Collaborative Research: Statistical Inference for High-dimensional Spatial-Temporal Process Models

Spatial data science and other emerging technologies related to Geographic Information Systems are increasingly conspicuous in scientific discoveries. Scientists in a variety of disciplines today have unprecedented access to massive spatial and temporal databases comprising high resolution remote sensed measurements. Statistical modeling and analysis for such data need to account for spatial associations and variations at multiple levels while attempting to recognize underlying patterns and potentially complex relationships. Traditional statistical hypothesis testing is no longer adequate for these scientific problems and statisticians are increasingly turning to specialized methods for analyzing complex spatial-temporal data. However, there continue to remain substantial theoretical and methodological bottlenecks with regard to the interpretation of statistical models. This project will address these problems by developing probabilistic machine learning tools for spatial-temporal Big Data that can have far-reaching public health, economic, environmental, and scientific implications. Several innovations in statistical theory, methodologies and computational algorithms are envisioned that will inform basic science and policy questions arising in diverse disciplines using geographic information sciences. Key educational components include dissemination of technologies across the scientific communities including data scientists, engineers, foresters, ecologists, and climate scientists. The Principal Investigators will train the next generation of data scientists through dissemination efforts for graduate students in STEM fields.

The PIs aim to blend innovative theory, methods and applications to advance knowledge of spatial-temporal stochastic processes with an emphasis on their properties for high-dimensional inference. This domain of spatial statistics has witnessed a burgeoning of models and methods for Big Data analysis. New classes of models have emerged from the judicious use of directed acyclic graphs (DAGs) that are being applied to massive datasets comprising several millions of spatiotemporal coordinates. Theoretical explorations envisioned in this project will focus upon statistical inference on the process parameters and the underlying spatial process. The PIs intend to perform rigorous investigations into statistical inference for high-dimensional spatio-temporal processes to derive micro-ergodic parameters for such models that will be consistently estimable and, at the same time, yield consistent predictive inference. The PIs will develop new methodologies that cast high-dimensional stochastic processes into computationally practicable frameworks by embedding graphical Gaussian processes within hierarchical frameworks for jointly modeling highly multivariate spatial data. Innovative statistical theory and methods will be developed and used to construct sparsity-inducing graphical spatio-temporal models to accommodate massive numbers of outcomes and capture complex dependencies among variables across massive numbers of locations. The planned theoretical explorations into the inferential properties of newly emerging scalable spatio-temporal processes will produce novel statistical contributions. The PIs will provide probability-based uncertainty quantification and will substantially enhance the understanding of physical and natural processes underlying various problems in the physical, environmental and biomedical sciences and in public health.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.