Collaborative Research: Statistical Inference for High-dimensional Spatial-Temporal Process Models

合作研究：高维时空过程模型的统计推断

基本信息

批准号：
2113779
负责人：
Wenpin Tang
金额：
$ 12.09万
依托单位：
Columbia University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2021
资助国家：
美国
起止时间：
2021-07-01 至 2024-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2113779&HistoricalAwards=false
关键词：
Collaborative Research Statistical Inference dimensional

项目摘要

Spatial data science and other emerging technologies related to Geographic Information Systems are increasingly conspicuous in scientific discoveries. Scientists in a variety of disciplines today have unprecedented access to massive spatial and temporal databases comprising high resolution remote sensed measurements. Statistical modeling and analysis for such data need to account for spatial associations and variations at multiple levels while attempting to recognize underlying patterns and potentially complex relationships. Traditional statistical hypothesis testing is no longer adequate for these scientific problems and statisticians are increasingly turning to specialized methods for analyzing complex spatial-temporal data. However, there continue to remain substantial theoretical and methodological bottlenecks with regard to the interpretation of statistical models. This project will address these problems by developing probabilistic machine learning tools for spatial-temporal Big Data that can have far-reaching public health, economic, environmental, and scientific implications. Several innovations in statistical theory, methodologies and computational algorithms are envisioned that will inform basic science and policy questions arising in diverse disciplines using geographic information sciences. Key educational components include dissemination of technologies across the scientific communities including data scientists, engineers, foresters, ecologists, and climate scientists. The Principal Investigators will train the next generation of data scientists through dissemination efforts for graduate students in STEM fields. The PIs aim to blend innovative theory, methods and applications to advance knowledge of spatial-temporal stochastic processes with an emphasis on their properties for high-dimensional inference. This domain of spatial statistics has witnessed a burgeoning of models and methods for Big Data analysis. New classes of models have emerged from the judicious use of directed acyclic graphs (DAGs) that are being applied to massive datasets comprising several millions of spatiotemporal coordinates. Theoretical explorations envisioned in this project will focus upon statistical inference on the process parameters and the underlying spatial process. The PIs intend to perform rigorous investigations into statistical inference for high-dimensional spatio-temporal processes to derive micro-ergodic parameters for such models that will be consistently estimable and, at the same time, yield consistent predictive inference. The PIs will develop new methodologies that cast high-dimensional stochastic processes into computationally practicable frameworks by embedding graphical Gaussian processes within hierarchical frameworks for jointly modeling highly multivariate spatial data. Innovative statistical theory and methods will be developed and used to construct sparsity-inducing graphical spatio-temporal models to accommodate massive numbers of outcomes and capture complex dependencies among variables across massive numbers of locations. The planned theoretical explorations into the inferential properties of newly emerging scalable spatio-temporal processes will produce novel statistical contributions. The PIs will provide probability-based uncertainty quantification and will substantially enhance the understanding of physical and natural processes underlying various problems in the physical, environmental and biomedical sciences and in public health.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.

空间数据科学和其他与地理信息系统相关的新兴技术在科学发现中日益引人注目。如今，各个学科的科学家可以前所未有地访问包含高分辨率遥感测量结果的海量空间和时间数据库。此类数据的统计建模和分析需要考虑多个级别的空间关联和变化，同时尝试识别潜在的模式和潜在的复杂关系。传统的统计假设检验不再足以解决这些科学问题，统计学家越来越多地转向专门的方法来分析复杂的时空数据。然而，在统计模型的解释方面仍然存在重大的理论和方法瓶颈。该项目将通过开发用于时空大数据的概率机器学习工具来解决这些问题，这些工具可能对公共卫生、经济、环境和科学产生深远的影响。预计统计理论、方法论和计算算法方面的几项创新将为使用地理信息科学的不同学科中出现的基础科学和政策问题提供信息。关键的教育内容包括在科学界（包括数据科学家、工程师、林务员、生态学家和气候科学家）传播技术。首席研究员将通过对 STEM 领域研究生的传播工作来培训下一代数据科学家。 PI 旨在融合创新理论、方法和应用，以推进时空随机过程的知识，重点关注其高维推理特性。空间统计领域见证了大数据分析模型和方法的蓬勃发展。有向无环图 (DAG) 的明智使用催生了新型模型，这些模型被应用于包含数百万个时空坐标的海量数据集。该项目设想的理论探索将集中于过程参数和潜在空间过程的统计推断。 PI 打算对高维时空过程的统计推断进行严格的调查，以便为此类模型导出微遍历参数，这些参数将始终可估计，同时产生一致的预测推断。 PI 将开发新的方法，通过将图形高斯过程嵌入分层框架中，将高维随机过程转化为计算上可行的框架，以联合建模高度多元的空间数据。将开发创新的统计理论和方法，并用于构建稀疏性图形时空模型，以适应大量结果并捕获大量位置的变量之间的复杂依赖关系。计划对新兴可扩展时空过程的推理特性进行的理论探索将产生新的统计贡献。 PI 将提供基于概率的不确定性量化，并将大大增强对物理、环境和生物医学科学以及公共卫生领域各种问题背后的物理和自然过程的理解。该奖项反映了 NSF 的法定使命，并被认为值得通过以下方式获得支持：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。