Mining Extreme Values: Climate and Natural Hazards

The analysis and modeling of extreme values have traditionally relied on extreme value theory (EVT), which in turn has tended to focus on limiting or asymptotic cases and assumptions of independence. However, disciplines from climate science and digital mapping to infrastructure security and transportation, have been generating massive volumes of data with multidimensional and multivariable dependence, long-memory and long-range associations, and nonlinear interactions, from remote or in-situ sensors and computational models. This motivates the need for automated descriptive and predictive analysis of extremes. The size and complexity of data does not preclude the rarity of the extreme events, but presents the possibility of information extraction from related ancillary variables, or covariates. An empirical analysis of spatiotemporal autoand cross-correlation structures of extremes, statistical behavior of EVT on finite and noisy data, as well as the impact of noise, nonlinearity and variability, may lead to novel formulations for understanding extremes and their correlations. Based on the results of preliminary data analysis, we proposed using graphical model based on tail dependence for description and analysis of spatial and covariate dependence structure among extremes time-series. Besides providing insights on climate change or natural hazards and the consequences for climate change science or the reinsurance industry, the methods can be generalized to multiple domains ranging from water resources planning and critical infrastructures security to finance, telecommunications, cybersecurity and mapping technologies.