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

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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.