Integrated Nested Laplace Approximations for Large-Scale Spatiotemporal Bayesian Modeling

SIAM Journal on Scientific Computing, Volume 46, Issue 4, Page B448-B473, August 2024.
Abstract. Bayesian inference tasks continue to pose a computational challenge. This especially holds for spatiotemporal modeling, where high-dimensional latent parameter spaces are ubiquitous. The methodology of integrated nested Laplace approximations (INLA) provides a framework for performing Bayesian inference applicable to a large subclass of additive Bayesian hierarchical models. In combination with the stochastic partial differential equation (SPDE) approach, it gives rise to an efficient method for spatiotemporal modeling. In this work, we build on the INLA-SPDE approach by putting forward a performant distributed memory variant, INLADIST, for large-scale applications. To perform the arising computational kernel operations, consisting of Cholesky factorizations, solving linear systems, and selected matrix inversions, we present two numerical solver options: a sparse CPU-based library and a novel blocked GPU-accelerated approach which we propose. We leverage the recurring nonzero block structure in the arising precision (inverse covariance) matrices, which allows us to employ dense subroutines within a sparse setting. Both versions of INLADIST are highly scalable, capable of performing inference on models with millions of latent parameters. We demonstrate their accuracy and performance on synthetic as well as real-world climate dataset applications.