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Abstract We propose a statistical downscaling method to produce fine-resolution climate projections. A multivariate spatial statistical model is developed to jointly analyse high-resolution remote sensing data and coarse-resolution climate model outputs. With a basis function representation, the resulting model can achieve efficient computation and describe potentially nonstationary spatial dependence. We implement our method to produce downscaled sea surface temperature projections over the Great Barrier Reef region from CMIP6 Earth system models. Compared with the state of the art, our method reduces the mean squared predictive error substantially and produces a predictive distribution enabling holistic uncertainty quantification analyses. 

ABSTRACT Accounting for uncertainty in model selection is crucial for statistical inference and data‐driven decision‐making, particularly with high‐dimensional data. While multiple studies have focused on constructing model confidence sets, a practical and informative visualization tool to assist in decision‐making under such uncertainty has been lacking. This paper introduces an intuitive visualization tool, the graph of ranking from solution paths (GRASP), designed to provide instant insights into model selection uncertainty. Additionally, GRASP accounts for the uncertainty of variable importance, enabling decision‐makers to assess each variable under uncertainty. Based on an innovative selection procedure that utilizes the entire solution path, a feature importance score and bootstrap techniques, GRASP effectively visualizes the uncertainty of model selection, as demonstrated by our numerical examples. Furthermore, we propose a novel measure of uncertainty based on GRASP, providing a single‐number summary of selection uncertainty. This measure incorporates the concept of the flat norm, traditionally used in geometry and physics. Our simulation studies and numerical examples confirm that this measure accurately and robustly quantifies uncertainty. 

Abstract 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.