Modeling spatial extremes via ensemble-of-trees of pairwise copulas

Assessing the risk of extreme events in a spatial domain, such as hurricanes, floods and droughts, presents unique significance in practice. Unfortunately, the existing extreme-value statistical models are typically not feasible for practical large-scale problems. Graphical models are capable of handling enormous number of variables, yet have not been explored in the realm of extreme-value analysis. To bridge the gap, an extreme-value graphical model is introduced in this paper, i.e., ensemble-of-trees of pairwise copulas (ETPC). In the proposed graphical model, extreme-value marginal distributions are stitched together by means of pairwise copulas, which in turn are the building blocks of the ensemble of trees. By exploiting this particular structure, novel efficient inference algorithms are derived that are applicable to large-scale statistical problems involving extreme values. It is proven that, under mild conditions, the ETPC model exhibits the favorable property of tail-dependence between an arbitrary pair of sites (variables), and therefore is reliable to capture the dependence between extremes at different sites. Real data results further demonstrate the advantages of the ETPC model.