#### Vol. 11, No. 2, 2020

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Maximum likelihood degree of the two-dimensional linear Gaussian covariance model

### Jane Ivy Coons, Orlando Marigliano and Michael Ruddy

Vol. 11 (2020), No. 2, 107–123
##### Abstract

In algebraic statistics, the maximum likelihood degree of a statistical model is the number of complex critical points of its log-likelihood function. A priori knowledge of this number is useful for applying techniques of numerical algebraic geometry to the maximum likelihood estimation problem. We compute the maximum likelihood degree of a generic two-dimensional subspace of the space of $n×n$ Gaussian covariance matrices. We use the intersection theory of plane curves to show that this number is $2n-3$.

##### Keywords
algebraic geometry, algebraic statistics, linear Gaussian covariance models, intersection theory, plane curves, maximum likelihood estimation, maximum likelihood degree
##### Mathematical Subject Classification 2010
Primary: 13P25, 14C17, 14H50, 62H12
##### Milestones
Received: 10 September 2019
Revised: 20 May 2020
Accepted: 8 June 2020
Published: 28 December 2020
##### Authors
 Jane Ivy Coons Department of Mathematics North Carolina State University Raleigh, NC United States Orlando Marigliano Max-Planck-Institute for Mathematics in the Sciences Leipzig Germany Michael Ruddy Max-Planck-Institute for Mathematics in the Sciences Leipzig Germany