Nonstationary cross-covariance functions for multivariate spatio-temporal random fields

Salvaña, Mary Lai O.; Genton, Marc G.

doi:10.1016/j.spasta.2020.100411

Cited by 27 publications

(17 citation statements)

References 97 publications

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“…Several studies discussed in previous sections, for example, Rodrigues & Diggle (2010), Ip & Li (2015) and Porcu et al (2016), also tackled the multivariate case. A more thorough review of MCCMs can be found in Salvaña & Genton (2020), who proposed a class of non-stationary Lagrangian MCCMs too. Spatiotemporal covariance models have also been discussed in Cressie & Wikle (2011), Montero et al (2015), Christakos (2017) and Wikle et al (2019).…”

Section: Multivariate Cross-covariance Models (Mccms)mentioning

confidence: 99%

Space-Time Covariance Structures and Models

Chen

Genton

Sun

2021

Annu. Rev. Stat. Appl.

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In recent years, interest has grown in modeling spatio-temporal data generated from monitoring networks, satellite imaging, and climate models. Under Gaussianity, the covariance function is core to spatio-temporal modeling, inference, and prediction. In this article, we review the various space-time covariance structures in which simplified assumptions, such as separability and full symmetry, are made to facilitate computation, and associated tests intended to validate these structures. We also review recent developments on constructing space-time covariance models, which can be separable or nonseparable, fully symmetric or asymmetric, stationary or nonstationary, univariate or multivariate, and in Euclidean spaces or on the sphere. We visualize some of the structures and models with visuanimations. Finally, we discuss inference for fitting space-time covariance models and describe a case study based on a new wind-speed data set. Expected final online publication date for the Annual Review of Statistics, Volume 8 is March 8, 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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Section: Multivariate Cross-covariance Models (Mccms)mentioning

confidence: 99%

Space-Time Covariance Structures and Models

Chen

Genton

Sun

2021

Annu. Rev. Stat. Appl.

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“…Multivariate processes (see, e.g., Genton & Kleiber, 2015; Le & Zidek, 2006; Salvaña & Genton, 2020, and references therein), has received relatively limited developments in the context of massive data. Bayesian models are attractive for inference on multivariate spatial processes because they can accommodate uncertainties in the process parameters more flexibly through their hierarchical structure.…”

Section: Introductionmentioning

confidence: 99%

High‐dimensional multivariate geostatistics: A Bayesian matrix‐normal approach

2021

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Joint modeling of spatially oriented dependent variables is commonplace in the environmental sciences, where scientists seek to estimate the relationships among a set of environmental outcomes accounting for dependence among these outcomes and the spatial dependence for each outcome. Such modeling is now sought for massive data sets with variables measured at a very large number of locations. Bayesian inference, while attractive for accommodating uncertainties through hierarchical structures, can become computationally onerous for modeling massive spatial data sets because of its reliance on iterative estimation algorithms. This article develops a conjugate Bayesian framework for analyzing multivariate spatial data using analytically tractable posterior distributions that obviate iterative algorithms. We discuss differences between modeling the multivariate response itself as a spatial process and that of modeling a latent process in a hierarchical model. We illustrate the computational and inferential benefits of these models using simulation studies and analysis of a vegetation index data set with spatially dependent observations numbering in the millions.

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“…Multivariate processes (see, e.g., Genton and Kleiber, 2015;Salvaña and Genton, 2020;Le and Zidek, 2006, and references therein), has received relatively limited developments in the context of massive data. Bayesian models are attractive for inference on multivariate spatial processes because they can accommodate uncertainties in the process parameters more flexibly through their hierarchical structure.…”

Section: Introductionmentioning

confidence: 99%

High-dimensional Multivariate Geostatistics: A Bayesian Matrix-Normal Approach

Zhang,

Banerjee,

Finley

2020

Preprint

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Joint modeling of spatially-oriented dependent variables are commonplace in the environmental sciences, where scientists seek to estimate the relationships among a set of environmental outcomes accounting for dependence among these outcomes and the spatial dependence for each outcome. Such modeling is now sought for very large data sets where the variables have been measured at a very large number of locations. Bayesian inference, while attractive for accommodating uncertainties through their hierarchical structures, can become computationally onerous for modeling massive spatial data sets because of their reliance on iterative estimation algorithms. This manuscript develops a conjugate Bayesian framework for analyzing multivariate spatial data using analytically tractable posterior distributions that do not require iterative algorithms. We discuss differences between modeling the multivariate response itself as a spatial process and that of modeling a latent process. We illustrate the computational and inferential benefits of these models using simulation studies and real data analyses for a Vege Indices dataset with observed locations numbering in the millions.

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Nonstationary cross-covariance functions for multivariate spatio-temporal random fields

Cited by 27 publications

References 97 publications

Space-Time Covariance Structures and Models

Space-Time Covariance Structures and Models

High‐dimensional multivariate geostatistics: A Bayesian matrix‐normal approach

High-dimensional Multivariate Geostatistics: A Bayesian Matrix-Normal Approach

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