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Increasingly large and complex spatial datasets pose massive inferentialchallenges due to high computational and storage costs. Our study is motivatedby the KAUST Competition on Large Spatial Datasets 2023, which taskedparticipants with estimating spatial covariance-related parameters andpredicting values at testing sites, along with uncertainty estimates. Wecompared various statistical and deep learning approaches throughcross-validation and ultimately selected the Vecchia approximation techniquefor model fitting. To overcome the constraints in the R package GpGp, whichlacked support for fitting zero-mean Gaussian processes and direct uncertaintyestimation-two things that are necessary for the competition, we developedadditional \texttt{R} functions. Besides, we implemented certainsubsampling-based approximations and parametric smoothing for skewed samplingdistributions of the estimators. Our team DesiBoys secured victory in two outof four sub-competitions, validating the effectiveness of our proposedstrategies. Moreover, we extended our evaluation to a large real spatialsatellite-derived dataset on total precipitable water, where we compared thepredictive performances of different models using multiple diagnostics.

Exploring the Efficacy of Statistical and Deep Learning Methods for Large Spatial Datasets: A Case Study