Bayesian and Regularization Methods for Spatial Homogeneity Pursuit with Large Datasets

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Spatial data arises from the research of diverse disciplines such as agricultural, geological, economic and social sciences. In many application problems, practitioners are interested in studying the associations between spatial responses and a set of explanatory variables. With the increasing availability of big spatial data, there is a great need to investigate the spatially varying patterns in such associations. In particular, detecting clustering patterns in spatial relations is desired since it allows practitioners to have straightforward interpretations of local associations. In this project, the PI will develop new statistical models and efficient computation algorithms for spatial homogeneity pursuit with both strong theoretical flavor and realistic practical considerations. The overall approach is interdisciplinary in nature. It integrates the advancements in statistics, machine learning, computation, and geosciences. In this project, the PI will consider a varying coefficient regression model to study the clustered relationship between responses and covariates. In particular, tree-based regularization methods will be developed to encourage spatial homogeneity between regression coefficients at neighboring locations. The PI will design both penalized optimizations and Bayesian MCMC algorithms to implement the proposed models. The performance of the proposed methods will be tested with simulation studies and applied to real-life applications. The PI will also study theoretical properties concerning the behavior of the regularization methods by combining the approximation theory of piecewise constant functions, combinatorial and algebraic graph theory, and high dimensional asymptotic theories.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.