Statistical Model Building with Generalized Splines

本研究涉及开发和测试用于估计多变量函数的改进方法，给出了分散的、有噪声的、异构的直接和间接观测以及各种先验信息。建立了正在开发的方法的理论性质，并在已知“真相”的模拟数据的试验台中研究了方法的性质。开发了有效的数值算法，同时实现了统计和计算目标。最后在实际观测数据集上对方法进行了验证。所有研究的一个统一主题是利用再现核希尔伯特空间方法，结合交叉验证，无偏风险和似然技术。正在开发的统计和数值方法在几个广泛的领域具有适用性：(1)用于分析复杂的医疗和人口数据集，以估计风险因素；(2)用于分析非常大的环境数据集，目的是提取和呈现数据集中可用的最大数量的信息；特别强调的是在气候变化方面的应用(3)改进和更好地理解监督机器学习中使用的方法，以及(4)分析从动态系统（如不断变化的大气或海洋）获得的数据，以及分析用于分析这些数据的数学模型（如数值天气预报或海洋模型）的优缺点。

Wahba 9704758 This research involves the development and testing of improved methods for estimating functions of many variables, given scattered, noisy, heterogeneous direct and indirect observations and prior information of various kinds. Theoretical properties of the methods under development are established, and properties of the methods are also studied in test beds with simulated data where the `truth' is known. Efficient numerical algorithms are developed which simultaneously implement statistical and computational objectives. Finally the methods are tested on real observational data sets. A unifying theme in all of the research is the exploitation of reproducing kernel Hilbert space methods, combined with cross validation, unbiased risk and likelihood techniques. The statistical and numerical methods being developed have applicability in several broad areas: (1) to the analysis of complicated medical and demographic data sets for the purpose of risk factor estimation (2) to the analysis of very large environmental data sets with the goal of extracting and presenting the maximal amount of information available in the data set; particular emphasis is on application to climate change (3) to the improvement and better understanding of methods used in supervised machine learning, and (4) to the analysis of data that is obtained from dynamical systems such as the evolving atmosphere or ocean, and the analysis of the strengths and weaknesses of mathematical models (such as numerical weather prediction or ocean models) that are used in the analysis of such data.