Max-linear graphical models with heavy-tailed factors on trees of transitive tournaments
(2024) Advances in Applied Probability — Vol. 56, n° 2, p. 621-665 (2024)
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- Abstract
- 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 graph, which we call a tree of transitive tournaments. The latter is a block graph 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 behaviour of a Markov random field. We are also interested in the identifiability of the model parameters in the case when 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.
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Citations
Asenova, S., & Segers, J. (2024). Max-linear graphical models with heavy-tailed factors on trees of transitive tournaments. Advances in Applied Probability, 56(2), 621-665. https://doi.org/10.1017/apr.2023.46 (Original work published 2024)