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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.

We investigate the 20-year-average boreal winter temperatures generated by an ensemble of six regional climate models (RCMs) in phase I of the North American Regional Climate Change Assessment Program. We use the long-run average (20-year integration) to smooth out variability and to capture the climate properties from the RCM outputs. We find that, although the RCMs capture the large-scale climate variation from coast to coast and from south to north similarly, their outputs can differ substantially in some regions. We propose a Bayesian hierarchical model to synthesize information from the ensemble of RCMs, and we construct a consensus climate signal with each RCM contributing to the consensus according to its own variability parameter. The Bayesian methodology enables us to make posterior inference on all the unknowns, including the large-scale fixed effects and the small-scale random effects in the consensus climate signal and in each RCM. The joint distributions of the consensus climate and the outputs from the RCMs are also investigated through posterior means, posterior variances and posterior spatial quantiles. We use a spatial random-effects model in the Bayesian hierarchical model and, consequently, we can deal with the large data sets of fine resolution outputs from all the RCMs. Additionally, our model allows a flexible spatial covariance structure without assuming stationarity or isotropy.