We study the problem of maximum likelihood estimation for $3$-dimensional linear spaces of $3\times 3$ symmetric matrices from the point of view of algebraic statistics where we view these nets of conics as linear concentration or linear covariance models of Gaussian distributions on $\mathbb{R}^3$. In particular, we study the reciprocal surfaces of nets of conics which are rational surfaces in $\mathbb{P}^5$. We show that the reciprocal surfaces are projections from the Veronese surface and determine their intersection with the polar nets. This geometry explains the maximum likelihood degrees of these linear models. We compute the reciprocal maximum likelihood degrees. This work is based on Wall's classification of nets of conics from 1977.

翻译：我们从代数统计的角度研究3美元乘以3美元的3美元对称基体的3维线性空间的最大可能性估计问题,我们认为这些二次曲线网是线性浓度或高山分布的线性共变模型,以$mathbb{R ⁇ 3美元计算,特别是,我们用$\mathbb{P ⁇ 5美元研究合理表面的二次曲线网的对等表面。我们表明,对等表面是从Veronese表面预测的,并确定了它们与极地网的交叉点。这种几何学解释这些线性模型的最大可能性。我们计算了对等最大可能性度。这项工作以1977年以来Wall对二次曲线网的分类为基础。