TY - JOUR

T1 - Extreme-value graphical models with multiple covariates

AU - Yu, H.

AU - Dauwels, J.

AU - Jonathan, P.

PY - 2014

Y1 - 2014

N2 - To assess the risk of extreme events such as hurricanes, earthquakes, and floods, it is crucial to develop accurate extreme-value statistical models. Extreme events often display heterogeneity (i.e., nonstationarity), varying continuously with a number of covariates. Previous studies have suggested that models considering covariate effects lead to reliable estimates of extreme events distributions. In this paper, we develop a novel statistical model to incorporate the effects of multiple covariates. Specifically, we analyze as an example the extreme sea states in the Gulf of Mexico, where the distribution of extreme wave heights changes systematically with location and storm direction. In the proposed model, the block maximum at each location and sector of wind direction are assumed to follow the Generalized Extreme Value (GEV) distribution. The GEV parameters are coupled across the spatio-directional domain through a graphical model, in particular, a three-dimensional (3D) thin-membrane model. Efficient learning and inference algorithms are developed based on the special characteristics of the thin-membrane model. We further show how to extend the model to incorporate an arbitrary number of covariates in a straightforward manner. Numerical results for both synthetic and real data indicate that the proposed model can accurately describe marginal behaviors of extreme events. © 2014 IEEE.

AB - To assess the risk of extreme events such as hurricanes, earthquakes, and floods, it is crucial to develop accurate extreme-value statistical models. Extreme events often display heterogeneity (i.e., nonstationarity), varying continuously with a number of covariates. Previous studies have suggested that models considering covariate effects lead to reliable estimates of extreme events distributions. In this paper, we develop a novel statistical model to incorporate the effects of multiple covariates. Specifically, we analyze as an example the extreme sea states in the Gulf of Mexico, where the distribution of extreme wave heights changes systematically with location and storm direction. In the proposed model, the block maximum at each location and sector of wind direction are assumed to follow the Generalized Extreme Value (GEV) distribution. The GEV parameters are coupled across the spatio-directional domain through a graphical model, in particular, a three-dimensional (3D) thin-membrane model. Efficient learning and inference algorithms are developed based on the special characteristics of the thin-membrane model. We further show how to extend the model to incorporate an arbitrary number of covariates in a straightforward manner. Numerical results for both synthetic and real data indicate that the proposed model can accurately describe marginal behaviors of extreme events. © 2014 IEEE.

KW - Covariates

KW - Extreme events modeling

KW - Gaussian graphical models

KW - Kronecker product

KW - Laplacian matrix

KW - Extreme events

KW - Laplacian matrices

U2 - 10.1109/TSP.2014.2358955

DO - 10.1109/TSP.2014.2358955

M3 - Journal article

VL - 62

SP - 5734

EP - 5747

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

SN - 1053-587X

IS - 21

ER -