Scalable Modeling of Environmental Systems

由于科学家的目标是研究更大、更复杂的环境系统，适合这些数据集所需的模型需要相应地缩放。具体来说，在大范围内，空间系统往往表现出区域特征，因此拟合单一的全球模型可能导致有偏见的预测和推断。然而，区域模式往往缺乏全球可解释性和跨区域共享信息的能力。目前处理非平稳性的方法通常是结合平稳过程来诱导非平稳行为，或者使用“图像扭曲”来扭曲地理空间，使其趋于平稳。前者通常导致缺乏全局可解释性，而后者则经常由于“折叠”问题而导致有偏见的估计。通过建立一个对这些非平稳系统建模的推理框架，本研究旨在开发灵活的全球模型，以处理现代环境系统研究中遇到的多样化和结构化空间系统。******这项研究建立在PI在非平稳建模和贝叶斯计算方面的早期工作的基础上，依赖于非平稳空间建模和最新的蒙特卡罗方法的构建块。PI作为非平稳建模维数展开方法的鼻祖，也具有蒙特卡罗科学计算的背景，为本文的研究奠定了基础。早期的结果是非常有希望的，并暗示所提出的框架具有巨大的潜力，作为一个统一的基础上，模拟大规模的空间过程。除了早期成果之外，PI还有一个明确的概念和数学过程，以解决将提议的框架从假设到实施的剩余挑战。******提出的研究旨在不仅建立非平稳空间过程建模的理论基础，而且还建立技术和计算工具，以便在从大气科学到农业风险建模的广泛应用中实施该方法。通过为非平稳建模提供一个通用的统一框架，提出的研究同时提高了环境建模统计模型的可解释性，并拓宽了进一步科学研究的潜力。这些进步将由配套的软件来推动，与PI促进和传播可复制研究的历史保持一致

As scientists aim to study larger and more complex environmental systems, the models required to fit these data sets need to scale accordingly. Specifically, across large domains, spatial systems tend to exhibit regional characteristics such that fitting a single global model can lead to biased predictions and inference. Regional models, however, often lack global interpretability and the ability to share information across regions. Current approaches to handling nonstationarity generally combine stationary processes to induce nonstationary behavior, or employ 'image warping' to contort geographic space toward stationarity. While the former often results in a lack of global interpretability, the latter frequently results in biased estimates due to an issue known as 'folding'. By building an inferential framework for modeling these nonstationary systems, the proposed research seeks to develop flexible global models that can handle the diverse and structured spatial systems encountered in modern studies of environmental systems.******This research builds on the PI's earlier work in nonstationary modeling and Bayesian computation, relying on building blocks from both nonstationary spatial modeling and the latest in Monte Carlo methods. The PI, being the originator of the dimension expansion approach to nonstationary modeling, also has background in Monte Carlo scientific computing to lay the foundation for the proposed research. Early results are very promising, and hint that the proposed framework holds tremendous potential as a unifying foundation on which to model large-scale spatial processes. In addition to early results, the PI has a clear course, both conceptual and mathematical, to address the remaining challenges to take the proposed framework from hypothesis through implementation.******The proposed research aims to build not only a theoretical basis on which to model nonstationary spatial processes, but also the technical and computational tools to implement the methodology across a wide range of applications ranging from atmospheric science to agricultural risk modeling. By providing a general unified framework for nonstationary modeling, the proposed research simultaneously improves the interpretability of statistical models for environmental modeling and broadens the potential for further scientific investigations. Such advances will be stimulated by accompanying software, keeping with the PI's history of promoting and disseminating reproducible research.**