Extremes of Markov random fields on block graphs

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 2022013, LIDAM Discussion Papers ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: We study the joint occurrence of large values of a Markov random field or undirected graphical model associated to a block graph. On such graphs, containing trees as specialcases, we aim to generalize recent results for extremes of Markov trees. Every pair ofnodes in a block graph is connected by a unique shortest path. These paths are shownto determine the limiting distribution of the properly rescaled random field given that a fixed variable exceeds a high threshold. When the sub-vectors induced by the blocks follow Hüsler–Reiss extreme value copulas, the global Markov property of the original field induces a particular structure on the parameter matrix of the limiting max-stable Hüsler–Reiss distribution. The multivariate Pareto version of the latter turns out to be an extremal graphical model according to the original block graph. Moreover, thanks to these algebraic relations, the parameters are still identifiable even if some variables are latent.

Keywords: Markov random field; graphical model; block graph; multivariate extremes; tail dependence; latent variable; Hüsler–Reiss distribution; conditional independence (search for similar items in EconPapers)
Pages: 27
Date: 2022-01-01
New Economics Papers: this item is included in nep-dcm and nep-rmg
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