Highly Scalable Bayesian Geostatistical Modeling via Meshed Gaussian Processes on Partitioned Domains

We introduce a class of scalable Bayesian hierarchical models for the analysis of massive geostatistical datasets. The underlying idea combines ideas on high-dimensional geostatistics by partitioning the spatial domain and modeling the regions in the partition using a sparsity-inducing directed acyclic graph (DAG). We extend the model over the DAG to a well-defined spatial process, which we call the meshed Gaussian process (MGP). A major contribution is the development of an MGPs on tessellated domains, accompanied by a Gibbs sampler for the efficient recovery of spatial random effects. In particular, the cubic MGP (Q-MGP) can harness high-performance computing resources by executing all large-scale operations in parallel within the Gibbs sampler, improving mixing and computing time compared to sequential updating schemes. Unlike some existing models for large spatial data, a Q-MGP facilitates massive caching of expensive matrix operations, making it particularly apt in dealing with spatiotemporal remote-sensing data. We compare Q-MGPs with large synthetic and real world data against state-of-the-art methods. We also illustrate using Normalized Difference Vegetation Index data from the Serengeti park region to recover latent multivariate spatiotemporal random effects at millions of locations. The source code is available at github.com/mkln/meshgp. for this article are available online.

Automated summary

We introduce a class of scalable Bayesian hierarchical models for the analysis of massive geostatistical datasets. The models combine ideas on high-dimensional geostatistics, partitioning the spatial domain, and sparsity-inducing directed acyclic graphs (DAGs). A major contribution is the development of a meshed Gaussian process (MGP) on tessellated domains, along with a Gibbs sampler for efficient recovery of spatial random effects. The cubic MGP (Q-MGP) improves mixing and computing time by executing large-scale operations in parallel within the Gibbs sampler.