time and discrete-time settings. The error estimates are in three different metrics: strong convergence, convergence of ergodic averages, and uniform-in-time weak convergence.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17037",
  "author_total": 2,
  "authors": [
    {
      "name": "Antonin Della Noce"
    },
    {
      "name": "Urbain Vaes"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/epk54vhbmwyxz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17037",
  "fulltext_url": null,
  "id": "epk54vhbmwyxz",
  "issns": [],
  "landing_url": "https://hal.science/hal-05843830v1",
  "language": "en",
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
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      "arxiv",
      "cs.NA"
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      "arxiv",
      "math.NA"
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      "hal",
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  "pdf_url": "https://arxiv.org/pdf/2610.17037",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/epk54vhbmwyxz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:03Z",
      "native_id": "hal-05843830",
      "source": "hal",
      "url": "https://hal.science/hal-05843830v1"
    },
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.17037",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17037"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Analysis of a zeroth-order multiscale sampler: strong convergence, convergence of ergodic averages and weak convergence",
  "title_text": "Analysis of a zeroth-order multiscale sampler: strong convergence, convergence of ergodic averages and weak convergence",
  "type": "preprint",
  "updated_at": "2026-10-31T12:20:56Z",
  "url": "https://research.draconitic.com/paper/epk54vhbmwyxz",
  "venue": "HAL",
  "versions": []
}