{
  "abstract": "We investigate the accuracy and computational efficiency of posterior approximations for gravitational-wave (GW) parameter estimation based on Fisher Matrix and its higher-order extension, the Derivative Approximation for LIkelihoods (DALI), in the context of tests of General Relativity using parameterized deviations in the inspiral waveforms (the TIGER formalism). We adopt the \\texttt{IMRPhenomD} waveform and compare the exact posterior sampling to the following approximations in increasing order of complexity: the traditional Fisher Matrix, the Fisher sampling (singlet-DALI), the doublet-DALI and the triplet-DALI. We find that both singlet and doublet-DALI are significantly faster than the exact posterior by factors between 20 and 1000, depending on the inspiral SNRs -- larger gains correspond to larger SNRs. These gains are considerably larger for more complete waveforms, such as \\texttt{IMRPhenomHM}. To evaluate the accuracy of the approximations, we use Jensen-Shannon divergence. We conclude that both singlet and doublet-DALI systematically improves over the standard Fisher Matrix approximation, while triplet-DALI shows large variability, limiting its practical advantage. We also introduce a code with a new implementation of Fisher and DALI analysis (Symbolic DALI, \\texttt{SymDALI}) which computes derivatives symbolically via \\textit{Wolfram Language}.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.38399",
  "author_total": 4,
  "authors": [
    {
      "name": "Felipe A. da Silva Barbosa"
    },
    {
      "name": "Davi C. Rodrigues"
    },
    {
      "name": "Josiel Mendonça Soares de Souza"
    },
    {
      "name": "Miguel Quartin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6m47rwbkhvnxh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.38399",
  "fulltext_url": null,
  "id": "6m47rwbkhvnxh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.38399",
  "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",
      "astro-ph.CO"
    ],
    [
      "arxiv",
      "astro-ph.IM"
    ],
    [
      "arxiv",
      "gr-qc"
    ],
    [
      "arxiv",
      "physics.data-an"
    ],
    [
      "openalex",
      "3103|Pulsars and Gravitational Waves Research"
    ]
  ],
  "openalex": "W7215100619",
  "pdf_url": "https://arxiv.org/pdf/2609.38399",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6m47rwbkhvnxh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:48Z",
      "native_id": "2609.38399",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.38399"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.CO",
      "subfield": "cosmology"
    },
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.IM",
      "subfield": "instrumentation-methods"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.data-an",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Fisher and DALI posterior approximations for testing gravity with gravitational waves",
  "title_text": "Fisher and DALI posterior approximations for testing gravity with gravitational waves",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:48Z",
  "url": "https://research.draconitic.com/paper/6m47rwbkhvnxh",
  "venue": "arXiv",
  "versions": []
}