{
  "abstract": "In pulsar timing array analyses, the stochastic process describing the gravitational wave background is typically modeled using a Fourier basis at discrete frequencies with an interval $\\sim 0.1~\\mathrm{yr}^{-1}$, with a diagonal Fourier-domain covariance determined by the power spectral density at the corresponding frequencies. Although this rank-reduced modeling significantly accelerates likelihood evaluation and provides a good approximation in many scenarios, it can lead to biased parameter inference because it is insensitive to spectral features on scales smaller than $\\sim 0.1~\\mathrm{yr}^{-1}$. We introduce a better construction of the low-rank covariance for low-frequency processes by maximizing the log-likelihood averaged over an ensemble of realizations drawn from the true model likelihood. In this approach, the basis-domain covariance matrix is sensitive to the entire model spectrum and is generally non-diagonal. Using two mock datasets, we demonstrate improved likelihood accuracy and more faithful recovery of spectral features compared to the conventional Fourier-diagonal model. Benchmark tests show that this new model requires a computational cost comparable to that of the conventional approach.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33444",
  "author_total": 3,
  "authors": [
    {
      "name": "Heling Deng"
    },
    {
      "name": "Ken D. Olum"
    },
    {
      "name": "Rutger van Haasteren"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cxmygx14xg519.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33444",
  "fulltext_url": null,
  "id": "cxmygx14xg519",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33444",
  "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.IM"
    ],
    [
      "arxiv",
      "gr-qc"
    ],
    [
      "openalex",
      "3103|Pulsars and Gravitational Waves Research"
    ]
  ],
  "openalex": "W7223887352",
  "pdf_url": "https://arxiv.org/pdf/2610.33444",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cxmygx14xg519.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2610.33444",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33444"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.IM",
      "subfield": "instrumentation-methods"
    },
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Accurate pulsar timing array likelihoods: better low-rank covariance for gravitational wave background",
  "title_text": "Accurate pulsar timing array likelihoods: better low-rank covariance for gravitational wave background",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:35Z",
  "url": "https://research.draconitic.com/paper/cxmygx14xg519",
  "venue": "arXiv",
  "versions": []
}