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

This paper presents the development of a spatial block-Nearest Neighbor Gaussian process (blockNNGP) for location-referenced large spatial data. The key idea behind this approach is to divide the spatial domain into several blocks which are dependent under some constraints. The cross-blocks capture the large-scale spatial dependence, while each block captures the smallscale spatial dependence. The resulting blockNNGP enjoys Markov properties reflected on its sparse precision matrix. It is embedded as a prior within the class of latent Gaussian models, thus fast Bayesian inference is obtained using the integrated nested Laplace approximation (INLA). The performance of the blockNNGP is illustrated on simulated examples, a comparison of our approach with other methods for analyzing large spatial data and applications with Gaussian and non-Gaussian real data.