Collaborative Research: Rates of Change and Boundary Assessment in Spatiotemporal Processes

This project aims to develop theory and methodology required for statistical inference on spatiotemporal rates of change or gradients, followed by extending their use to assess boundaries that track significant changes in spatiotemporal response. The current stage of spatial and temporal data science bears witness to the recording of massive spatiotemporally indexed data for the purpose of tracking changes in spatial and temporal variables. This project outlines the details of the methodology and software development for quantifying and understanding change within large and complex spatiotemporally referenced datasets. These are closely related to machine learning and artificial intelligence, and the developments are motivated by substantive questions arising in various fields where assessing regions of rapid change in space and time is crucial. The focus of applications is on biomedical and neuroimaging datasets, and the project provides research training opportunities for graduate students. Extending the statistical inference to larger domains, we leverage a low-rank projection-based approximation to exact Gaussian processes. The project will also develop classes of highly scalable Bayesian factor models and Graphical predictive processes for jointly modeling highly multivariate spatiotemporal data. The project will conduct rigorous investigations into statistical inference for rates of change associated with predictive processes and graphical predictive processes. The project aims to derive probability distributions that facilitate posterior inference within a Bayesian setting. This is followed by extending the inference to smooth surfaces within space-time that track rapid directional change. 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. NSF Award ID: 2515899 | Program: 01002627DB NSF RESEARCH & RELATED ACTIVIT | Principal Investigator: Didong Li | Institution: University of North Carolina at Chapel Hill, CHAPEL HILL, NC | Award Amount: $100,000 View on NSF Award Search: https://www.nsf.gov/awardsearch/show-award/?AWD_ID=2515899 View on Research.gov: https://www.research.gov/awardapi-service/v1/awards/2515899.html