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In algebraic statistics, the maximum likelihood degree of a statistical modelis the number of complex critical points of its log-likelihood function. Apriori knowledge of this number is useful for applying techniques of numericalalgebraic geometry to the maximum likelihood estimation problem. We compute themaximum likelihood degree of a generic two-dimensional subspace of the space of$n\times n$ Gaussian covariance matrices. We use the intersection theory ofplane curves to show that this number is $2n-3$.

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