{
  "abstract": "Ground-based cosmic microwave background (CMB) experiments filter their time-ordered data to remove $1/f$ noise and ground pickup, which removes or mixes the large angular scales where primordial $B$ modes peak. A common remedy is a pseudo-$C_\\ell$ estimator with harmonic $B$-purification and a transfer function measured from simulations. Another applies it after a matrix-based $E/B$ purification of the maps. We extend the quadratic maximum-likelihood (QML) estimator of CosmoForge to filtered maps, treating the filter exactly: a linear filter conjugates the estimator's ingredients without altering its structure. The same holds for the pixel-based likelihood of CosmoForge, which gives the smallest error bar achievable on the same maps. We compare all methods in a simplified setup under several map-level filters through the error bars on bandpowers and on the tensor-to-scalar ratio $r$. QML sits $2$ to $4\\%$ above the pixel-likelihood bound on $σ(r)$ in every filter state. At low noise, the pure pseudo-$C_\\ell$ $σ(r)$ is $1.21$ times QML's without filtering, $3.0$ times under a scan filter along stripes of constant declination, and $3.7$ times under one from a toy constant-elevation scan. The matrix-purified pseudo-$C_\\ell$ $σ(r)$ is at most $1.03$ times QML's except under the constant-elevation filters, where it reaches $1.10$. These factors shrink towards unity at higher noise. The pure pseudo-$C_\\ell$ gap comes from apodisation and from harmonic $E/B$ separation; pixel-space separation closes it, except under the constant-elevation filters, which attenuate modes rather than remove them and widen the gap. QML stays within a few per cent of the optimal error bars without the tuning and simulated transfer functions of the pseudo-$C_\\ell$ pipelines. Thus, CosmoForge provides a robust framework for power-spectrum estimation and inference on filtered maps. (Abridged)",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18012",
  "author_total": 1,
  "authors": [
    {
      "name": "Giacomo Galloni"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0fzc26qxkg6n9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18012",
  "fulltext_url": null,
  "id": "0fzc26qxkg6n9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18012",
  "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.CO"
    ],
    [
      "openalex",
      "3103|Cosmology and Gravitation Theories"
    ]
  ],
  "openalex": "W7221785896",
  "pdf_url": "https://arxiv.org/pdf/2610.18012",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0fzc26qxkg6n9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:11Z",
      "native_id": "2610.18012",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18012"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.CO",
      "subfield": "cosmology"
    }
  ],
  "title": "CosmoForge II. An exact treatment of arbitrary linear filters in quadratic maximum-likelihood power spectrum estimation",
  "title_text": "CosmoForge II. An exact treatment of arbitrary linear filters in quadratic maximum-likelihood power spectrum estimation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:11Z",
  "url": "https://research.draconitic.com/paper/0fzc26qxkg6n9",
  "venue": "arXiv",
  "versions": []
}