Mathematical Sciences: Statistical Model Building with Generalized Splines

该项目进一步发展了新的数学、统计和计算方法，用于对多个变量的响应函数进行经验估计。数据可以是直接的、间接的或仅针对隐式定义的函数。新的样条光滑化将扩展到方差分析技术。具体问题包括模型选择(选择要包括的模型组件)、改进的计算方法以允许对许多变量和非常大的数据集进行有效的拟合、开发适用于二项和其他非高斯响应以及隐含问题的方法。统计模型旨在预测给定预测变量的指定值的结果，或描述预测变量与结果之间的关系，或观察随着预测因素或属性的变化，响应可能如何变化。使用平滑样条开发经验统计模型有望在科学研究中广泛应用，从搜索大规模人口数据中的风险因素或环境退化的风险因素，到数值天气预报系统的各个方面，再到机器学习。

This project develops further new mathematical, statistical and computational methods for the empirical estimation of response functions of several to many variables. Data may be direct, indirect or only on functions implicitly defined. The new spline smoothing will be extended to analysis of variance techniques. Particular problems include model selection (choice of model components to include), improved computational methods to allow efficient fitting with many variables and very large data sets, development of methods appropriate to binomial and other non-Gaussian responses and to implicit problems. Statistical models are intended to predict outcomes given specified values of the predictor variables or to describe the relationships between predictors and outcomes, or to see how responses may change as predicting factors or attributes change. Developing empirical statistical models using smoothing splines promises to be widely applicable in scientific research, ranging from the search for risk factors in large scale demographic data or for risk factors in environmental degradation, to aspects of a numerical weather forecasting system, to machine learning.