论文标题
对具有最大似然度的一维离散模型进行分类
Classifying one-dimensional discrete models with maximum likelihood degree one
论文作者
论文摘要
我们根据其理性参数化提出了所有具有最大似然度的一维离散统计模型的分类。我们展示了如何使用有限数量的简单操作来从较小的“基本模型”的成员中构建所有这些模型。我们介绍了“ Chipsplitting Games”，这是一类网格上的组合游戏，我们用来代表基本模型。这种组合视角使我们能够证明概率单纯$Δ_n$在$ n \ leq 4 $中只有有限的基本模型。
We propose a classification of all one-dimensional discrete statistical models with maximum likelihood degree one based on their rational parametrization. We show how all such models can be constructed from members of a smaller class of 'fundamental models' using a finite number of simple operations. We introduce 'chipsplitting games', a class of combinatorial games on a grid which we use to represent fundamental models. This combinatorial perspective enables us to show that there are only finitely many fundamental models in the probability simplex $Δ_n$ for $n\leq 4$.
