# Modelling multivariate extreme value distributions via Markov trees

arXiv: https://arxiv.org/abs/2208.02627 · HTML: https://mlsanity.com/paper/2208.02627/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jul 2022.

## Built on by (most cited first, 1 of 1)

- [Extremal graphical modeling with latent variables via convex optimization](https://mlsanity.com/paper/2403.09604/) (2024)

## Abstract (arXiv)

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 max-stable distributions into a Markov random field with respect to a tree. Although in general not max-stable itself, this Markov tree is attracted by a multivariate max-stable distribution. The latter serves as a tree-based approximation to an unknown max-stable 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 as edge weights. The distributions of pairs of connected variables can be fitted in various ways. The resulting tree-structured max-stable distribution allows for inference on rare event probabilities, as illustrated on river discharge data from the upper Danube basin.