Collaborative Research: Hierarchical Sparsity-Inducing Gaussian Process Models for Bayesian Inference on Large Spatiotemporal Datasets

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With the increasing capabilities of geographical referencing and remote-sensing technologies such as Geographical Information Systems (GIS) and Global Positioning Systems (GPS) that can identify geographical coordinates with a simple hand-held device, scientists and researchers in a variety of disciplines today have unprecedented access to spatially-referenced data. From identifying spatial disparities in health standards to more precise weather predictions, GIS technology is used today in almost every sphere of human life with beneficial effects that can be far-reaching. Statistical modeling and analysis for spatial data constitute a key element in harnessing the scientific potential of GIS and related technologies. As the scientific community moves into a data-rich era, there is unprecedented opportunity to build an understanding about how environmental ecosystems function and how they will respond to changing environmental conditions. This research project will advance data modeling in disciplines as diverse as forestry, ecology, public and environmental health, meteorology, engineering, and the geosciences. It will help discover complex scientific relationships, which, in turn, will lead to better analysis and understanding of our environment and how our ecosystem is evolving.Analysts and researchers using GIS technology are increasingly faced with analyzing massive amounts of spatial data. With spatial and spatial-temporal data becoming increasingly high-dimensional -- both in terms of number of observed locations and the number of observations per location -- scientists are seeking to hypothesize extremely complex relationships. Not surprisingly, statistical models accounting for spatial associations have become an enormously active area of research over the last decade and, in particular, hierarchical models capturing variation at multiple scales have become extremely popular for spatial modeling. These, in turn, lead to rather complex models that are computationally expensive and unfeasible even for moderately sized data sets. This project recognizes the increased computational demands in statistical modeling of large high-dimensional spatial and spatial-temporal data and offers a model-based setup to tackle a wide variety of data analytic problems. The emphasis of this project is on rigorous and principled statistical methodology that can be implemented on standard computing platforms, thereby ensuring accessibility for a very wide group of researchers. The project outlines a suite of spatial models that easily scale to massive databases and have a broad range of applications. Theoretical and methodological innovations that enhance current methods will be presented, and their practical implications will be illustrated using freely distributed open-source statistical software products developed as a part of this project.