Scalable Spatio-Temporal Smoothing via Hierarchical Sparse Cholesky Decomposition

Abstract

We propose an approximation to the forward-filter-backward-sampler (FFBS) algorithm for large-scale spatio-temporal smoothing. FFBS is commonly used in Bayesian statistics when working with linear Gaussian state-space models, but it requires inverting covariance matrices which have the size of the latent state vector. The computational burden associated with this operation effectively prohibits its applications in high-dimensional settings. We propose a scalable spatio-temporal FFBS approach based on the hierarchical Vecchia approximation of Gaussian processes, which has been previously successfully used in spatial statistics. On simulated and real data, our approach outperformed a low-rank FFBS approximation.

Spatio-temporal Event Studies for Air Quality Assessment under Cross-sectional Dependence

“…algorithm. For recent reviews on Kalman filtering for spatio-temporal models seeFerreira et al (2022),Jurek and Katzfuss (2022a), andJurek and Katzfuss (2022b). The maximum likelihood estimates of the parameters are computed using the EM algorithm, which is implemented together with the parameter variance-covariance matrix computation in D-STEM packageWang et al (2021) for MATLAB.…”