  This paper presents the development of a spatial block-Nearest Neighbor
Gaussian process (block-NNGP) 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 small-scale
spatial dependence. The resulting block-NNGP enjoys Markov properties reflected
on its sparse precision matrix. It is embedded as a prior within the class of
latent Gaussian models, thus Bayesian inference is obtained using the
integrated nested Laplace approximation (INLA). The performance of the
block-NNGP is illustrated on simulated examples and massive real data for
locations in the order of $10^4$.
