Adaptive Dependent Data Models via Graph-Informed Shrinkage and Sparsity

该研究项目将推进相关数据的统计建模和计算策略。相关数据广泛而重要。许多社会经济、文化和政治数据都是以空间区域为单位进行测量的，大多数经济数据都是按时间顺序排列的，相互依赖，现代监测系统以近乎连续的分辨率记录社会、环境和经济暴露数据。然而，这种不断增长的依赖数据已经超过了这些数据的统计方法和算法的发展。该项目将开发新的统计工具，使研究人员能够从这些依赖性数据中提取可靠的信息并作出决定。开发的方法将受到以下领域的具体，及时和重要问题的激励：地方选举和重新划分;通货膨胀建模和预测;经济，健康和城市数据的空间模式提取;以及监测和暴露数据的建模。该项目将为本科生和研究生提供培训和指导，开发公开可用的软件和可视化工具，并展示地方，州和联邦政府数据。该研究项目将开发新的统计工具，以充分捕获广泛的数据依赖关系，为大规模数据集提供计算可扩展性，并利用依赖结构进行更具适应性和本地化的估计，不确定性量化和缺失数据的插补。未建模的依赖性使推断次优或无效，导致分析不足和错误的结论。此外，相关数据通常是高维的，具有大量的缺失，导致显著的计算和统计挑战。在贝叶斯框架内，该项目将同时整合以下方面的依赖性：（i）信号模型，以提供平滑和正则化;（ii）伴随的收缩或稀疏先验，以增强局部自适应性;以及（iii）可扩展后验推理的计算和数值策略。依赖性将被编码为将观察单位链接在一起的图，例如时间顺序或功能数据的连续观察，图像或网格数据的相邻像素，以及空间数据的相邻区域单位，以及许多其他示例。这种基于图形的公式化将为统一和推进广泛的模型、收缩和稀疏先验以及相关数据的推理算法奠定基础。将开发的工具将针对各种环境进行定制，包括趋势估计和插补、收缩或稀疏先验、图形信息回归分析、因子模型和离散数据等。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知识价值和更广泛的影响审查标准进行评估来支持。

This research project will advance statistical modeling and computing strategies for dependent data. Dependent data are widespread and important. Many socioeconomic, cultural, and political data are measured on spatial areal units, most economic data are time-ordered and co-dependent, and modern monitoring systems record social, environmental, and economic exposure data at near-continuous resolutions. However, this growing abundance of dependent data has outpaced the development of statistical methods and algorithms for such data. The project will develop new statistical tools that will allow researchers to extract reliable information and make decisions from such dependent data. The methods to be developed will be motivated by specific, timely, and important problems in the following areas: local elections and redistricting; inflation modeling and forecasting; spatial pattern extraction for economic, health, and urban data; and modeling of monitoring and exposure data. The project will provide training and mentoring for undergraduate and graduate students, develop publicly available software and visualization tools, and showcase local, state, and federal government data.This research project will develop new statistical tools to adequately capture a broad array of data dependencies, provide computational scalability for massive datasets, and leverage the dependence structures for more adaptive and localized estimation, uncertainty quantification, and imputation of missing data. Unmodeled dependence renders inferences suboptimal or invalid, resulting in underpowered analyses and erroneous conclusions. In addition, dependent data are often high-dimensional with substantial missingness, leading to significant computational and statistical challenges. Within a Bayesian framework, the project will simultaneously integrate the dependence in (i) the model for the signal to provide smoothness and regularization, (ii) the accompanying shrinkage or sparsity prior for enhanced local adaptivity, and (iii) the computational and numerical strategies for scalable posterior inference. Dependence will be encoded as a graph that links together observational units, such as consecutive observations for time-ordered or functional data, adjacent pixels for image or lattice data, and neighboring areal units for spatial data, among many other examples. This graph-based formulation will lay the foundation to unify and advance a broad collection of models, shrinkage and sparsity priors, and inference algorithms for dependent data. The tools to be developed will be customized for a variety of settings, including trend estimation and imputation, shrinkage or sparsity priors, graph-informed regression analysis, factor models, and discrete data, among others.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.