Graphical models with heavy-tailed factors can be used to model extremal dependence or causality between extreme events. In a Bayesian network, variables are recursively defined in terms of their parents according to a directed acyclic graph (DAG). We focus on max-linear graphical models with respect to a special type of graphs, which we call a tree of transitive tournaments. The latter are block graphs combining in a tree-like structure a finite number of transitive tournaments, each of which is a DAG in which every two nodes are connected. We study the limit of the joint tails of the max-linear model conditionally on the event that a given variable exceeds a high threshold. Under a suitable condition, the limiting distribution involves the factorization into independent increments along the shortest trail between two variables, thereby imitating the behavior of a Markov random field. We are also interested in the identifiability of the model parameters in case some variables are latent and only a subvector is observed. It turns out that the parameters are identifiable under a criterion on the nodes carrying the latent variables which is easy and quick to check.

翻译：重尾因子图模型可用于模拟极端事件之间的极值依赖性或因果关系。在贝叶斯网络中，变量依据有向无环图（DAG）通过其父节点递归定义。我们聚焦于一类特殊图结构下的最大线性图模型，即传递竞赛树。此类图结构将有限个传递竞赛（一种每对节点均有连接的有向无环图）以树状形式组合成块图。我们研究在给定某变量超过高阈值事件条件下，最大线性模型联合尾部的极限分布。在适当条件下，该极限分布呈现沿两变量间最短路径的独立增量分解特性，从而模拟马尔可夫随机场的行为。此外，我们关注当部分变量为潜变量且仅观测子向量时模型参数的可识别性问题。结果表明，在满足携带潜变量节点的特定判据下（该判据易于快速验证），模型参数具有可识别性。