Modeling Extremal Processes

This lecture covers the motivation behind extremal limit theorems, maxima, point processes, Gaussian processes, Poisson process theory, exceedances, and applications in multivariate extremes. It discusses statistics and models for extremes of time series, focusing on spatial and space-time problems. The lecture emphasizes the need for exploratory methods, fitting extremal models suitable for spatial problems, and simulating rare events. It also delves into Swiss summer temperatures from 2001 to 2005, illustrating extreme values in various locations. The lecture concludes with discussions on extremal processes, inference for max-stable processes, and modeling extreme events.