  A key challenge in spatial statistics is the analysis for massive
spatially-referenced data sets. Such analyses often proceed from Gaussian
process specifications that can produce rich and robust inference, but involve
dense covariance matrices that lack computationally exploitable structures. The
matrix computations required for fitting such models involve floating point
operations in cubic order of the number of spatial locations and dynamic memory
storage in quadratic order. Recent developments in spatial statistics offer a
variety of massively scalable approaches. Bayesian inference and hierarchical
models, in particular, have gained popularity due to their richness and
flexibility in accommodating spatial processes. Our current contribution is to
provide computationally efficient exact algorithms for spatial interpolation of
massive data sets using scalable spatial processes. We combine low-rank
Gaussian processes with efficient sparse approximations. Following recent work
by [1], we model the low-rank process using a Gaussian predictive process (GPP)
and the residual process as a sparsity-inducing nearest-neighbor Gaussian
process (NNGP). A key contribution here is to implement these models using
exact conjugate Bayesian modeling to avoid expensive iterative algorithms.
Through the simulation studies, we evaluate performance of the proposed
approach and the robustness of our models, especially for long range
prediction. We implement our approaches for remotely sensed light detection and
ranging (LiDAR) data collected over the US Forest Service Tanana Inventory Unit
(TIU) in a remote portion of Interior Alaska.
