Mathematical Sciences: Statistical Model Building with Generalized Splines

数学科学：用广义样条建立统计模型

• 批准号: 9121003
• 负责人: Grace Wahba
• 金额: $ 24.95万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-01 至 1998-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9121003&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Statistical; Model; Building

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.

本项目进一步发展了新的数学、统计和计算方法，用于数到多变量响应函数的经验估计。数据可以是直接的、间接的，也可以只是隐式定义的函数上的数据。新的样条平滑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，以允许有效地拟合许多变量和非常大的数据集，开发适合二项和其他非高斯响应的方法以及隐式问题。统计模型的目的是在给定预测变量的特定值的情况下预测结果，或描述预测变量与结果之间的关系，或观察反应如何随着预测因素或属性的变化而变化。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，从大规模人口数据中的风险因素或环境退化中的风险因素的搜索，到数值天气预报系统的各个方面，再到机器学习。