{
  "abstract": "Many statistical models involve parameter-dependent normalizing constants that are computationally intractable, creating substantial obstacles to standard Bayesian inference. Although existing likelihood-based algorithms can often circumvent these constants, their uncertainty quantification may be poorly calibrated under model misspecification. To address these challenges, we propose SME-BETEL, a semiparametric Bayesian framework that combines score matching estimating equations with Bayesian exponentially tilted empirical likelihood. The resulting posterior avoids evaluation of normalizing constants and does not require learning-rate calibration. Building on this framework, we develop a new score matching criterion for mixed-domain data, extending SME-BETEL to models whose observations combine components from different sample spaces. This construction enables robust Bayesian inference for mixed-domain doubly-intractable models. We establish consistency and asymptotic normality of the score matching estimator, and prove a Bernstein-von Mises theorem for the SME-BETEL posterior. These results show that SME-BETEL credible sets are asymptotically calibrated to the sampling variability of the score matching estimator, yielding valid frequentist coverage under model misspecification. Simulation studies show that SME-BETEL remains competitive under correct specification and substantially improves uncertainty quantification under misspecification. An ozone-monitoring application demonstrates the practical utility of the mixed-domain construction for spatial preferential modeling.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01783",
  "author_total": 3,
  "authors": [
    {
      "name": "Jiongran Wang"
    },
    {
      "name": "Debdeep Pati"
    },
    {
      "name": "Anirban Bhattacharya"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8hm7zvnxdyt55.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01783",
  "fulltext_url": null,
  "id": "8hm7zvnxdyt55",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01783",
  "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",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "2613|Markov Chains and Monte Carlo Methods"
    ]
  ],
  "openalex": "W7207827436",
  "pdf_url": "https://arxiv.org/pdf/2609.01783",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8hm7zvnxdyt55.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:29Z",
      "native_id": "2609.01783",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01783"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Robust Bayesian Inference for Unnormalized Models with Mixed-Domain Data",
  "title_text": "Robust Bayesian Inference for Unnormalized Models with Mixed-Domain Data",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:29Z",
  "url": "https://research.draconitic.com/paper/8hm7zvnxdyt55",
  "venue": "arXiv",
  "versions": []
}