In this article, we introduce a new family of lattice polytopes with rational linear precision. For this purpose, we define a new class of discrete statistical models that we call multinomial staged tree models. We prove that these models have rational maximum likelihood estimators (MLE) and give a criterion for these models to be log-linear. Our main result is then obtained by applying Garcia-Puente and Sottile’s theorem that establishes a correspondence between polytopes with rational linear precision and log-linear models with rational MLE. Throughout this article, we also study the interplay between the primitive collections of the normal fan of a polytope with rational linear precision and the shape of the Horn matrix of its corresponding statistical model. Finally, we investigate lattice polytopes arising from toric multinomial staged tree models, in terms of the combinatorics of their tree representations.

在本文中，我们介绍了具有合理线性精度的新晶格多面体族。为此，我们定义了一类新的离散统计模型，我们称之为多项分级树模型。我们证明了这些模型具有合理的最大似然估计量 (MLE)，并为这些模型提供了对数线性的标准。然后，我们的主要结果是通过应用 Garcia-Puente 和 Sottile 定理获得的，该定理建立了具有理性线性精度的多面体与具有理性 MLE 的对数线性模型之间的对应关系。在整篇文章中，我们还研究了具有合理线性精度的多面体正常扇形的原始集合与其相应统计模型的霍恩矩阵的形状之间的相互作用。最后，