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- Title
Max-linear graphical models with heavy-tailed factors on trees of transitive tournaments.
- Authors
Asenova, Stefka; Segers, Johan
- 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.
- Subjects
MARKOV random fields; DIRECTED acyclic graphs; TOURNAMENTS; LATENT variables; BAYESIAN analysis; MULTIPLY transitive groups; RANDOM fields
- Publication
Advances in Applied Probability, 2024, Vol 56, Issue 2, p621
- ISSN
0001-8678
- Publication type
Article
- DOI
10.1017/apr.2023.46