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 $\Delta_n$ for $n\leq 4$.
翻译:我们建议对所有单维离散统计模型进行分类, 最大可能性为一种, 以其合理准称为基础。 我们用数量有限的简单操作来显示所有这些模型是如何从小类“ 基本模型” 的成员中构建的。 我们引入了“ 芯片分解游戏 ”, 即我们用来代表基本模型的网格上的组合游戏 。 这种组合式观点让我们能够显示, 概率为简单x$\ Delta_n$ 用于$nleq 4 的概率只有有限的许多基本模型 。