{
  "abstract": "Approximate Bayesian computation (ABC) replaces likelihood evaluation by simulation and comparison of observed and synthetic data. We establish minimax-rate guarantees for nonparametric ABC under random-series priors with simulable finite-dimensional coordinates. The contraction theorem uses local prior mass, bounds on ABC acceptance probabilities, and control of prior mass outside a sieve. In fixed-design orthogonal-series regression with centered $g$-and-$k$ errors, an infinite Gaussian series prior with a compact scale hyperprior yields minimax-rate contraction and a minimax-rate clipped posterior mean. In compound Poisson decompounding, only random sums are observed and the target is the underlying jump density. With an unknown count intensity in a fixed compact subinterval of $(0,π/2)$, we prove stability of the zero-count-augmented trigonometric population summaries and use a square-root Gaussian series prior on the space of probability density functions. Over bounded periodic Sobolev classes of smoothness $α>d/2$, a polynomially enlarged synthetic sample yields ABC contraction at rate $n^{-α/(2α+d)}$ and posterior mean squared risk of order $n^{-2α/(2α+d)}$, matching a lower bound for the aggregate-observation model. Rejection-ABC Monte Carlo approximations inherit these rates under sufficient sampling budgets.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.15648",
  "author_total": 1,
  "authors": [
    {
      "name": "Hien Duy Nguyen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4486f6kzwf57j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.15648",
  "fulltext_url": null,
  "id": "4486f6kzwf57j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.15648",
  "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.TH"
    ],
    [
      "openalex",
      "2613|Markov Chains and Monte Carlo Methods"
    ]
  ],
  "openalex": "W7203666054",
  "pdf_url": "https://arxiv.org/pdf/2608.15648",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4486f6kzwf57j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2608.15648",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.15648"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "On the minimax-rate optimality of approximate Bayesian computation in nonparametric problems",
  "title_text": "On the minimax-rate optimality of approximate Bayesian computation in nonparametric problems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:10Z",
  "url": "https://research.draconitic.com/paper/4486f6kzwf57j",
  "venue": "arXiv",
  "versions": []
}