Max-linear graphical models with heavy-tailed factors on trees of transitive tournaments
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| Format: | Preprint |
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2022
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| _version_ | 1866914252340592640 |
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| author | Segers, Johan Asenova, Stefka |
| author_facet | Segers, Johan Asenova, Stefka |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_14938 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Max-linear graphical models with heavy-tailed factors on trees of transitive tournaments Segers, Johan Asenova, Stefka Methodology 60B12, 60G70, 62H22 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. |
| title | Max-linear graphical models with heavy-tailed factors on trees of transitive tournaments |
| topic | Methodology 60B12, 60G70, 62H22 |
| url | https://arxiv.org/abs/2209.14938 |