Conjugate Nearest Neighbor Gaussian Process Models for Efficient Statistical Interpolation of Large Spatial Data

• Activity Number: 121 - Handling Large Dimensionality, Skewness and Non-Stationarity Through Multi-Resolution Spatial Modeling
• Type: Topic Contributed
• Date/Time: Monday, July 29, 2019 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics and the Environment
• Author(s): Andrew Finley* and Shinichiro Shirota and Sudipto Banerjee
• Companies: Michigan State University and University of California, Los Angeles and UCLA
• Keywords: large spatially-referenced datasets; Gaussian process; nonstationarity; multiresolution; forestry; MCMC

Abstract

Spatial modeling for large to massive datasets have witnessed a surge in interest with a variety of highly scalable likelihood approximations being proposed. This domain has several interesting aspects to it, one of which is adherence to the smoothness of the original process while ensuring superior predictive performance. Our current contribution builds upon classes of models that combine low-rank Gaussian processes with efficient sparse approximations. The underlying spatial process is expressed as a sum of a low-rank Gaussian process and a residual process. We model the low-rank process using a Gaussian predictive process and the residual process as a sparsity-inducing nearest-neighbor Gaussian process (NNGP). With an aim to deliver statistical prediction for datasets in the 10's of millions of observations, we define a highly efficient conjugate NNGP model. Through the simulation studies, we demonstrate superior performance and robustness of our models. We implement our approaches for remote portion of Interior Alaska.