Collaborative Research: Multi-distribution, Multivariate, and Multiscale Spatio-Temporal Models with Applications to Official Statistics

该研究项目将为复杂的时空数据开发统计方法。该项目的动机是在许多现代联邦数据集中发现的共同特征，如美国人口普查局的美国社区调查（ACS）和雇主纵向家庭动态（LEHD）计划。公共使用的ACS和LEHD数据集是巨大的，并且在美国不同地区和不同时间段具有关于许多不同人口和经济指标的大量信息。该项目将开发针对这些类型的联邦数据的统计方法。该项目将增进统计科学的知识，研究结果将对政府机构的工作具有价值。由于许多学科，如神经科学，人口统计学和计量经济学，也处理复杂的数据，这项研究的结果将是广泛有用的。将开发软件包并向公众提供。研究人员将教育和培训研究生和本科生。使用分层方法，本研究项目将开发贝叶斯方法，为相关的多分布和多尺度（空间和时间）时空数据建立计算效率高的统计模型。该项目有三个目标。在目标1中，研究人员将开发分布理论，允许对由来自多个分布的数据组成的高维数据集进行计算有效的分析，例如高斯数据，计数和伯努利数据。在目标2中，研究人员将开发在高维、多分布和多变量时空数据设置中进行小区域估计的方法。在目标3中，研究人员将开发方法来减轻高维，多分布和多尺度时空数据设置中的聚合误差。在该项目中开发的方法将使用基函数和空间变化的支持，以促进降维，并帮助计算。该项目还将利用向量自回归模型、Karhunen-Loeve展开和共轭多元分布理论来开发对科学界和联邦界都有用的原则性方法。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。

This research project will develop statistical methodology for complex spatio-temporal data. The project is motivated by common features found in many modern federal datasets such as the U.S. Census Bureau's American Community Survey (ACS) and the Longitudinal Employer Household Dynamics (LEHD) program. The public-use ACS and LEHD datasets are enormous and have an overwhelming amount of information on many different demographic and economic indicators, at different U.S. regions and different time periods. This project will develop statistical methods that are tailored to these types of federal data. The project will advance knowledge within the statistical sciences, and the results of this research will be of value to the work of government agencies. Because many subject-matter disciplines, such as neuroscience, demography, and econometrics, also deal with complex data, the results of this research will be broadly useful. Software packages will be developed and made publicly available. The investigators will educate and train both graduate and undergraduate students.Using a hierarchical approach, this research project will develop Bayesian methodologies for computationally efficient statistical models for dependent multi-distributional and multiscale (in space and time) spatio-temporal data. The project has three aims. In aim 1, the investigators will develop distribution theory that allows for computationally efficient analysis of high-dimensional datasets that consist of data from multiple distributions, such as Gaussian data, counts, and Bernoulli data. In aim 2, the investigators will develop approaches to small-area estimation in the high-dimensional, multi-distributional, and multivariate spatio-temporal data setting. In aim 3, the investigators will develop approaches to mitigate aggregation error in the high-dimensional, multi-distributional, and multiscale spatio-temporal data setting. The methodologies developed in the project will use basis functions and spatial change of support to facilitate dimension reduction and to aid in computation. This project also will make use of vector auto-regressive models, the Karhunen-Loeve expansion, and conjugate multivariate distribution theory to develop principled methodologies that are useful for both the scientific and federal communities.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.