Mathematical Sciences: Statistical Model Building with Generalized Splines

该项目进一步发展新的数学，统计 和计算方法的经验估计 多个变量的响应函数。 数据可以 直接、间接或仅在隐式定义的函数上。 的 将一种新的样条平滑方法推广到方差分析中 技术. 具体问题包括模型选择（选择 模型组件包括），改进的计算方法 为了允许与许多变量和非常大的 数据集，制定适用于二项式和 其他非高斯响应和隐式问题。 统计模型旨在预测给定的结果， 预测变量的指定值或描述 预测因素和结果之间的关系，或者看看如何 响应可以随着预测因素或属性的改变而改变。 使用平滑样条开发经验统计模型 有望广泛应用于科学研究， 从大规模人口统计数据中寻找风险因素 或环境退化的风险因素， 数值天气预报系统，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.