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Scalable spatio‐temporal smoothing via hierarchical sparse Cholesky decomposition

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  • Marcin Jurek
  • Matthias Katzfuss

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.

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  • Marcin Jurek & Matthias Katzfuss, 2023. "Scalable spatio‐temporal smoothing via hierarchical sparse Cholesky decomposition," Environmetrics, John Wiley & Sons, Ltd., vol. 34(1), February.
    • Handle: RePEc:wly:envmet:v:34:y:2023:i:1:n:e2757
    DOI: 10.1002/env.2757
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    References listed on IDEAS

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    Cited by:

    1. Xin Wang & Xin Zhang, 2024. "Scanner: Simultaneously temporal trend and spatial cluster detection for spatial‐temporal data," Environmetrics, John Wiley & Sons, Ltd., vol. 35(5), August.

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