Project Grant 2210456

This three-year project grant from the National Science Foundation's Mathematical and Physical Sciences program, totaling $359,940, will support the development of new statistical models and algorithms for analyzing large, spatially-dependent data sets collected from complex domains with irregular boundaries. Specifically, the awardee, Texas A&M University, will introduce a class of nonstationary models that can flexibly characterize potentially heterogeneous spatial dependence while respecting irregular geometries. A novel manifold partition model will detect locally stationary structures by allowing flexible partition boundaries. Additionally, a framework will be developed to build a valid stochastic process model integrating local models. Both parameter estimation and prediction can then be performed under a unified framework, capturing discontinuities as well as smoothness in spatial random fields. The research is also expected to yield new scalable and parallelizable inference tools leveraging locally stationary assumptions. Performance will be evaluated through simulation and application to real-world problems across interdisciplinary fields involving geosciences, climate, environment, public health, social sciences, and traffic statistics.