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

虽然过去十年在预测数据矩阵中的缺失条目方面取得了相当大的进展，但现有方法在一个重要的科学问题上表现出了令人清醒的性能和一些局限性：在空间和时间上表征植物性状，如植物高度，种子质量，叶面积和叶氮。详细的全球植物特征地图将能够准确量化陆地生态系统功能，如农业和森林生产力，以及调节大气中的二氧化碳水平。该项目使用地球上最大和最全面的植物性状数据库（TRY，www.try-db.org），以相对精细的尺度在大多数陆地表面上详细描述植物功能性状和性状多样性。在这样做的过程中，该项目产生了第一个详细的不确定性量化地图的植物性状在地球上所有主要的土地生态系统，以及他们的未来预测。该项目培养了新一代跨学科的科学家，他们可以跨越计算机科学，空间统计学和地球科学之间的传统界限。该项目的研究在贝叶斯概率模型方面取得了实质性进展，用于矩阵间隙填充或矩阵完成，以及时空间隙填充，重点是连续领域。特别是，该项目开发的概率矩阵完成模型，可以结合特定领域的层次结构，如植物分类或系统发育树，以及在不同的环境制度的空间变化。该项目还开发了基于时空过程模型沿着与高度可扩展的推理方法，基于动态最近邻高斯过程的连续字段的间隙填充方法。预计这些模型和方法的影响将超出生态系统功能量化的范围。

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.