Scalable Modeling of Environmental Systems

随着科学家们的目标是研究更大、更复杂的环境系统，拟合这些数据集所需的模型需要相应地扩展。具体而言，在大的域中，空间系统往往表现出区域特征，因此拟合单个全局模型可能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是联合收割机结合平稳过程来诱导非平稳行为，或者采用“图像扭曲”来扭曲地理空间以达到平稳性。虽然前者经常导致缺乏全局可解释性，但由于被称为“折叠”的问题，后者经常导致有偏差的估计。通过建立这些非平稳系统建模的推理框架，拟议的研究旨在开发灵活的全球模型，可以处理在现代环境系统研究中遇到的多样性和结构化的空间系统。

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.