Empirical likelihood methods and statistical applications in climate studies

我的建议包括两个项目，第一个是关于统计方法，第二个是关于统计在气候学中的应用。 我的第一个项目侧重于经验似然方法，使我们能够从数据中推断人口特征。它不需要复杂的模型，并充分利用了当今廉价而快速的计算能力。例如，人们可以使用这种方法来计算人口的真实平均身高的区间估计，而不知道人口的身高分布。经验似然法是由斯坦福大学的阿特·欧文教授在80年代末提出的一种现代推理方法。它现在已发展成为统计人员的一个重要和有力的工具。我已经对经验似然理论做出了贡献。我现在的重点是处理影响经验似然法准确性的技术约束问题。这是一个重要的问题，引起了包括UBC陈嘉华教授和欧文教授在内的著名研究人员的注意。我希望能找到一个更好的办法来解决这个问题。 我的第二个项目是关于重建历史温度的方法，这对理解全球变暖很重要。我们只有从工业革命（大约1850年）开始的温度记录。为了理解近几十年来的变暖，我们需要一个长期的历史视角，这需要对1850年之前的全球温度进行可靠的估计/重建。我的项目将研究一个统计模型，用于使用替代数据（如树轮和冰芯数据）和其他气候变量估计历史温度。这是一个与全球变暖研究直接相关的重要问题。统计学家和气候学家以及政府都对它感兴趣。

My proposal consists of two projects, the first of which is concerned with statistical methodology and the second is concerned with statistical applications in climatology. My first project focuses on the empirical likelihood method which enables us to make inference on population characteristics from data. It does not require elaborate models and takes full advantage of the inexpensive and fast computing power available today. For example, one may use this method to compute an interval estimate for the true average height of a population without knowing the height distribution of the population. The empirical likelihood method is a modern method of inference introduced by Professor Art Owen at Stanford University in the late 80's. It has now evolved into an important and powerful tool for statisticians. I have already made contributions to the empirical likelihood theory. My focus now is on the problem of handling a technical constraint which affects the accuracy of the empirical likelihood method. This is an important problem which has attracted the attention of prominent researchers including Professor Jiahua Chen at UBC and Professor Owen himself. I hope to find a better solution to the problem. My second project is concerned with methods for historical temperature reconstruction which is important for understanding global warming. We only have temperature records from the time of the industrial revolution (roughly 1850) and onwards. To appreciate the warming in recent decades, we need a long-term historical perspective which requires reliable estimation/reconstruction of global temperature before 1850. My project will study a statistical model for estimating the historical temperature using proxy data such as tree ring and ice core data and other climate variables. This is an important problem directly related to research on global warming. It is of interest to statisticians and climatologists as well as the government.