Extreme values and robustness

极值的随机模拟对许多领域都很重要。当许多结构设计依赖于基于数据的方法来估计设计荷载时，洪水、大风、大降水（雨、雪或冰）等的发生率和严重程度的估计对工程来说是必不可少的。对可能的极端荷载的低估会导致灾难性的结构破坏；回想一下冰暴过后输电塔的状态。

The stochastic modeling of extremes is important to many fields. Estimation of the incidence and severity of floods, large winds, large precipitations (rain, snow, or ice), and so on are essential to engineering when many structural designs rely on data-based methodologies for the estimation of design loads. Underestimation of probable extreme loads leads to catastrophic structural failure; recall the state of the transmission towers after the Ice Storms. This area of modeling is also important in insurance and finance. Insurance companies face probable large (catastrophic) claims and a company's solvency depends critically on the size and the frequency of large claims. The issue is very real with recent environmental disasters such as Hurricane Andrew, the Mississippi floods, the 1998 Ice Storms, and Hurricane Katrina causing havoc and eventual financial failures in the insurance industry. On the financial markets, large price movements are rare, but important. We recall the October 1987 market drop, and we have yet to find the bottom in the October 2008 drop. Increases in volatility of daily stock market indices have attracted much attention from both practitioners and researchers. Companies (and individuals) have taken on huge losses due to unexpected market moves. We need accurate measures of market and insurance risks and that requires accurate modeling of the distribution of large losses and claims. Many agree that there is a lack of practical statistical methodology in this area. Some progress has been made in the last few years: more realistic models accounting for non-stationarity and correlation; modest multivariate models making better use of available data; Bayesian analyses incorporating ''expert'' knowledge; and robust models identifying and downweighting ''small'' extremes (reducing underestimation). However, there is still a long way to go. The purpose of the proposed research is to further the progress made by these recent methodologies and develop new methods.