Extreme Values and Robust Statistics

在这项研究中，我们开发了统计模型和工具，以更好地了解气候和环境科学中时间序列的极端行为，并在存在异常观测时从数据中提取信息。我们为温度，降雨等极端事件开发统计模型，这些模型可以处理这些过程的复杂性质，并能够利用我们在任何尺度上对这些物理过程的了解，以更好地理解这些过程的极端行为如何改变，正在改变，以及未来可能发生的变化。 还有许多其他领域需要这些类型的统计模型，例如：海洋学，水文学，气候学，可靠性，经济学，再保险和金融。简而言之，如果对极端事件的频率和规模估计不足，可能会产生破坏性影响，例如：波高，水位，热浪，结构负荷，保险索赔和股票回报。我们开发了鲁棒的依赖估计方法，以了解环境或能源数据之间的时变依赖的动态，这些数据经常由于设备故障或网络过载而出现跳跃或尖峰，以及许多其他原因。这些强大的方法是需要在许多应用中异常的观察存在于许多现实生活中的数据集，他们导致经典的统计程序产生不良的推断。 我们还开发了强大的方法来筛选科学数据中可用的数千个解释变量，以便应用变量选择或预测方法，并最终找到重要的关系。筛选方法用于找到与疾病最相关的基因或图像中与疾病识别最相关的像素。*

In this research, we develop statistical models and tools to gain a better understanding of the extreme behaviour of time series in climate and environmental sciences, and extract information from data when aberrant observations are present.******We develop statistical models for the extreme occurrences of temperature, rainfall, etc, that can handle the complex nature of these processes and are able to exploit knowledge that we have about such physical processes at any scale to gain a better comprehension of how the extreme behaviour of these processes has changed, is changing, and is likely to change in the future. There are many other areas that require these types of statistical models, for example: oceanography, hydrology, climatology, reliability, economics, reinsurance, and finance. In short, where inadequate estimates of the frequency and size of extreme occurrences can have a devastating impact, for example: wave heights, water levels, heat waves, structural load, insurance claims, and equity returns.******We develop robust dependence estimation methods to understand the dynamics of the time-varying dependence among environmental or energy data which often experience jumps or spikes due to equipment malfunctions or network overloads, among numerous other causes. These robust methods are required in numerous applications as aberrant observations are present in many real-life data sets and they cause classical statistical procedures to yield poor inference. We also develop robust methods to screen the many thousands of explanatory variables available in scientific data so that variable selection or prediction methods can then be applied, and significant relationships ultimately be found. Screening methods are used, for example, to find the genes which are most relevant to a disease or the pixels in an image which are most pertinent to its identification.********