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Abstract:
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Advances in modeling weather extremes are crucial for risk assessment. In this work, we explore two possible and related approaches to tackle high-dimensional extremes: clustering and dimension reduction. In particular, the extreme observations can be grouped in distinct clusters forming the nodes of a tree, which could represent, e.g., different regions in a large spatial domain. The dependence within and between groups of variables can be described by the max-stable nested logistic model by virtue of its inherent hierarchical dependence structure. Embedding the nested logistic model in a Bayesian framework, we build a Reversible-Jump Markov Chain Monte Carlo (RJ-MCMC) algorithm able to estimate the hidden tree structure from the data. This allows us to cluster variables that behave similarly and to achieve dimension reduction if some clusters of variables are found to be completely independent.
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