  Even though Nearest Neighbor Gaussian Processes (NNGP) alleviate considerably
MCMC implementation of Bayesian space-time models, they do not solve the
convergence problems caused by high model dimension. Frugal alternatives such
as response or collapsed algorithms are an answer.gree Our approach is to keep
full data augmentation but to try and make it more efficient. We present two
strategies to do so. The first scheme is to pay a particular attention to the
seemingly trivial fixed effects of the model. We show empirically that
re-centering the latent field on the intercept critically improves chain
behavior. We extend this approach to other fixed effects that may interfere
with a coherent spatial field. We propose a simple method that requires no
tuning while remaining affordable thanks to NNGP's sparsity. The second scheme
accelerates the sampling of the random field using Chromatic samplers. This
method makes long sequential simulation boil down to group-parallelized or
group-vectorized sampling. The attractive possibility to parallelize NNGP
likelihood can therefore be carried over to field sampling. We present a R
implementation of our methods for Gaussian fields in the public repository
https://github.com/SebastienCoube/Improving_NNGP_full_augmentation . An
extensive vignette is provided. We run our implementation on two synthetic toy
examples along with the state of the art package spNNGP. Finally, we apply our
method on a real data set of lead contamination in the United States of America
mainland.
