Collaborative Research: High-Dimensional Spatial-Temporal Modeling and Inference for Large Multi-Source Environmental Monitoring Systems

遥感技术和地理信息系统继续带来科学发现方面的巨大发展。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。对这类数据进行统计建模和分析往往需要在多个层面上计算空间关联和变化，同时试图识别科学变量之间的潜在模式和可能的复杂关系。传统的统计假设检验不再适合这些推理目标，统计学家越来越多地转向多层次或分层建模结构来分析复杂的时空数据。然而，随着科学家们遇到遥感数据中的数据泛滥，需要专门的“大数据”技术，仍然存在大量的计算瓶颈。PIS将在森林结构、地形和与天气有关的事件(例如风暴)方面的科学进步的背景下，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，这些事件可能对公共卫生、经济、环境和安全产生深远影响。还设想了统计和计算方法以及相关软件开发方面的若干创新。拟议的数据产品将为波多黎各在飓风伊尔玛和玛丽亚之后提供森林破坏/变化的量化和滑坡风险评估。关键的教育组成部分包括在科学界传播拟议的技术，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。PIS计划通过对STEM领域的本科生和研究生进行传播努力，培养下一代数据科学家。绩效指标将制定一个统计框架，用于对高维遥感数据进行详细的案例研究和数据分析，其中“高维”指的是(1)空间位置；(2)时间点；(3)对策或结果中的一个或全部。PIS将在丰富的贝叶斯分层框架内引入可大规模扩展的多变量空间过程模型，以获得对基本数据生成过程的完全基于模型的推理。提出了创新的统计方法，以便在涉及数千万个空间位置、数千个时间点以及可能涉及数百个遥感变量的规模上实施分层模型。这些模型的巨大可扩展性将通过稀疏性诱导的时空过程和其他图形模型、矩阵变量低阶模型、共轭贝叶斯分布理论和使用一组后验分布的近似的元学习范例来实现。将探索加强现有方法的理论结果，以及迄今为止规模空前的几个拟议的案例研究。PI将在涉及海量数据集的各种实验中开发一整套空间模型。由于海量数据集是可以有效检测复杂关系的地方，所提出的方法非常适合于对复杂的科学现象进行建模。将为飓风伊尔玛和玛丽亚之后波多黎各的森林损害/变化和山体滑坡风险评估提供关键的实质性推断和统计量化。PIS将提供基于概率的不确定性量化，并将大大增强科学界对风暴相关损失评估的理解。这一奖项反映了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。

Remote sensing technologies and Geographic Information Systems continue to bring about dramatic developments in scientific discovery. 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 often entail reckoning with spatial associations and variations at multiple levels while attempting to recognize underlying patterns and potentially complex relationships among the scientific variables. Traditional statistical hypothesis testing is no longer adequate for these inferential objectives and statisticians are increasingly turning to multi-level or hierarchical modeling structures for analyzing complex spatial-temporal data. However, there continue to remain substantial computational bottlenecks as scientists encounter the data deluge in remote-sensed data that demand specialized "BIG DATA" technologies. The PIs will address these problems by developing probabilistic machine learning tools for spatial-temporal BIG DATA within the context of scientific advancements in forest structure, topography, and weather-related events (e.g., storms) that can have far-reaching public health, economic, environmental, and security implications. Several innovations in statistical and computational methods and related software development are envisioned. The proposed data products will offer quantification of forest damage/change and landslide risk assessment for Puerto Rico following hurricanes Irma and Maria. Key educational components include dissemination of proposed technologies across the scientific communities including data scientists, engineers, foresters, ecologists, and climate scientists. The PIs plan to train the next generation of data scientists through dissemination efforts for undergraduate and graduate students in STEM fields. The PIs will develop a statistical framework for executing elaborate case studies and data analysis on high-dimensional remotely sensed data, where "high dimension" alludes to one or all of a massive number of (i) spatial locations; (ii) time points; and (iii) responses or outcomes. The PIs will introduce massively scalable multivariate spatial process models within a rich Bayesian hierarchical framework to obtain fully model-based inference for the underlying data generating process. Innovative statistical methodologies are proposed to implement hierarchical models at scales involving tens of millions of spatial locations, thousands of time points and possibly hundreds of remote-sensed variables. The massive scalability of these models will be achieved through sparsity-inducing spatial-temporal processes and other graphical models, matrix-variate low-rank models, conjugate Bayesian distribution theory, and meta-learning paradigms using approximations of a collection of posterior distributions. Theoretical results that enhance current methods will be explored as will be several proposed case studies at hitherto unprecedented scales. The PIs will develop a full suite of spatial models in a wide variety of experiments involving massive data sets. Since massive data sets are where complex relationships can be detected effectively, the proposed methods are well-suited for modeling complex scientific phenomena. Key substantive inference and statistical quantification will be offered for forest damage/change and landslide risk assessment for Puerto Rico following hurricanes Irma and Maria. The PIs will provide probability-based uncertainty quantification and will substantially enhance the scientific community's understanding of storm-related damage assessment.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.