{
  "abstract": "We develop two complementary Bayesian procedures for analytic inference under informative sampling. The first constructs a coherent likelihood by modeling the sample-level distribution of the design weight given the study variable and recovering the conditional inclusion probability through the identity of Sverchkov and Pfeffermann (2004); it is the Bayesian counterpart of a recently proposed conditional-likelihood estimator, attains the model-based efficiency bound under the correctly specified sample-level joint model, and can be biased otherwise. The second uses the same weight model only as input to a Neyman-orthogonalized analog of the design-weighted score and applies the loss-likelihood bootstrap; the resulting credible intervals are asymptotically sandwich-correct under Poisson sampling, and the posterior remains centered at the truth under misspecification of the weight model, although the working model can still affect the first-order variance. A beta regression on the population-level inclusion probability, inducing a beta prime sample-level weight distribution, serves as the parametric default. A data-adaptive implementation of the second procedure estimates the efficient factor $\\barπ(x,y)=1/E_p(W\\mid x,y)$ by a design-weighted Gamma/log-link regression and uses it in a joint one-step loss-likelihood bootstrap for the analytic parameter; its validity requires no rate conditions on the nuisance fit. We illustrate both procedures with simulations and Canadian Workforce data.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.16225",
  "author_total": 3,
  "authors": [
    {
      "name": "Kosuke Morikawa"
    },
    {
      "name": "Jae Kwang Kim"
    },
    {
      "name": "Won Chang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6abvp3whh47ax.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.16225",
  "fulltext_url": null,
  "id": "6abvp3whh47ax",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.16225",
  "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",
      "stat.ME"
    ],
    [
      "openalex",
      "2613|Survey Sampling and Estimation Techniques"
    ]
  ],
  "openalex": "W7213437129",
  "pdf_url": "https://arxiv.org/pdf/2609.16225",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6abvp3whh47ax.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:51Z",
      "native_id": "2609.16225",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.16225"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Coherent and robust Bayesian inference under informative sampling via sample-level weight models",
  "title_text": "Coherent and robust Bayesian inference under informative sampling via sample-level weight models",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:51Z",
  "url": "https://research.draconitic.com/paper/6abvp3whh47ax",
  "venue": "arXiv",
  "versions": []
}