Probabilistic forecasts describe uncertainty in future outcomes and support decision making. Standard verification tools are often weak for tail behavior, although extreme outcomes usually matter most for risk. This talk introduced a general framework for tail calibration, linked it to standard calibration notions, and discussed connections with peaks-over-threshold methods in extreme value theory.

The talk showed how regular vine structures can decompose and construct high-dimensional extreme-value models through bivariate components. It covered simulation for X-vine multivariate Pareto models, parameter estimation, and model selection from threshold excesses, with applications and extensions toward quantile regression in extreme covariate regions.

Robust extreme-event analysis in numerical models often needs very long simulations or very large ensembles. Rare-event algorithms reduce this burden using cloning and suppression strategies that oversample trajectories associated with target events. The presentation highlighted applications to temperature and sea-ice extremes, with perspectives for tipping points and early-warning validation.