A statistical methodology is presented to model extreme values from non-stationary environmental processes. The methodology is based on a generalized Pareto model for peaks over threshold of the environmental process combined with a Voronoi representation for the variation of extreme value model parameters with multi-dimensional covariates. Bayesian inference using reversible-jump MCMC, incorporating Metropolis-Hastings within Gibbs sampling, is used to estimate the joint posterior distribution of all parameters of the Voronoi representation. The methodology is applied to characterise extreme ocean storm severity with direction and season. The fitted model is validated by comparing the characteristics of data simulated under the model with those of the original sample data. Further, the model is used to estimate the distribution of maxima of peaks over threshold corresponding to return periods much longer than the period of the original data.
Keywords
Extreme value, multi-dimensional covariate, Voronoi partition, Bayesian inference, Gibbs sampling and Metropolis-Hastings, reversible-jump MCMC, ocean wave, return value.
Reference
Jonathan, Ph. (2021), ‘Cynrychioliad amharamedrig ar gyfer cyd-newidynnau amlddimensiynol mewn model gwerthoedd eithaf, â chymhwysiad eigionegol’, Gwerddon, 33, 68–84. https://doi.org/10.61257/LPRT3992