{
  "abstract": "In astrophysics, the distributions of fluxes or intensities of populations of sources provide insight into the structure and evolution of the universe. We propose a science-driven hierarchical Bayesian framework to estimate the X-ray flux distribution of a population of galaxies. The distribution is parameterized via a broken power law model, formulated as a mixture of Pareto distributions, and is fit using data from a combination of non-representative X-ray and optical surveys. Because fainter sources are less likely to be detected, astronomical surveys suffer from incompleteness at the low-intensity end, and dedicated survey simulations are used to study the resulting missing-data pattern and determine the form of corrections. We introduce a methodology to combine data from two (or more) surveys with different incompleteness functions. This allows us to leverage deeper surveys (e.g., optical) to more fully characterize the X-ray log(N)-log(S) (where fewer sources are detected). We take advantage of a well-calibrated characterization of the missing-data pattern, particularly in X-ray surveys, to make incompleteness corrections for sources that are not detected in either survey. The proposed model is validated using a simulation study designed to mimic the Chandra Deep Field South (CDF-S), demonstrating accurate recovery of the flux distribution even under high proportions of systematic incompleteness. Finally, we apply our proposed method to data from the CDF-S.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37855",
  "author_total": 6,
  "authors": [
    {
      "name": "Maximilian Autenrieth"
    },
    {
      "name": "David A. van Dyk"
    },
    {
      "name": "Vinay Kashyap"
    },
    {
      "name": "Andreas Zezas"
    },
    {
      "name": "Aneta Siemiginowska"
    },
    {
      "name": "David C. Stenning"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/darkeswn2ws6v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37855",
  "fulltext_url": null,
  "id": "darkeswn2ws6v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37855",
  "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",
      "astro-ph.GA"
    ],
    [
      "arxiv",
      "astro-ph.IM"
    ],
    [
      "arxiv",
      "stat.AP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.37855",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/darkeswn2ws6v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:23Z",
      "native_id": "2610.37855",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37855"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.GA",
      "subfield": "galaxies"
    },
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.IM",
      "subfield": "instrumentation-methods"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.AP",
      "subfield": "statistics"
    }
  ],
  "title": "Combining Multiple Incomplete Astronomical Surveys to Estimate Galaxy Flux Distributions",
  "title_text": "Combining Multiple Incomplete Astronomical Surveys to Estimate Galaxy Flux Distributions",
  "type": "preprint",
  "updated_at": "2026-11-01T12:21:00Z",
  "url": "https://research.draconitic.com/paper/darkeswn2ws6v",
  "venue": "arXiv",
  "versions": []
}