Likelihood Geometry
Likelihood Geometry
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似然几何
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
B. Sturmfels
中科院分区：
文献类型：
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作者：
June Huh;B. Sturmfels
我们研究概率单形的代数子集上单项函数的临界点。Zariski闭包上临界点的个数是嵌入射影簇的拓扑不变量，称为它的最大似然度。我们介绍了这一理论及其统计动机。介绍了许多组合代数几何中最受欢迎的对象：环状簇、无判别式、超平面排列、Grassmannians和行列式簇。得到了几个新的结果，特别是关于似然对应及其双度的结果。这些笔记是为第二作者在2013年6月在Levico Terme举办的CIME-CIRM组合代数几何夏季课程上的讲座而写的。
We study the critical points of monomial functions over an algebraic subset of the probability simplex. The number of critical points on the Zariski closure is a topological invariant of that embedded projective variety, known as its maximum likelihood degree. We present an introduction to this theory and its statistical motivations. Many favorite objects from combinatorial algebraic geometry are featured: toric varieties, Adiscriminants, hyperplane arrangements, Grassmannians, and determinantal varieties. Several new results are included, especially on the likelihood correspondence and its bidegree. These notes are written for the second author’s lectures at the CIME-CIRM summer course on Combinatorial Algebraic Geometry at Levico Terme in June 2013.