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This paper presents the development of a spatial block-Nearest NeighborGaussian process (block-NNGP) for location-referenced large spatial data. Thekey idea behind this approach is to divide the spatial domain into severalblocks which are dependent under some constraints. The cross-blocks capture thelarge-scale spatial dependence, while each block captures the small-scalespatial dependence. The resulting block-NNGP enjoys Markov properties reflectedon its sparse precision matrix. It is embedded as a prior within the class oflatent Gaussian models, thus Bayesian inference is obtained using theintegrated nested Laplace approximation (INLA). The performance of theblock-NNGP is illustrated on simulated examples and massive real data forlocations in the order of $10^4$.

Fast Bayesian inference of Block Nearest Neighbor Gaussian process for large data