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A key challenge in spatial statistics is the analysis for massivespatially-referenced data sets. Such analyses often proceed from Gaussianprocess specifications that can produce rich and robust inference, but involvedense covariance matrices that lack computationally exploitable structures. Thematrix computations required for fitting such models involve floating pointoperations in cubic order of the number of spatial locations and dynamic memorystorage in quadratic order. Recent developments in spatial statistics offer avariety of massively scalable approaches. Bayesian inference and hierarchicalmodels, in particular, have gained popularity due to their richness andflexibility in accommodating spatial processes. Our current contribution is toprovide computationally efficient exact algorithms for spatial interpolation ofmassive data sets using scalable spatial processes. We combine low-rankGaussian processes with efficient sparse approximations. Following recent workby [1], we model the low-rank process using a Gaussian predictive process (GPP)and the residual process as a sparsity-inducing nearest-neighbor Gaussianprocess (NNGP). A key contribution here is to implement these models usingexact conjugate Bayesian modeling to avoid expensive iterative algorithms.Through the simulation studies, we evaluate performance of the proposedapproach and the robustness of our models, especially for long rangeprediction. We implement our approaches for remotely sensed light detection andranging (LiDAR) data collected over the US Forest Service Tanana Inventory Unit(TIU) in a remote portion of Interior Alaska.

Conjugate Nearest Neighbor Gaussian Process Models for Efficient Statistical Interpolation of Large Spatial Data