{
  "abstract": "Bayesian pseudo-posteriors based on moment conditions, such as Bayesian empirical likelihood (EL) and Bayesian exponentially tilted empirical likelihood (ETEL), provide a robust route to Bayesian inference when the model is specified only through moment restrictions, but their computation is often prohibitive. In this work, we address two barriers to Bayesian pseudo-inference under moment restrictions. First, scalable sampling is challenging for tall data because the pseudo-likelihoods are not log-additive across observations, so standard likelihood-subsampling methods do not apply. Second, in simulation-based and latent-variable problems, the moment function itself may be defined through an intractable expectation, making full-data pseudo-posterior inference infeasible. We develop a new family of subsampled pseudo-posteriors that replaces the full-data pseudo-posterior with an aggregate of mini-batch pseudo-posteriors. We show that naive mini-batching induces a shifted-mixture distortion, yielding aggregates that are correctly centered but overly diffuse. To remove this distortion, we introduce moment-function-level control variates that align mini-batch moment equations around a reference estimator and recover the full-data posterior shape. For Bayesian ETEL, we establish finite-sample total variation bounds to the full-data pseudo-posterior, allowing discontinuous and intractable moment functions. Numerical experiments show that the method applies broadly across moment-condition-based Bayesian pseudo-inference, closely approximates full-data pseudo-posteriors, and substantially reduces computational cost.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05308",
  "author_total": 2,
  "authors": [
    {
      "name": "Wenshuo Zhao"
    },
    {
      "name": "Rong Tang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/csxr4spm8xe59.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05308",
  "fulltext_url": null,
  "id": "csxr4spm8xe59",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05308",
  "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",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Markov Chains and Monte Carlo Methods"
    ]
  ],
  "openalex": "W7211912323",
  "pdf_url": "https://arxiv.org/pdf/2609.05308",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/csxr4spm8xe59.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.05308",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05308"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Subsampled Pseudo-posteriors for Scalable Bayesian Moment-condition Inference",
  "title_text": "Subsampled Pseudo-posteriors for Scalable Bayesian Moment-condition Inference",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:25Z",
  "url": "https://research.draconitic.com/paper/csxr4spm8xe59",
  "venue": "arXiv",
  "versions": []
}