Improving performances of MCMC for Nearest Neighbor Gaussian Process models with full data augmentation

Even though Nearest Neighbor Gaussian Processes (NNGP) alleviate MCMC implementation of Bayesian space-time models considerably, they do not solve the convergence problems caused by high model dimension. Frugal alternatives such as response or collapsed algorithms are one answer. An alternative approach is to keep full data augmentation, but to try and make it more efficient. Two strategies are presented. The first is to pay particular attention to the seemingly trivial fixed effects of the model. Empirical exploration shows that re-centering the latent field on the intercept critically improves chain behavior. Theoretical elements support those observations. Besides the intercept, other fixed effects may have trouble mixing. This problem is addressed by interweaving, a simple method that requires no tuning, while remaining affordable thanks to the sparsity of NNGPs.

The second accelerates sampling of the random field using Chromatic samplers. This method boils long sequential simulation down to group-parallelized or group-vectorized sampling. The attractive possibility for parallelizing NNGP density can therefore be carried over to field sampling.

A R implementation of the two methods for Gaussian fields is freely available¹, an extensive vignette is provided. The presented implementation is run on two synthetic toy examples, along with the state of the art package spNNGP. Finally, the methods are applied to a real data set of lead contamination on the mainland of the United States of America.