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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]

The constellation of Earth-observing satellites now produces atmospheric greenhouse gas concentration estimates across multiple years. Their global coverage is providing additional information on the global carbon cycle. These products are combined with complex inversion systems to infer the magnitude of carbon sources and sinks around the globe. Multiple factors, including the atmospheric transport model and satellite product aggregation method, can impact flux estimates. Functional analysis of variance (ANOVA) invokes a spatio-temporal statistical model to efficiently estimate common flux signals across multiple inversions, and partitions variability across the discrete factors considered. The approach is illustrated on inversion experiments with different satellite retrieval aggregation methods and identifies significant flux anomalies in the presence of mode differences across aggregation methods. Functional ANOVA is also applied to a recent flux model intercomparison project (MIP), and the relative magnitudes of transport model effects and data source (satellite versus in situ) are similar but exhibit slightly different importance for inversions over different continents. [ABSTRACT FROM AUTHOR]

People are increasingly concerned with understanding their personal environment, including possible exposure to harmful air pollutants. To make informed decisions on their day-to-day activities, they are interested in real-time information on a localized scale. Publicly available, fine-scale, high-quality air pollution measurements acquired using mobile monitors represent a paradigm shift in measurement technologies. A methodological framework utilizing these increasingly fine-scale measurements to provide real-time air pollution maps and short-term air quality forecasts on a fine-resolution spatial scale could prove to be instrumental in increasing public awareness and understanding. The Google Street View study provides a unique source of data with spatial and temporal complexities, with the potential to provide information about commuter exposure and hot spots within city streets with high traffic. We develop a computationally efficient spatiotemporal model for these data and use the model to make short-term forecasts and high-resolution maps of current air pollution levels. We also show via an experiment that mobile networks can provide more nuanced information than an equally sized fixed-location network. This modeling framework has important real-world implications in understanding citizens' personal environments, as data production and real-time availability continue to be driven by the ongoing development and improvement of mobile measurement technologies. for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement. [ABSTRACT FROM AUTHOR]

We propose a new class of filtering and smoothing methods for inference in high-dimensional, nonlinear, non-Gaussian, spatio-temporal state-space models. The main idea is to combine the ensemble Kalman filter and smoother, developed in the geophysics literature, with state-space algorithms from the statistics literature. Our algorithms address a variety of estimation scenarios, including online and off-line state and parameter estimation. We take a Bayesian perspective, for which the goal is to generate samples from the joint posterior distribution of states and parameters. The key benefit of our approach is the use of ensemble Kalman methods for dimension reduction, which allows inference for high-dimensional state vectors. We compare our methods to existing ones, including ensemble Kalman filters, particle filters, and particle MCMC. Using a real data example of cloud motion and data simulated under a number of nonlinear and non-Gaussian scenarios, we show that our approaches outperform these existing methods. for this article are available online. [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]

Gaussian process (GP) regression is a exible, nonparametric approach to regression that naturally quantifies uncertainty. In many applications, the number of responses and covariates are both large, and a goal is to select covariates that are related to the response. For this setting, we propose a novel, scalable algorithm, coined VGPR, which optimizes a penalized GP log-likelihood based on the Vecchia GP approximation, an ordered conditional approximation from spatial statistics that implies a sparse Cholesky factor of the precision matrix. We traverse the regularization path from strong to weak penalization, sequentially adding candidate covariates based on the gradient of the log-likelihood and deselecting irrelevant covariates via a new quadratic constrained coordinate descent algorithm. We propose Vecchia-based mini-batch subsampling, which provides unbiased gradient estimators. The resulting procedure is scalable to millions of responses and thousands of covariates. Theoretical analysis and numerical studies demonstrate the improved scalability and accuracy relative to existing methods. [ABSTRACT FROM AUTHOR]