Dependence in the tail of the distribution can differ from that in the bulk of the distribution. A basic tenet of a univariate extreme value analysis is to discard the bulk of the data and only analyze the data considered to be extreme. This is true for multivariate problems as well. We will first introduce a framework for describing tail dependence. The probabilistic framework of regular variation has strong ties to classical extreme value theory and provides a framework for describing tail dependence. We will introduce regular variation and the angular measure which fully describes tail dependence. We will then briefly look at applications which have used this regular variation framework. We investigate the Pineapple Express phenomenon which can cause heavy rain and flooding on the Pacific Coast and determine whether regional climate models are able to produce this phenomenon. In another project, we perform data mining for extremes to determine the meteorological conditions which lead to the most extreme ground level ozone measurements. This is joint work with Grant Weller (Carnegie Mellon/Savvysherpa Inc.) and Brook Russell (CSU).
Daniel S Cooley