{"type":"journal_article","language":[{"iso":"eng"}],"abstract":[{"text":"We study maximum likelihood estimation in Gaussian graphical models from a geometric point of view. An algebraic elimination criterion allows us to find exact lower bounds on the number of observations needed to ensure that the maximum likelihood estimator (MLE) exists with probability one. This is applied to bipartite graphs, grids and colored graphs. We also study the ML degree, and we present the first instance of a graph for which the MLE exists with probability one, even when the number of observations equals the treewidth.","lang":"eng"}],"citation":{"ama":"Uhler C. Geometry of maximum likelihood estimation in Gaussian graphical models. <i>Annals of Statistics</i>. 2012;40(1):238-261. doi:<a href=\"https://doi.org/10.1214/11-AOS957\">10.1214/11-AOS957</a>","ista":"Uhler C. 2012. Geometry of maximum likelihood estimation in Gaussian graphical models. Annals of Statistics. 40(1), 238–261.","ieee":"C. Uhler, “Geometry of maximum likelihood estimation in Gaussian graphical models,” <i>Annals of Statistics</i>, vol. 40, no. 1. Institute of Mathematical Statistics, pp. 238–261, 2012.","short":"C. Uhler, Annals of Statistics 40 (2012) 238–261.","mla":"Uhler, Caroline. “Geometry of Maximum Likelihood Estimation in Gaussian Graphical Models.” <i>Annals of Statistics</i>, vol. 40, no. 1, Institute of Mathematical Statistics, 2012, pp. 238–61, doi:<a href=\"https://doi.org/10.1214/11-AOS957\">10.1214/11-AOS957</a>.","apa":"Uhler, C. (2012). Geometry of maximum likelihood estimation in Gaussian graphical models. <i>Annals of Statistics</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/11-AOS957\">https://doi.org/10.1214/11-AOS957</a>","chicago":"Uhler, Caroline. “Geometry of Maximum Likelihood Estimation in Gaussian Graphical Models.” <i>Annals of Statistics</i>. Institute of Mathematical Statistics, 2012. <a href=\"https://doi.org/10.1214/11-AOS957\">https://doi.org/10.1214/11-AOS957</a>."},"publist_id":"3767","oa_version":"Preprint","date_published":"2012-02-01T00:00:00Z","volume":40,"year":"2012","day":"01","status":"public","corr_author":"1","publisher":"Institute of Mathematical Statistics","publication":"Annals of Statistics","date_updated":"2024-10-09T20:54:52Z","scopus_import":1,"_id":"2959","author":[{"id":"49ADD78E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7008-0216","first_name":"Caroline","full_name":"Uhler, Caroline","last_name":"Uhler"}],"acknowledgement":"I wish to thank Bernd Sturmfels for many helpful discus- sions and Steffen Lauritzen for introducing me to the problem of the existence of the MLE in Gaussian graphical models. I would also like to thank two referees who provided helpful comments on the original version of this paper.\r\n","intvolume":"        40","quality_controlled":"1","department":[{"_id":"CaUh"}],"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1012.2643"}],"publication_status":"published","page":"238 - 261","doi":"10.1214/11-AOS957","title":"Geometry of maximum likelihood estimation in Gaussian graphical models","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","month":"02","oa":1,"issue":"1","date_created":"2018-12-11T12:00:33Z"}