Modelling multivariate extreme value distributions via Markov trees | Vidéo | Carmin.tv

00:00:00 / 00:00:00

Modelling multivariate extreme value distributions via Markov trees

By Johan Segers

Appears in collection : Adaptive and High-Dimensional Spatio-Temporal Methods for Forecasting / Méthodes spatio-temporelles adaptatives et en grande dimension pour la prédiction

Multivariate extreme value distributions are a common choice for modelling multivariate extremes. In high dimensions, however, the construction of flexible and parsimonious models is challenging. We propose to combine bivariate extreme value distributions into a Markov random field with respect to a tree. Although in general not an extreme value distribution itself, this Markov tree is attracted by a multivariate extreme value distribution. The latter serves as a tree-based approximation to an unknown extreme value distribution with the given bivariate distributions as margins. Given data, we learn an appropriate tree structure by Prim's algorithm with estimated pairwise upper tail dependence coefficients or Kendall's tau values as edge weights. The distributions of pairs of connected variables can be fitted in various ways. The resulting tree-structured extreme value distribution allows for inference on rare event probabilities, as illustrated on river discharge data from the upper Danube basin.

Information about the video

Date of recording 26/09/2022
Date of publication 10/10/2022
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Luca Recanzone
Format MP4

Citation data

DOI 10.24350/CIRM.V.19961603
Cite this video Segers, Johan (26/09/2022). Modelling multivariate extreme value distributions via Markov trees. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19961603
URL https://dx.doi.org/10.24350/CIRM.V.19961603

Domain(s)

Methodology

Bibliography

HU, Shuang, PENG, Zuoxiang, et SEGERS, Johan. Modelling multivariate extreme value distributions via Markov trees. arXiv preprint arXiv:2208.02627, 2022. - https://arxiv.org/abs/2208.02627
ASENOVA, Stefka et SEGERS, Johan. Extremes of Markov random fields on block graphs. arXiv preprint arXiv:2112.04847, 2021. - https://doi.org/10.48550/arXiv.2112.04847

MSC codes

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow

Copyright Carmin.tv 2025

Give feedback