Recursive Nearest Neighbor Co-Kriging Models for Big Multiple Fidelity Spatial Data Sets

Large datasets are daily gathered from different remote sensing platforms and statistical models are usually used to combine them by accounting for spatially varying bias corrections. The statistical inference of these models is usually based on Markov chain Monte Carlo (MCMC) samplers which involve updating a high-dimensional random effect vector and hence present slow mixing and convergence. To overcome this and enable fast inference in big spatial data problems, we propose the recursive nearest neighbor co-kriging (RNNC) model and use it as a framework which allows us to develop two computationally efficient inferential procedures: a) the collapsed RNNC that reduces the posterior sampling space by integrating out the latent processes, and b) the conjugate RNNC which is an MCMC free inference that significantly reduces the computational time without sacrificing prediction accuracy. The good computational and predictive performance of our proposed algorithms are demonstrated on benchmark examples and the analysis of the High-resolution Infrared Radiation Sounder data gathered from two NOAA polar orbiting satellites in which we managed to reduce the computational time from multiple hours to just a few minutes.