TY - JOUR
T1 - INTEGRATED NESTED LAPLACE APPROXIMATIONS FOR LARGE-SCALE SPATIOTEMPORAL BAYESIAN MODELING
AU - Gaedke-Merzhauser, Lisa
AU - Krainski, Elias
AU - Janalik, Radim
AU - Rue, Hävard
AU - Schenk, Olaf
N1 - Publisher Copyright:
© 2024 Society for Industrial and Applied Mathematics Publications. All rights reserved.
PY - 2024
Y1 - 2024
N2 - 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, INLA\mathrm{D}\mathrm{I}\mathrm{S}\mathrm{T}, 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 INLA\mathrm{D}\mathrm{I}\mathrm{S}\mathrm{T} 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.
AB - 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, INLA\mathrm{D}\mathrm{I}\mathrm{S}\mathrm{T}, 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 INLA\mathrm{D}\mathrm{I}\mathrm{S}\mathrm{T} 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.
KW - Bayesian inference
KW - climate modeling
KW - high-performance computing
KW - parallel computing methodologies
KW - spatiotemporal modeling
UR - http://www.scopus.com/inward/record.url?scp=85198709425&partnerID=8YFLogxK
U2 - 10.1137/23M1561531
DO - 10.1137/23M1561531
M3 - Article
AN - SCOPUS:85198709425
SN - 1064-8275
VL - 46
SP - B448-B473
JO - SIAM Journal on Scientific Computing
JF - SIAM Journal on Scientific Computing
IS - 4
ER -