---
_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'
...