Problems in Statistical Model Building

项目摘要统计建模中的几个问题。这项研究是为了进一步发展平滑样条方差分析和相关的变分方法，用于多变量函数估计和统计模型建立，以便这些方法可以用于分析非常大的复杂的异质数据集，如在人口医学研究、环境和气候数据分析以及各种领域的分类问题中。这些方法是灵活的非参数方法，但通常包含常用的参数化族作为特例。一般方法在以下步骤中进行：(I)提出适合于特定应用领域的模型族，(Ii)开发用于拟合模型所需的新的数值算法，(Ii)开发用于调整模型和提供精度估计的进一步方法，(Iii)开发与方法的特性有关的信息，包括在已知“真理”的情况下对真实模拟观测进行测试，(Iv)将所得到的方法应用于重要的数据集，期望从这些数据中提取通过标准参数方法无法获得的信息。该项目的目的是向医学科学家提供，环境和大气科学以及有监督的机器学习，这是更有效地分析其数据的新的有用工具。提出的任务是开发新的方法，以便在跟踪人口随时间推移的复杂人口研究中更有效地进行数据分析，收集有助于了解可能的风险因素与各种疾病的发病率和进展之间的关系的信息。还提出了以下任务：开发适合于理解具有“非标准”间接观测数据的大型环境和大气数据集中的各种感兴趣因素之间的关系的新方法；开发一些具有广泛适用性的分类新方法，以便在从高维空间的大数据集学习的基础上建立分类算法。

PROJECT ABSTRACTProblems in Statistical Model Building. Grace Wahba, PI.This research is to further the development of Smoothing Spline ANOVA and related variational methods for multivariate function estimation and statistical model building, so that these methods may be used in analyses of very large complex heterogenous data sets as occur in demographic medical studies, environmental and climatic data analyses and classification problems in a variety of areas. These methods are flexible nonparametric methods, but generally contain commonly used parametric families as special cases. The general approach proceeds in the following steps: (i)propose families of models that are appropriate for specific areas of application, (ii) develop new numerical algorithms as required for fitting the models, (ii) develop further methods for tuning the models and providing accuracy estimates, (iii) develop information concerning the properties of the methods, including testing on realistic simulated observations where the `truth' is known, (iv) and applying the resulting methods to important data sets, with the expectation of extracting information from these data that is not obtainable by standard parametric methods.The goal of this project is provide to scientists in medical, environmental and atmospheric sciences and supervised machine learning, new and useful tools to more efficiently analyze their data. Tasks are proposed to develop new methods that are appropriate for more efficient data analysis in complex demographic studies which follow populations over time, collecting information useful for understanding relationships between possible risk factors and the incidence and progression of various diseases. Tasks are also proposed for the development of new methods that are appropriate for understanding relationships among various factors of interest in large environmental and atmospheric data sets with `non-standard' indirect observational data; and for exploiting some new methods in classification that have wide applicability for building classification algorithms based on learning from large data sets in very high dimensional spaces.