Estimating a directed tree for extremes
Ngoc Mai Tran, Johannes Buck, Claudia Klüppelberg
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2024 · Volume 86 · Issue 3
Abstract
We propose a new method to estimate a root-directed spanning tree from extreme data. Prominent example is a river network, to be discovered from extreme flow measured at a set of stations. Our new algorithm utilizes qualitative aspects of a max-linear Bayesian network, which has been designed for modelling causality in extremes. The algorithm estimates bivariate scores and returns a root-directed spanning tree. It performs extremely well on benchmark data and on new data. We prove that the new estimator is consistent under a max-linear Bayesian network model with noise. We also assess its strengths and limitations in a small simulation study.
Keywords
Bayesian network, causal inference, directed acyclic graph, extreme value analysis, graphical model, max-linear model
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