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.

中文翻译：

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通过分层稀疏 Cholesky 分解实现可扩展的时空平滑

我们提出了一种用于大规模时空平滑的前向滤波器后向采样器 (FFBS) 算法的近似值。当处理线性高斯状态空间模型时，FFBS 通常用于贝叶斯统计，但它需要反转具有潜在状态向量大小的协方差矩阵。与此操作相关的计算负担有效地禁止了它在高维设置中的应用。我们提出了一种基于高斯过程的分层 Vecchia 近似的可扩展时空 FFBS 方法，该方法以前已成功用于空间统计。在模拟数据和真实数据上，我们的方法优于低秩 FFBS 近似。