{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/optimal-estimation-of-the-binned-mask-free-1","title":"Optimal Estimation of the Binned Mask-Free Power Spectrum, Bispectrum, and Trispectrum on the Full Sky: Tensor Edition","arxiv_id":"2306.03915","date":"2023-06-06","proceeding":null,"authors":["Oliver H. E. Philcox"],"abstract":"We derive optimal estimators for the binned two-, three-, and four-point correlators of statistically isotropic tensor fields defined on the sphere, in the presence of arbitrary beams, inpainting, and masking. This is a conceptually straightforward extension of the associated scalar field Philcox (2023), but upgraded to include spin-$2$ fields such as Cosmic Microwave Background polarization and galaxy shear, and parity-violating physics in all correlators. All estimators can be realized using spin-weighted spherical harmonic transforms and Monte Carlo summation and are are implemented in the public code PolyBin, with computation scaling, at most, with the total number of bins. We perform a suite of validation tests verifying that the estimators are unbiased and, in limiting regimes, minimum variance. These facilitate general binned analyses of higher-point functions, and allow constraints to be placed on various phenomena, such as non-separable inflationary physics (novelly including polarized trispectra), non-linear evolution in the late Universe, and cosmic parity-violation.","url_abs":"https://arxiv.org/abs/2306.03915v2","url_pdf":"https://arxiv.org/pdf/2306.03915v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"optimal-estimation-of-the-binned-mask-free-1","repo_url":"https://github.com/oliverphilcox/polybin","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}