--- _id: '3308' abstract: - lang: eng text: We study multivariate normal models that are described by linear constraints on the inverse of the covariance matrix. Maximum likelihood estimation for such models leads to the problem of maximizing the determinant function over a spectrahedron, and to the problem of characterizing the image of the positive definite cone under an arbitrary linear projection. These problems at the interface of statistics and optimization are here examined from the perspective of convex algebraic geometry. acknowledgement: B. Sturmfels is supported in part by NSF grants DMS-0456960 and DMS-0757236. C. Uhler is supported by an International Fulbright Science and Technology Fellowship. author: - first_name: Bernd full_name: Sturmfels, Bernd last_name: Sturmfels - first_name: Caroline full_name: Caroline Uhler id: 49ADD78E-F248-11E8-B48F-1D18A9856A87 last_name: Uhler orcid: 0000-0002-7008-0216 citation: ama: Sturmfels B, Uhler C. Multivariate Gaussians, semidefinite matrix completion, and convex algebraic geometry. Annals of the Institute of Statistical Mathematics. 2010;62(4):603-638. doi:10.1007/s10463-010-0295-4 apa: Sturmfels, B., & Uhler, C. (2010). Multivariate Gaussians, semidefinite matrix completion, and convex algebraic geometry. Annals of the Institute of Statistical Mathematics. Springer. https://doi.org/10.1007/s10463-010-0295-4 chicago: Sturmfels, Bernd, and Caroline Uhler. “Multivariate Gaussians, Semidefinite Matrix Completion, and Convex Algebraic Geometry.” Annals of the Institute of Statistical Mathematics. Springer, 2010. https://doi.org/10.1007/s10463-010-0295-4. ieee: B. Sturmfels and C. Uhler, “Multivariate Gaussians, semidefinite matrix completion, and convex algebraic geometry,” Annals of the Institute of Statistical Mathematics, vol. 62, no. 4. Springer, pp. 603–638, 2010. ista: Sturmfels B, Uhler C. 2010. Multivariate Gaussians, semidefinite matrix completion, and convex algebraic geometry. Annals of the Institute of Statistical Mathematics. 62(4), 603–638. mla: Sturmfels, Bernd, and Caroline Uhler. “Multivariate Gaussians, Semidefinite Matrix Completion, and Convex Algebraic Geometry.” Annals of the Institute of Statistical Mathematics, vol. 62, no. 4, Springer, 2010, pp. 603–38, doi:10.1007/s10463-010-0295-4. short: B. Sturmfels, C. Uhler, Annals of the Institute of Statistical Mathematics 62 (2010) 603–638. date_created: 2018-12-11T12:02:35Z date_published: 2010-08-01T00:00:00Z date_updated: 2021-01-12T07:42:33Z day: '01' doi: 10.1007/s10463-010-0295-4 extern: 1 intvolume: ' 62' issue: '4' main_file_link: - open_access: '1' url: http://arxiv.org/abs/0906.3529 month: '08' oa: 1 page: 603 - 638 publication: Annals of the Institute of Statistical Mathematics publication_status: published publisher: Springer publist_id: '3332' quality_controlled: 0 status: public title: Multivariate Gaussians, semidefinite matrix completion, and convex algebraic geometry type: journal_article volume: 62 year: '2010' ...