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

Scalable Spatio-Temporal Smoothing via Hierarchical Sparse Cholesky Decomposition