  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.

Computation