TY - JOUR

T1 - Conditional Extremes with Graphical Models

AU - Farrell, Aiden

AU - Eastoe, Emma

AU - Lee, Clement

PY - 2024/11/26

Y1 - 2024/11/26

N2 - Multivariate extreme value analysis quantifies the probability and magnitude of joint extreme events. River discharges from the upper Danube River basin provide a challenging dataset for such analysis because the data, which is measured on a spatial network, exhibits both asymptotic dependence and asymptotic independence. To account for both features, we extend the conditional multivariate extreme value model (CMEVM) with a new approach for the residual distribution. This allows sparse (graphical) dependence structures and fully parametric prediction. Our approach fills a current gap in statistical methodology for graphical extremes, where existing models require asymptotic independence. Further, the model can be used to learn the graphical dependence structure when it is unknown a priori. To support inference in high dimensions, we propose a stepwise inference procedure that is computationally efficient and loses no information or predictive power. We show our method is flexible and accurately captures the extremal dependence for the upper Danube River basin discharges.

AB - Multivariate extreme value analysis quantifies the probability and magnitude of joint extreme events. River discharges from the upper Danube River basin provide a challenging dataset for such analysis because the data, which is measured on a spatial network, exhibits both asymptotic dependence and asymptotic independence. To account for both features, we extend the conditional multivariate extreme value model (CMEVM) with a new approach for the residual distribution. This allows sparse (graphical) dependence structures and fully parametric prediction. Our approach fills a current gap in statistical methodology for graphical extremes, where existing models require asymptotic independence. Further, the model can be used to learn the graphical dependence structure when it is unknown a priori. To support inference in high dimensions, we propose a stepwise inference procedure that is computationally efficient and loses no information or predictive power. We show our method is flexible and accurately captures the extremal dependence for the upper Danube River basin discharges.

KW - Extremal dependence

KW - graphical extremes

KW - conditional multivariate extremes

KW - sparsity

KW - river networks

M3 - Journal article

JO - arXiv.org

JF - arXiv.org

ER -