On the use of graphical models to model extreme events with multiple covariates - Cheng, Jingjing. (2013)
Gaussian graphical models are widely used for modelling the covariates dependence of extreme events. Most extreme events are physical process that has underlying mechanism, which depends on certain covariate factors. Hence, modelling covariate dependence would significantly enhance the accuracy of estimation of the distribution parameters and thus is an imperative component of extreme events modelling. In this work, we focused on marginal analysis of extreme wave heights at hurricane dominated Gulf of Mexico We used generalised extreme value distribution to model the tail behaviour of wave height data, and we used thin membrane models to capture the spatial and direction dependence of the tail distribution parameters. The thin membrane priors introduce smoothing parameters which enhance accuracy of estimation of extreme value distribution parameters. The algorithm used to estimate the parameters is expectation maximisation. The contribution of this work is a novel and accurate model to model spatial and directional dependence of the extreme wave heights at the Gulf of Mexico. We used the expectation maximisation algorithm to estimate the parameters empirically based entirely on the data. Efficiency of the algorithm has been improved by using eigenvalues and eigenvectors.