Hierarchical Bayesian Nearest Neighbor Co-Kriging Gaussian Process Models; An Application to Intersatellite Calibration
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Recent advancements in remote sensing technology and the increasing size of satellite constellations allows massive geophysical information to be gathered daily on a global scale by numerous platforms of different fidelity. The auto-regressive co-kriging model is a suitable framework to analyse such data sets because it accounts for cross-dependencies among different fidelity satellite outputs. However, its implementation in multifidelity large spatial data-sets is practically infeasible because its computational complexity increases cubically with the total number of observations. In this paper, we propose a nearest neighbour co-kriging Gaussian process that couples the auto-regressive model and nearest neighbour GP by using augmentation ideas; reducing the computational complexity to be linear with the total number of spatial observed locations. The latent process of the nearest neighbour GP is 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 which can be implemented in parallel computational environments. 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.
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