A class of nonseparable and nonstationary spatial temporal covariance functions

Fuentes, Montserrat; Chen, Li; Davis, Joseph E.

doi:10.1002/env.891

Cited by 68 publications

(45 citation statements)

References 30 publications

(29 reference statements)

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“…In the first context, it is increasingly obvious that real-world spatio-temporal processes are non-separable (and often non-stationary), with very complicated spatio-temporal interactions (e.g., nonlinearity). However, we note that many new spatio-temporal model classes have been developed in recent years, and this remains an active and vital area of research (e.g., Cressie and Huang 1999;Gneiting 2002;Ma 2003;Stein 2005;Fuentes et al 2008;Gregori et al 2008;Zastavnyi and Porcu 2009). In the case of the second issue, for problems in the environmental sciences, the size of covariance matrices necessary to describe the joint spatio-temporal structure of the underlying process is often prohibitive.…”

Section: Introductionmentioning

confidence: 98%

A general science-based framework for dynamical spatio-temporal models

Wikle

Hooten

2010

TEST

178

203

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Spatio-temporal statistical models are increasingly being used across a wide variety of scientific disciplines to describe and predict spatially-explicit processes that evolve over time. Correspondingly, in recent years there has been a significant amount of research on new statistical methodology for such models. Although descriptive models that approach the problem from the second-order (covariance) perspective are important, and innovative work is being done in this regard, many real-world processes are dynamic, and it can be more efficient in some cases to characterize the associated spatio-temporal dependence by the use of dynamical models. The chief challenge with the specification of such dynamical models has been related to the curse of dimensionality. Even in fairly simple linear, first-order Markovian, Gaussian error settings, statistical models are often over parameterized. Hierarchical models have proven invaluable in their ability to deal to some extent with this issue by allowing dependency among groups of parameters. In addition, this framework has allowed for the specification of science based parameterizations (and associated prior distributions) in which classes of deterministic dynamical models (e.g., partial differential equations (PDEs), integro-difference equations (IDEs), matrix models, and agent-based models) are used to guide specific parameterizations. Most of the focus for the application of such models in statistics has been in the linear case. The problems mentioned above with linear dynamic models are compounded in the case of nonlinear models. In this sense, the need for coherent and sensible model parameterizations is not only helpful, it is essential. Here, we present an overview of a framework for incorporating scientific information to motivate dynamical spatio-temporal models. First, we illustrate the methodology with the linear case. We then develop a general nonlinear spatio-temporal framework that we call general quadratic nonlinearity and demonstrate that it accommodates many different classes of scientific-based parameterizations as special cases. The model is presented in a hierarchical Bayesian framework and is illustrated with examples from ecology and oceanography.

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Section: Introductionmentioning

confidence: 98%

A general science-based framework for dynamical spatio-temporal models

Wikle

Hooten

2010

TEST

178

203

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“…Many of them do not lead to a closed-form expression for the resulting covariance function. Fuentes et al (2008) propose an interesting example of nonseparable covariance functions generated using spectral densities. A nonparametric test for separability is derived in Crujeiras et al (2009) on the basis of an estimator of the spectral density.…”

Section: Z(s I T I )) Of Real Linear Combinations Of Z(s T)mentioning

confidence: 99%

A general class of nonseparable space-time covariance models

Fonseca¹,

Steel²

2011

Environmetrics

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The aim of this work is to construct nonseparable, stationary covariance functions for processes that vary continuously in space and time. Stochastic modelling of phenomena over space and time is important in many areas of application. But choice of an appropriate model can be difficult as we need to ensure that we use valid covariance structures. A common choice for the process is a product of purely spatial and temporal random processes. In this case, the resulting process possesses a separable covariance function. Although these models are guaranteed to be valid, they are severely limited, since they do not allow space-time interactions. We propose a general and flexible class of valid nonseparable covariance functions through mixing over separable models. The proposed model allows for different degrees of smoothness across space and time and long-range dependence in time. Moreover, the proposed class has as particular cases several popular covariance models proposed in the literature such as the Matérn and the Cauchy Class. We use a Markov chain Monte Carlo sampler for Bayesian inference and apply our modelling approach to the Irish wind data.

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“…Gneiting et al (2006) posit theorems for symmetric and separable specifications, the Cressie-Huang and the Gneiting model, and stationarity. Fuentes et al (2008) propose a nonstationary and nonseparable spectral density specification for which separability is a special case. Finally, Calder (2007) proposes a Bayesian specification that includes priors on initial points in time.…”

Section: Space-time Autoregressive Structuresmentioning

confidence: 99%

Deriving Space-Time Variograms from Space-Time Autoregressive (STAR) Model Specifications

Griffith

Heuvelink

2012

Lecture Notes in Geoinformation and Cartography

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ABSTRACT:Many geospatial science subdisciplines analyze variables that vary over both space and time. The space-time autoregressive (STAR) model is one specification formulated to describe such data. This paper summarizes STAR specifications that parallel geostatistical model specifications commonly used to describe space-time variation, with the goal of establishing synergies between these two modeling approaches. Resulting expressions for space-time correlograms derived from 1 st -order STAR models are solved numerically, and then linked to appropriate space-time semivariogram models.

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A class of nonseparable and nonstationary spatial temporal covariance functions

Cited by 68 publications

References 30 publications

A general science-based framework for dynamical spatio-temporal models

A general science-based framework for dynamical spatio-temporal models

A general class of nonseparable space-time covariance models

Deriving Space-Time Variograms from Space-Time Autoregressive (STAR) Model Specifications

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