{"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/solving-the-empirical-bayes-normal-means","title":"Solving the Empirical Bayes Normal Means Problem with Correlated Noise","arxiv_id":"1812.07488","date":"2018-12-18","proceeding":null,"authors":["Lei Sun","Matthew Stephens"],"abstract":"The Normal Means problem plays a fundamental role in many areas of modern\nhigh-dimensional statistics, both in theory and practice. And the Empirical\nBayes (EB) approach to solving this problem has been shown to be highly\neffective, again both in theory and practice. However, almost all EB treatments\nof the Normal Means problem assume that the observations are independent. In\npractice correlations are ubiquitous in real-world applications, and these\ncorrelations can grossly distort EB estimates. Here, exploiting theory from\nSchwartzman (2010), we develop new EB methods for solving the Normal Means\nproblem that take account of unknown correlations among observations. We\nprovide practical software implementations of these methods, and illustrate\nthem in the context of large-scale multiple testing problems and False\nDiscovery Rate (FDR) control. In realistic numerical experiments our methods\ncompare favorably with other commonly-used multiple testing methods.","url_abs":"http://arxiv.org/abs/1812.07488v2","url_pdf":"http://arxiv.org/pdf/1812.07488v2.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":"abstracts"},"code_links":[{"paper_slug":"solving-the-empirical-bayes-normal-means","repo_url":"https://github.com/LSun/cashr_paper","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}