{"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/testing-quadratic-maximum-likelihood","title":"Testing Quadratic Maximum Likelihood estimators for forthcoming Stage-IV weak lensing surveys","arxiv_id":"2207.10412","date":"2022-07-21","proceeding":null,"authors":["Alessandro Maraio","Alex Hall","Andy Taylor"],"abstract":"Headline constraints on cosmological parameters from current weak lensing surveys are derived from two-point statistics that are known to be statistically sub-optimal, even in the case of Gaussian fields. We study the performance of a new fast implementation of the Quadratic Maximum Likelihood (QML) estimator, optimal for Gaussian fields, to test the performance of Pseudo-Cl estimators for upcoming weak lensing surveys and quantify the gain from a more optimal method. Through the use of realistic survey geometries, noise levels, and power spectra, we find that there is a decrease in the errors in the statistics of the recovered E-mode spectra to the level of ~20% when using the optimal QML estimator over the Pseudo-Cl estimator on the largest angular scales, while we find significant decreases in the errors associated with the B-modes for the QML estimator. This raises the prospects of being able to constrain new physics through the enhanced sensitivity of B-modes for forthcoming surveys that our implementation of the QML estimator provides. We test the QML method with a new implementation that uses conjugate-gradient and finite-differences differentiation methods resulting in the most efficient implementation of the full-sky QML estimator yet, allowing us to process maps at resolutions that are prohibitively expensive using existing codes. In addition, we investigate the effects of apodisation, B-mode purification, and the use of non-Gaussian maps on the statistical properties of the estimators. Our QML implementation is publicly available and can be accessed from GitHub.","url_abs":"https://arxiv.org/abs/2207.10412v1","url_pdf":"https://arxiv.org/pdf/2207.10412v1.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":"testing-quadratic-maximum-likelihood","repo_url":"https://github.com/alexmaraio/weaklensingqml","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}