A polytrope is a tropical polyhedron that is also classically convex. We study the tropical combinatorial types of polytropes associated to weighted directed acyclic graphs (DAGs). This family of polytropes arises in algebraic statistics when describing the model class of max-linear Bayesian networks. We show how the edge weights of a network directly relate to the facet structure of the corresponding polytrope. We also give a classification of polytropes from weighted DAGs at different levels of equivalence. These results give insight on the statistical problem of identifiability for a max-linear Bayesian network.

翻译：多面热带体是一种同时满足经典凸性的热带多面体。本研究针对加权有向无环图（DAG）所关联的多面热带体的热带组合类型进行探讨。该多面热带体系列出现于代数统计学中描述极大线性贝叶斯网络模型类别时。我们揭示了网络边权如何直接影响对应多面热带体的面结构，并在不同等价层次上对加权有向无环图生成的多面热带体进行了分类。这些研究成果为极大线性贝叶斯网络的可辨识性统计问题提供了新的理论洞见。