Hierarchical Bayesian Nearest Neighbor Co-Kriging Gaussian Process Models; An Application to Intersatellite

Abstract

Recent advancements in remote sensing technology and the increasing size of satellite constellations allow for massive geophysical information to be gathered daily on a global scale by numerous platforms of different fidelity. The auto-regressive co-kriging model provides a suitable framework for the analysis of such data sets as it is able to account for cross-dependencies among different fidelity satellite outputs. However, its implementation in multifidelity large spatial data sets is practically infeasible because the computational complexity increases cubically with the total number of observations. In this paper, we propose a nearest neighbor co-kriging Gaussian process (GP) that couples the auto-regressive model and nearest neighbor GP by using augmentation ideas. Our model reduces the computational complexity to be linear with the total number of spatially observed locations. The spatial random effects of the nearest neighbor GP are augmented in a manner which allows the specification of semi-conjugate priors. This facilitates the design of an efficient MCMC sampler involving mostly direct sampling updates. The good predictive performance of the proposed method is demonstrated in a simulation study. We use the proposed method to analyze High-resolution Infrared Radiation Sounder data gathered from two NOAA polar orbiting satellites