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