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

TL;DR

This paper introduces a scalable Bayesian method for large spatial datasets using block-structured Gaussian processes, enabling efficient inference by exploiting sparsity and Markov properties.

Contribution

It develops a novel block-structured NNGP model that captures multi-scale spatial dependence and integrates it with INLA for fast Bayesian inference on large data.

Findings

Effective on simulated data with large spatial extent

Successfully applied to real datasets with 10,000+ locations

Achieves computational efficiency through sparse precision matrices

Abstract

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 $10^4$.