Scalable Modeling of Environmental Systems

随着科学家的目标是研究更大、更复杂的环境系统，适应这些数据集所需的模型需要相应地进行调整。具体地说，在大的领域中，空间系统往往表现出地区性特征，以至于符合单一的全球模型可能会导致有偏见的预测和推断。然而，区域模型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结合平稳过程来诱导非平稳性行为，或者使用“图像扭曲”来扭曲地理空间的平稳性。虽然前者往往导致缺乏全球可解释性，但后者往往由于一个被称为“折叠”的问题而导致估计有偏差。通过建立一个用于模拟这些非平稳系统的推理框架，拟议的研究试图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的空间系统。*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的构建块和最新的蒙特卡罗方法。PI是非平稳建模的维展开法的创始人，也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，并暗示拟议的框架具有巨大的潜力，作为模拟大规模空间过程的统一基础。除了早期的结果，PI还有一个明确的路线，包括概念和数学，以解决将拟议框架从假设到实施的剩余挑战。*拟议研究的目的不仅是建立一个对非平稳空间过程建模的理论基础，而且还建立在从大气科学到农业风险建模的广泛应用中实施该方法的技术和计算工具。通过为非平稳建模提供一个通用的统一框架，该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。这样的进步将由附带的软件刺激，与PI促进和传播可重复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.**