Name: Zaida Quiroz Cornejo
Institution: PUCP, Perú
Co-authors:  Marcos O. Prates, Dipak K. Dey


This work develops a valid spatial block-Nearest Neighbor Gaussian process (block-NNGP) for estimation and prediction of locationreferenced large spatial datasets. The key idea behind our approach is to subdivide the spatial domain into several blocks which are dependent under some constraints. The cross-blocks capture the large-scale spatial variation, while each block capture the small-scale dependence. The block-NNGP is embeded as a sparsity-inducing prior within a hierarchical modeling framework. Markov chain Monte Carlo (MCMC) algorithms are executed without storing or decomposing large matrices, while the sparse block precision matrix is efficiently computed through parallel computing. We also consider alternate MCMC algorithms through composite sampling for faster computing time, and more reproducible Bayesian inference. The performance of the blockNNGP is illustrated using simulation studies and applications with massive real data, for locations in the order of $10^4$.

Key Words: Bayesian hierarchical models, block-NNGP, compositesampling, large datasets, MCMC, parallel computing.