{
  "abstract": "The Multilevel Markov chain Monte Carlo algorithm accelerates Bayesian inversion by exploiting correlations between discretized quantities of interest across a hierarchy of model resolutions. A key practical parameter is the subsampling rate used to generate coarse-level proposals for the finer-level chains. Existing practice sets this rate equal to an integrated autocorrelation time as a proxy for proposal decorrelation, but this choice can be overly conservative and lead to substantial computational overhead. In this work we treat finite subsampling as an error-budget question. We derive a cost-error criterion for selecting a computationally efficient subsampling rate using estimates of sample variances, integrated autocorrelation times, and per-level costs. The criterion balances multilevel sampling errors across levels rather than enforcing approximate independence of the coarse proposals. We clarify the theoretical role of independence through an ideal reset-reference kernel, for which independent coarse proposals may be replaced by proposals generated from a reversible coarse-level kernel. We derive a Poisson-equation representation of the perturbation bias resulting from finite subsampling. Under a state-averaged lower-level forgetting assumption, this yields a conditional geometric perturbation-bias bound; in computation, the corresponding projected diagnostic is used as an empirical error-budget check. Numerical experiments on a highly autocorrelated elasticity beam benchmark show substantial reductions in computational cost compared with IAT-based subsampling. A second Darcy-flow inverse problem gives supporting evidence of qualitatively similar finite-subsampling behaviour in another elliptic benchmark.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07956",
  "author_total": 3,
  "authors": [
    {
      "name": "Lise Guilliams"
    },
    {
      "name": "Pieter Vanmechelen"
    },
    {
      "name": "Giovanni Samaey"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fer284616e3y1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07956",
  "fulltext_url": null,
  "id": "fer284616e3y1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07956",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "stat.CO"
    ],
    [
      "openalex",
      "2613|Markov Chains and Monte Carlo Methods"
    ]
  ],
  "openalex": "W7220960906",
  "pdf_url": "https://arxiv.org/pdf/2610.07956",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fer284616e3y1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.07956",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07956"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.CO",
      "subfield": "statistics"
    }
  ],
  "title": "Efficient subsampling-rate selection for practical Multilevel Markov chain Monte Carlo",
  "title_text": "Efficient subsampling-rate selection for practical Multilevel Markov chain Monte Carlo",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:32Z",
  "url": "https://research.draconitic.com/paper/fer284616e3y1",
  "venue": "arXiv",
  "versions": []
}