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），其中每个人都从一些连续的过程中生成数据，观察到错误。 我的建议集中在FDA的几个领域。 与能量消耗有关的潜变量方法。在第一个项目中，我开发了一种方法来分析一组建筑物的每小时耗电量数据，其中每个建筑物都有不同的（已知的）空调数量。 所使用的能源量取决于正在使用的空调数量，这是未知的。 在第二个项目中，一家水电公司拥有几个街区的总能源消耗数据，作为时间的函数，沿着还有几种消费者类型（如住宅、小企业）的报告数量。 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，沿着每个消费者类型的“典型使用曲线”。 微分算子在FDA中的应用。 微分算子在函数数据分析中有着悠久的历史。 他们出现在罚款，由此产生的方法有一个优雅的方式随机过程和贝叶斯估计。 微分算子也被显式地用于建模。 我将发展这些联系，以获得一个更统一和基于模型的方法。 FDA在动物育种和进化生物学中的作用。 在这种应用中，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来自具有已知谱系的依赖个体的数据来估计。我将开发新的方法，并比较新的和现有的方法来研究遗传结构。

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.