In this talk, I will discuss two multivariate extremes problems which arise from atmospheric studies. The first one is a "weather" problem and is theoretical in nature. Given a field of extremes observations (say the maximum precipitation in a given year), how can one describe and measure the spatial dependence? We propose using the madogram, a first-order variogram to estimate the extremal coefficient, a measure of dependence between extremes. The madogram has a convenient link to the extremal coefficient and nicely connects the theory of extremes to that of spatial statistics. The second problem is a "climate" problem. We model extreme precipitation for Colorado's Front Range in an effort to create a return-levels map for the region. We propose a Bayesian hierarchical model to pool the weather station data and provide spatial structure with which we can produce the desired map.
Refreshments will be served at 3:45 p.m. in Room 008 of the Statistics Building