Estimating a Directed Tree for Extremes

2021/02/11 by Tran, Ngoc Mai, Johannes S. Buck, Claudia Klüppelberg +2 · 2 citations
Computer Science · Mathematics · #Bayesian Modeling and Causal Inference #Census and Population Estimation

paper · pdf · doi:10.48550/arxiv.2102.06197

Abstract

We propose a new method to estimate a root-directed spanning tree from extreme data. A 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 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.

Cited by

• Minimum bounding polytropes for estimation of max-linear Bayesian networks
• Structural Causal Models for Extremes: an Approach Based on Exponent Measures

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• Extremes of structural causal models
• Structure learning for extremal tree models
• Estimating an Extreme Bayesian Network via Scalings
• Graphical Models for Extremes
• Bayesian model averaging over tree-based dependence structures for multivariate extremes