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

这项研究项目将开发复杂时空数据的统计方法。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)和纵向雇主家庭动态(LEHD)计划。公共使用的ACS和LEHD数据集是巨大的，拥有关于不同美国地区和不同时间段的许多不同人口和经济指标的压倒性信息。该项目将开发为这些类型的联邦数据量身定做的统计方法。该项目将促进统计科学中的知识，这项研究的结果将对政府机构的工作有价值。由于许多主题学科，如神经科学、人口学和计量经济学，也处理复杂的数据，这项研究的结果将广泛有用。将开发软件包并向公众提供。研究人员将对研究生和本科生进行教育和培训。这项研究项目将使用分层方法，为独立的、多分布和多尺度(在空间和时间)的时空数据开发计算高效的统计模型的贝叶斯方法。该项目有三个目标。在目标1中，研究人员将开发分布理论，允许对由多个分布的数据组成的高维数据集进行高效的计算分析，如高斯数据、计数和伯努利数据。在目标2中，研究人员将开发高维、多分布和多变量时空数据环境中的小区域估计方法。在目标3中，研究人员将开发在高维、多分布和多尺度时空数据环境中减少聚集误差的方法。该项目制定的方法将使用基函数和支持的空间变化，以促进降维和协助计算。该项目还将利用向量自回归模型、卡尔胡宁-洛伊夫展开和共轭多元分布理论来开发对科学和联邦社区都有用的原则性方法。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.