III: Medium: Collaborative Research: Bayesian Modeling and Inference for Quantifying Terrestrial Ecosystem Functions

虽然在过去的十年里，在预测数据矩阵中的缺失条目方面取得了长足的进步，但现有的方法在一个重要的科学问题上表现出了令人警醒的性能和一些局限性：在空间和时间上表征植物特征，如株高、种子质量、叶面积和叶氮。详细的全球植物特征地图将有助于准确量化陆地生态系统的功能，如农业和森林生产力，以及大气二氧化碳水平的调节。该项目使用地球上最大和最全面的植物特征数据库(try，www.try-db.org)，在相对较细的尺度上对大部分陆地表面的植物功能特征和特征多样性进行详细的描述。在这样做的过程中，该项目制作了第一张详细的不确定性量化的地球上所有主要陆地生态系统的植物特征地图以及它们的未来预测。该项目培养了能够跨越计算机科学、空间统计学和地球科学之间传统界限的新一代跨学科科学家。该项目的研究在填充矩阵缺口或矩阵补全的贝叶斯概率模型以及强调连续领域的时空缺口填充方面取得了实质性进展。特别是，该项目开发了概率矩阵完成模型，该模型可以纳入特定领域的层次结构，如植物分类学或系统发育树，以及不同环境制度的空间差异。该项目还开发了基于时空过程模型的连续领域的缺口填充方法，以及基于动态最近邻高斯过程的高度可扩展的推理方法。这些模型和方法预计将产生超出量化生态系统功能范围的影响。

While the past decade has seen considerable advances in predicting missing entries in data matrices, existing approaches have demonstrated sobering performance and several limitations in an important scientific problem: characterizing plant traits, such as plant height, seed mass, leaf area, and leaf nitrogen, over space and time. Detailed global maps of plant traits will enable accurate quantification of terrestrial ecosystem functions, such as agricultural and forest productivity, and regulation of atmospheric CO2 levels. This project uses the largest and most comprehensive plant trait database on the planet (TRY, www.try-db.org) to develop a detailed characterization of plant functional traits and trait diversity at relatively fine scales across most of the terrestrial land surface. In doing so, the project produces the first detailed uncertainty quantified maps of plant traits across all of earth's major land ecosystems as well as their future projections. The project trains a new generation of interdisciplinary scientists who can cross the traditional boundaries between computer science, spatial statistics, and the Earth sciences.The research in the project makes substantial advances on Bayesian probabilistic models for matrix gap filling or matrix completion, as well as spatiotemporal gap filling with emphasis on continuous fields. In particular, the project develops probabilistic matrix completion models which can incorporate domain specific hierarchies, such as plant taxonomic or phylogenetic trees, as well as spatial variations across different environmental regimes. The project also develops methods for gap filling in continuous fields based on spatiotemporal process models along with highly scalable inference methods based on dynamic nearest-neighbor Gaussian processes. The models and methods are expected to have impact beyond the scope of quantifying ecosystem functions.