Methodological Development of Functional Data Analysis, with Applications

现代数据集需要超越单变量和多变量分析的统计方法：它们需要功能数据分析(FDA)，即每个人从一些连续的过程中产生数据，并进行错误观察。我的提案集中在FDA的几个领域。 方法采用与能源消耗相关的潜变量。在第一个项目中，我开发了一些方法来分析一组建筑的每小时能耗数据，其中每栋建筑都有不同的(已知的)空调数量。能源使用量取决于正在使用的空调数量，这一点尚不清楚。在第二个项目中，一家水电公司在几个社区有关于总能源消耗随时间变化的数据，以及报告的几种消费类型(如住宅、小型企业)的数量。然而，报告的数字往往不等于实际数字。目标是估计每个社区的消费者类型的数量，以及每种消费者类型的“典型使用曲线”。 微分运算符在FDA中的使用。微分算子在函数数据分析方面有很长的历史。它们出现在惩罚中，由此产生的方法具有处理随机过程和贝叶斯估计的优雅方式。微分运算符也在建模中显式使用。我将发展这些联系，以便获得更统一和基于模型的方法。 动物育种和进化生物学中的食品和药物管理局。在这一应用中，连续过程的潜在遗传结构对于成功和有利可图的动物育种以及理解自然选择的力量和后果是重要的。这种遗传结构可以通过具有已知血统的依赖个人的数据来估计。我将开发新的方法，并比较新的和现有的研究遗传结构的方法。

Modern data sets require statistical methodology beyond that of univariate and multivariate analyses: they require Functional Data Analysis (FDA), where each individual generates data from some continuous process, observed with error. My proposal focuses on several areas of FDA. METHODS WITH LATENT VARIABLES WITH RELATION TO ENERGY CONSUMPTION. In the first project I develop methods to analyze hourly power consumption data from a group of buildings, where each building has a different (known) number of air conditioners. The amount of energy used depends on the number of air conditioners that are in use, which is unknown. In the second project, a hydro-electric company has data in several neighbourhoods on the total energy consumption as a function of time, along with the reported number of several consumer types (eg residential, small business). However the reported number is often not equal to the actual number. The goal is to estimate the number of consumer types in each neighbourhood, along with the "typical usage curve" for each consumer type. THE USE OF DIFFERENTIAL OPERATORS IN FDA. Differential operators have a long history in the analysis of functional data. They appear in penalties, with resulting methodology having an elegant way to stochastic processes and to Bayes estimation. Differential operators are also used explicitly in modeling. I will develop these connections, in order to obtain a more unified and model-based approach. FDA IN ANIMAL BREEDING AND EVOLUTIONARY BIOLOGY. In this application, the underlying genetic structure of the continuous process is important for successful and profitable animal breeding and for understanding the forces and consequences of natural selection. This genetic structure can be estimated via data from dependent individuals with known pedigree. I will develop new methods and compare new and existing methods for studying genetic structure.