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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 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. [ABSTRACT FROM AUTHOR]

Extreme weather events such as thunderstorms and tornadoes are of great concern as these events pose a significant threat to life, property, and economic stability. Because of the difficulty of gathering data on extreme events, this paper proposes modeling the conditions for extreme weather through large-scale indicators. The advantage of using large-scale indicators is that climate models can be used to generate data whereas climate models cannot generate data on extreme events themselves. This paper focuses on comparing spatio-temporal models for reanalysis data of large-scale indicators for extreme weather observed across the continental United States and Mexico. Results indicate that rigorous treatment of spatial and temporal dynamics is necessary. The models find that the intensity of conditions for extreme weather is particularly high for the central United States and the intensity of these conditions is increasing over time but the amount of increase may not be practically significant. Copyright © 2010 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]