Markov Random Fields, Geostatistics and Matrix-Free Computation

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In the past few decades, spatial statistics has become increasingly important in agriculture, epidemiology, geology, image analysis and environmental science. PI's prior research provided new perspectives in connecting two major branches of spatial statistics, namely the Markov random fields and geostatistics and in advancing fast statistical computations. At present, many important scientific applications demand use of complex spatial models and their multivariate and spatial-temporal versions. However, statistical computations of these complex spatial models have remained a challenge. The project derives new mathematical understanding on these complex spatial and spatial-temporal models, which then opens up the possibility of advancing various scalable statistical computations with minimal storage. The project will contribute to obtaining enhanced scientific understanding in studies such as arsenic and magnesium contamination and hydro-chemical analysis of groundwater and spatial and spatial temporal variations in opioid overdose cases in the United States.The project brings together mathematical and computational knowledge from different scientific fields to develop principled frameworks for spatial statistics and inference. The research aims to provide new understanding on (i) constructions of higher neighborhood order Gaussian Markov random fields, (ii) joint modeling of two or more spatial variables, and (iii) complex spatial-temporal models. Novel matrix-free computations are proposed to advance statistical inference. These computations include not just best linear unbiased predictions and residual maximum likelihood estimation, but also scalable Hamiltonian Monte Carlo methods. Applications will include mapping (1) heavy metal contamination in groundwater and (2) geographic variations in drug overdose cases across the United States. The project also aims to integrate research and educational activities through developing short courses and case studies on spatial statistics and scalable computation, and through providing valuable training and learning opportunities for graduate students.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.