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Bayesian hierarchical spatio-temporal smoothing for very large datasets

Journal Article


Abstract


  • 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 CO 2 measurements. © 2011 John Wiley & Sons, Ltd.

Publication Date


  • 2012

Citation


  • Katzfuss, M. & Cressie, N. A. (2012). Bayesian hierarchical spatio-temporal smoothing for very large datasets. Environmetrics, 23 (1), 94-107.

Scopus Eid


  • 2-s2.0-84855971533

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/2264

Number Of Pages


  • 13

Start Page


  • 94

End Page


  • 107

Volume


  • 23

Issue


  • 1

Abstract


  • 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 CO 2 measurements. © 2011 John Wiley & Sons, Ltd.

Publication Date


  • 2012

Citation


  • Katzfuss, M. & Cressie, N. A. (2012). Bayesian hierarchical spatio-temporal smoothing for very large datasets. Environmetrics, 23 (1), 94-107.

Scopus Eid


  • 2-s2.0-84855971533

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/2264

Number Of Pages


  • 13

Start Page


  • 94

End Page


  • 107

Volume


  • 23

Issue


  • 1