{
  "abstract": "This paper studies randomised quasi-Monte Carlo (RQMC) methods for Metropolis--Hastings (MH) algorithms, whose accept--reject discontinuity complicates RQMC analysis. To circumvent some of these complications, we study Array-RQMC for MH, with $N$ replicated chains evolved over a fixed time horizon $T$, where we make use of Hilbert sorting for joint multidimensional updates at each step. For one-dimensional MH and bounded-variation test functions, we prove a sampling mean squared error bound of $\\mathcal O_T(N^{-4/3})$ relative to the finite-horizon expectation. For product targets, coordinatewise Array-RQMC Metropolis-within-Gibbs retains this exponent for additive marginal bounded-variation tests, with constants that may depend on dimension. With Gaussian random-walk proposals, the bounds extend to scalar and additive marginal polynomials with an additional factor $(\\log N)^\\ell$, where $\\ell$ is the maximum polynomial degree. For joint updates in state dimension $p$ using $p$ proposal uniforms, we provide a conditional $\\mathcal O_T(N^{-1-1/(p+2)})$ framework under regularity assumptions that are not verified for the joint multidimensional examples. Numerical experiments support the verified one-dimensional theory and demonstrate variance reduction for joint Hilbert-sorted updates, including Bayesian logistic regression, while illustrating the limitations of these gains as dimension increases.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.36431",
  "author_total": 4,
  "authors": [
    {
      "name": "Jiarui Du"
    },
    {
      "name": "Josef Dick"
    },
    {
      "name": "Zexin Pan"
    },
    {
      "name": "Houying Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c07r92vab5sxf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36431",
  "fulltext_url": null,
  "id": "c07r92vab5sxf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.36431",
  "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.ME"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2612|Mathematical Approximation and Integration"
    ]
  ],
  "openalex": "W7224130615",
  "pdf_url": "https://arxiv.org/pdf/2610.36431",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c07r92vab5sxf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.36431",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36431"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Fixed-Horizon Error Rates for Array-RQMC Metropolis-Hastings",
  "title_text": "Fixed-Horizon Error Rates for Array-RQMC Metropolis-Hastings",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:53Z",
  "url": "https://research.draconitic.com/paper/c07r92vab5sxf",
  "venue": "arXiv",
  "versions": []
}