Project Grant 2515898

Federal Project Grant Award Summary

The National Science Foundation's Division of Mathematical Sciences awarded $120,000 to the University of California, Los Angeles (UCLA) under the Mathematical and Physical Sciences program (CFDA 47.049) for a three-year collaborative research project running from June 1, 2026 through May 31, 2029. The project develops statistical theory and methodology for inferring rates of change and gradients in spatiotemporal datasets, with applications to boundary assessment in regions experiencing significant spatiotemporal variation. The research outputs include methodological frameworks for quantifying change in large, complex spatiotemporally indexed datasets; scalable Bayesian factor models and graphical predictive processes for multivariate spatiotemporal data analysis; software tools for statistical inference on rates of change; and probability distributions enabling posterior inference within Bayesian frameworks for predictive processes.

The work addresses substantive applications in biomedical and neuroimaging research while advancing techniques closely related to machine learning and artificial intelligence for spatial-temporal data science. Deliverables leverage low-rank projection-based approximations to Gaussian processes and extend inference to smooth surfaces tracking rapid directional change across space-time domains. The project integrates research training opportunities for graduate students, aligning with the NSF's broader impacts requirements to strengthen the nation's scientific workforce and advance fundamental research in mathematical sciences.