Project Grant 2152999

This $119,999 National Science Foundation project grant under the Mathematical and Physical Sciences program (CFDA 47.049) will develop new Bayesian Gaussian process methods to enable scalable computation and capture of spatial heterogeneity for uncertainty quantification applications. Duke University will receive funding from August 1, 2022 to July 31, 2025 to create a Bayesian multi-scale residual learning framework with theoretical support. This framework will integrate predictive process approximation, blockwise shrinkage, and random recursive partitioning techniques to decompose Gaussian processes into cascades of residual processes at different resolutions. New recursive algorithms will provide linear computational and storage complexity scaling with observations. The resulting method guarantees serial and parallel efficiency while addressing issues in spatial statistics, computer experiments, machine learning, and nonparametric regression. Open-source software and interdisciplinary research training for students will also be delivered.