Natural hazards pose significant threats to public safety, infrastructure integrity, natural resources, and economic development. In recent years, the frequency and impacts of extreme events have increased substantially in many parts of the world fostering a paradigm shift from traditional stationary statistical models towards models capable of capturing the changing properties of extremes, i.e., nonstationary statistical models. The nonstationarity in such models can be defined by a temporal or process-informed dependence of the observed extremes on an explanatory variable (i.e., a physical driver). Further, a solely statistical-based model might lead to results inconsistent with physics, e.g. unrealistic wave heights in shallow waters. This highlights the need of traditional statistical models including physical constraints in the inference process.

The proposed short course presents the Matlab toolbox ProNEVA which enables users to perform Bayesian statistical analysis under the assumption of nonstationarity, and its latest extension ProNEVAwave specific for analyzing extreme wave heights considering physical constraints in the inference process. The main features of ProNEVA are: parameters estimation of Generalized Extreme Value distribution (GEV), Generalized Pareto distribution (GP), and Log Pearson type III distribution based on Bayesian inference approach; analysis under temporal and process-informed nonstationarity; uncertainty quantification; estimation of return period-return level values for nonstationary analysis (i.e., effective return level and waiting time). The extension ProNEVAwave is developed for statistical analysis of wave heights with the following features: events selection; parameter estimation of stationary GP distribution based on Bayesian inference considering physical constraints via informative priors; uncertainty quantification; estimation of return period-return level curves.

This hands-on short course will provide attendees with some basic knowledge of extreme value analysis under stationary and nonstationary assumptions. Attendees will have hands-on experience on how to apply ProNEVA and ProNEVAwave through a number of applications (e.g., modeling extreme wave heights).