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日益引人注目。今天，不同学科的科学家可以史无前例地访问包括高分辨率遥感测量在内的海量时空数据库。对这类数据的统计建模和分析需要考虑到多个层面上的空间关联和变化，同时试图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适合这些科学问题，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。该项目将通过开发时空大数据的概率机器学习工具来解决这些问题，这些工具可能会对公共健康、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利用地理信息科学为不同学科中出现的基础科学和政策问题提供信息。关键的教育组成部分包括在科学界传播技术，这些科学界包括数据科学家、工程师、林学家、生态学家和气候科学家。首席调查员将通过向STEM领域的研究生进行传播工作，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，以促进时空随机过程的知识，并强调其高维推理的特性。这一空间统计领域见证了大数据分析的模型和方法的蓬勃发展。由于对有向无环图(DAG)的合理使用，出现了一类新的模型，这些DAG正被应用于包含数百万时空坐标的海量数据集。本项目设想的理论探索将侧重于对过程参数和基本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，以得出此类模型的微遍历参数，这些参数将是一致可估计的，同时产生一致的预测推断。PIS将开发新的方法，通过在分层框架内嵌入图形高斯过程，将高维随机过程投射到计算可行的框架中，以联合建模高度多变量的空间数据。创新的统计理论和方法将被开发并用于构建稀疏性诱导的图形时空模型，以适应大量结果，并捕获大量地点变量之间的复杂依赖关系。对新出现的可伸缩时空过程的推论性质的有计划的理论探索将产生新的统计贡献。PIS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中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。

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.