论文标题
圆锥网的最大似然估计
Maximum Likelihood Estimation for Nets of Conics
论文作者
论文摘要
我们从代数统计的角度研究了$ 3 \ times 3 $对称矩阵的最大似然估计的最大可能性估计的问题，我们将这些圆锥形的网络视为线性浓度或线性浓度或线性协方差模型的高斯分布模型。特别是，我们研究了圆锥形网的相互表面，这些圆锥网是$ \ mathbb {p}^5 $中的理性表面。我们表明，相互的表面是来自Veronese表面的投影，并确定它们与极性网的相交。该几何形状解释了这些线性模型的最大似然度。我们计算相互的最大似然度。这项工作是基于Wall从1977年开始对圆锥网的分类。
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.
