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Bayesian hierarchical spatio‐temporal smoothing for very large datasets
Spatio‐temporal statistics is prone to the curse of dimensionality: one manifestation of this is inversion of the data–covariance matrix, which is not in general feasible for very‐large‐to‐massive datasets, such as those observed by satellite instruments. This becomes even more of a problem in fully Bayesian statistical models, where the inversion typically has to be carried out many times in Markov chain Monte Carlo samplers. Here, we propose a Bayesian hierarchical spatio‐temporal random effects (STRE) model that offers fast computation: Dimension reduction is achieved by projecting the process onto a basis‐function space of low, fixed dimension, and the temporal evolution is modeled using a dynamical autoregressive model in time. We develop a multiresolutional prior for the propagator matrix that allows for unknown (random) sparsity and shrinkage, and we describe how sampling from the posterior distribution can be achieved in a feasible way, even if this matrix is very large. Finally, we compare inference based on our fully Bayesian STRE model with that based on an empirical‐Bayesian STRE‐model approach, where parameters are estimated via an expectation‐maximization algorithm. The comparison is carried out in a simulation study and on a real‐world dataset of global satellite CO2 measurements. Copyright © 2011 John Wiley & Sons, Ltd.
Bayesian hierarchical spatio‐temporal smoothing for very large datasets
Spatio‐temporal statistics is prone to the curse of dimensionality: one manifestation of this is inversion of the data–covariance matrix, which is not in general feasible for very‐large‐to‐massive datasets, such as those observed by satellite instruments. This becomes even more of a problem in fully Bayesian statistical models, where the inversion typically has to be carried out many times in Markov chain Monte Carlo samplers. Here, we propose a Bayesian hierarchical spatio‐temporal random effects (STRE) model that offers fast computation: Dimension reduction is achieved by projecting the process onto a basis‐function space of low, fixed dimension, and the temporal evolution is modeled using a dynamical autoregressive model in time. We develop a multiresolutional prior for the propagator matrix that allows for unknown (random) sparsity and shrinkage, and we describe how sampling from the posterior distribution can be achieved in a feasible way, even if this matrix is very large. Finally, we compare inference based on our fully Bayesian STRE model with that based on an empirical‐Bayesian STRE‐model approach, where parameters are estimated via an expectation‐maximization algorithm. The comparison is carried out in a simulation study and on a real‐world dataset of global satellite CO2 measurements. Copyright © 2011 John Wiley & Sons, Ltd.
Bayesian hierarchical spatio‐temporal smoothing for very large datasets
Katzfuss, Matthias (author) / Cressie, Noel (author)
Environmetrics ; 23 ; 94-107
2012-02-01
14 pages
Article (Journal)
Electronic Resource
English
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