Recursive nearest neighbor co-kriging models for big multi-fidelity spatial data sets

Big datasets are gathered daily from different remote sensing platforms. Recently, statistical co-kriging models, with the help of scalable techniques, have been able to combine such datasets by using spatially varying bias corrections. The associated Bayesian inference for these models is usually facilitated via Markov chain Monte Carlo (MCMC) methods which present (sometimes prohibitively) slow mixing and convergence because they require the simulation of high-dimensional random effect vectors from their posteriors given large datasets. To enable fast inference in big data spatial problems, we propose the recursive nearest neighbor co-kriging (RNNC) model. Based on this model, we develop two computationally efficient inferential procedures: (a) the collapsed RNNC which reduces the posterior sampling space by integrating out the latent processes, and (b) the conjugate RNNC, an MCMC free inference which significantly reduces the computational time without sacrificing prediction accuracy. An important highlight of conjugate RNNC is that it enables fast inference in massive multifidelity data sets by avoiding expensive integration algorithms. The efficient computational and good predictive performances 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.