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

> **NSF 01002627DB NSF RESEARCH & RELATED ACTIVIT** · University of California-Los Angeles (CA) · $120,000

## Abstract

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 

## Key facts

- **NSF award ID:** 2515898
- **Awardee organization:** University of California-Los Angeles (CA)
- **SAM.gov UEI:** RN64EPNH8JC6
- **PI:** Sudipto Banerjee
- **Primary program:** 01002627DB NSF RESEARCH & RELATED ACTIVIT
- **All programs:** Artificial Intelligence (AI), Machine Learning Theory
- **Estimated total:** $120,000
- **Funds obligated:** $120,000
- **Transaction type:** Standard Grant
- **Period:** 06/01/2026 → 05/31/2029

## Primary source

NSF Award Search: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2515898

## Citation

> US National Science Foundation, Award 2515898, Collaborative Research: Rates of Change and Boundary Assessment in Spatiotemporal Processes. Retrieved via AI Analytics 2026-06-08 from https://api.ai-analytics.org/grant/nsf/2515898. Licensed CC0.

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