{"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/sidestepping-the-inversion-of-the-weak","title":"Sidestepping the inversion of the weak-lensing covariance matrix with Approximate Bayesian Computation","arxiv_id":"2112.03148","date":"2021-12-06","proceeding":null,"authors":["Martin Kilbinger","Emille E. O. Ishida","Jessi Cisewski-Kehe"],"abstract":"Weak gravitational lensing is one of the few direct methods to map the dark-matter distribution on large scales in the Universe, and to estimate cosmological parameters. We study a Bayesian inference problem where the data covariance $\\mathbf{C}$, estimated from a number $n_{\\textrm{s}}$ of numerical simulations, is singular. In a cosmological context of large-scale structure observations, the creation of a large number of such $N$-body simulations is often prohibitively expensive. Inference based on a likelihood function often includes a precision matrix, $\\Psi = \\mathbf{C}^{-1}$. The covariance matrix corresponding to a $p$-dimensional data vector is singular for $p \\ge n_{\\textrm{s}}$, in which case the precision matrix is unavailable. We propose the likelihood-free inference method Approximate Bayesian Computation (ABC) as a solution that circumvents the inversion of the singular covariance matrix. We present examples of increasing degree of complexity, culminating in a realistic cosmological scenario of the determination of the weak-gravitational lensing power spectrum for the upcoming European Space Agency satellite Euclid. While we found the ABC parameter estimate variances to be mildly larger compared to likelihood-based approaches, which are restricted to settings with $p < n_{\\textrm{s}}$, we obtain unbiased parameter estimates with ABC even in extreme cases where $p / n_{\\textrm{s}} \\gg 1$. The code has been made publicly available to ensure the reproducibility of the results.","url_abs":"https://arxiv.org/abs/2112.03148v2","url_pdf":"https://arxiv.org/pdf/2112.03148v2.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":"sidestepping-the-inversion-of-the-weak","repo_url":"https://github.com/emilleishida/corrmatrix_abc","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"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}