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

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的地位日益突出。今天，各个学科的科学家都可以前所未有地访问由高分辨率遥感测量数据组成的海量空间和时间数据库。这些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已经不足以解决这些科学问题，统计学家们越来越多地转向专门的方法来分析复杂的时空数据。然而，在解释统计模型方面，仍然存在重大的理论和方法瓶颈。该项目将通过为时空大数据开发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。统计理论、方法和计算算法方面的若干创新设想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传播技术，包括数据科学家、工程师、林业工作者、生态学家和气候科学家。首席研究员将通过为STEM领域的研究生提供传播工作来培训下一代数据科学家。 PI旨在融合创新的理论，方法和应用，以推进时空随机过程的知识，重点是它们的高维推理属性。这个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）被应用于包含数百万个时空坐标的海量数据集，通过明智地使用DAG，已经出现了新的模型类别。在这个项目中设想的理论探索将集中在统计推断的过程参数和基本的空间过程。PI旨在对高维时空过程的统计推断进行严格的调查，以获得这些模型的微遍历参数，这些参数将是一致的可估计的，同时产生一致的预测推断。PI将开发新的方法，通过在分层框架中嵌入图形高斯过程，将高维随机过程转换为计算上可行的框架，以联合建模高度多元的空间数据。创新的统计理论和方法将被开发和用于构建稀疏诱导图形时空模型，以适应大量的结果，并捕捉跨大量位置的变量之间的复杂依赖关系。计划中的理论探索到新出现的可扩展的时空过程的推理特性将产生新的统计贡献。PI将提供基于概率的不确定性量化，并将大大提高物理和自然过程的理解，在物理，环境和生物医学科学和公共health.This奖项反映了NSF的法定使命，并已被认为是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的支持。

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.