Mathematical Sciences: Statistical Model Building with Generalized Splines

这项研究将涉及样条函数。样条函数及其在多个变量中的各种推广已被证明对于建立描述大型数据集中多变量物理现象的经验模型非常有用。该项目的一般方法是开发所提出的半参数模型的理论性质，通过蒙特卡罗模拟研究评估它们在实践中的工作效果，最后，在选定的“真实”实验数据集上尝试这些方法。这个项目是在统计的一般领域，重点是高速计算。样条函数模型需要新的统计和数值技术，以使数据从各种可能的模型中进行选择，以拟合这些模型，并提供尽可能多的关于模型预测可能有多准确的信息。这项研究的大部分是由AFSOR和NASA支持的。该奖项支持研究生在项目中工作。

This research will involve spline functions. Spline functions and their various generalizations in several variables have proved to be very useful for building empirical models which describe multivariate physical phenomena in large data sets. The general approach of this project is to develop theoretical properties of the proposed semi-parametric models, to assess how well they might be expected to work in practice by Monte Carlo simulation studies, and finally, to try the methods on selected "real" experimental data sets. This project is in the general area of statistics and focuses on high speed computing. The spline function models need new statistical and numerical techniques to let the data select from among various possible models, to fit these models, and to provide as much information as possible on how accurate the model forecast are likely to be. Most of this research is supported by AFSOR and NASA. This award supports a graduate student to work in the project.