Much of the work in atmospheric applications of extremes is largely descriptive. Characterizing return levels and other extreme quantities of interest is important, but does not help to explain the processes which lead to extreme outcomes. Conditional modeling for extremes has been a popular approach in atmospheric science as it ties extreme behavior to climatic conditions. However when the conditioning variable varies on a similar timescale as the response variable of interest, conditional extremes methods can be inappropriate. We will present an alternative bivariate approach.
Much of the current work in extremes statistics focuses on dependence. When modeling spatial dependence, there are existing models with sound theoretical background. The present challenge is in fitting these models to data sets of the dimension frequently found in atmospheric science.
Another present challenge in extremes statistics is dimension reduction. In non-spatial settings, present multivariate models are limited to relatively small dimension (5 or 6). We discuss the need for higher dimensional models and current work being done in dimension reduction.