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 2022031, LIDAM Discussion Papers 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 depen- dence or causality between extreme events. In a Bayesian network, variables are recur- sively 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 indepen- dent 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.

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: 36
Date: 2022-09-30
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Citations: View citations in EconPapers (1)

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