Max-linear graphical models with heavy-tailed factors on trees of transitive tournaments

Stefka Asenova and Johan Segers ()
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Stefka Asenova: Université catholique de Louvain, LIDAM/ISBA, Belgium
Johan Segers: Université catholique de Louvain, LIDAM/ISBA, Belgium

No 2023032, LIDAM Reprints ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

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.

Keywords: Max-linear model; heavy tails; extremal dependence; conditional dependence; probabilistic graphical model; directed acyclic graph; tournaments; extremes (search for similar items in EconPapers)
Pages: 37
Date: 2023-12-15
Note: In: Advances in Applied Probability, 2024
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Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvar:2023032

DOI: 10.1017/apr.2023.46

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