Space-time models based on random fields with local interactions

Hristopulos, Dionissios T.; Tsantili, Ivi C.

doi:10.1142/s0217979215410076

Cited by 7 publications

(15 citation statements)

References 74 publications

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“…Very interesting examples have been considered (under discrete-time setting) by Baxevani, Podgórski, and Rychlik (2003), and a wealth of sophisticated examples is provided by Baxevani, Caires, and Rychlik (2009), Baxevani et al (2011), andAilliot, Baxevani, Cuzol, Monbet, andRaillard (2011). Other models with special features have been recently proposed by Hristopulos and Tsantili (2016) and Hristopulos and Agou (2019).…”

Section: Classes With Special Featuresmentioning

confidence: 99%

30 Years of space–time covariance functions

Porcu

Furrer

Nychka

2020

WIREs Computational Stats

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In this article, we provide a comprehensive review of space–time covariance functions. As for the spatial domain, we focus on either the d‐dimensional Euclidean space or on the unit d‐dimensional sphere. We start by providing background information about (spatial) covariance functions and their properties along with different types of covariance functions. While we focus primarily on Gaussian processes, many of the results are independent of the underlying distribution, as the covariance only depends on second‐moment relationships. We discuss properties of space–time covariance functions along with the relevant results associated with spectral representations. Special attention is given to the Gneiting class of covariance functions, which has been especially popular in space–time geostatistical modeling. We then discuss some techniques that are useful for constructing new classes of space–time covariance functions. Separate treatment is reserved for spectral models, as well as to what are termed models with special features. We also discuss the problem of estimation of parametric classes of space–time covariance functions. An outlook concludes the paper. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Analysis of High Dimensional Data Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods Statistical and Graphical Methods of Data Analysis > Multivariate Analysis

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Section: Classes With Special Featuresmentioning

confidence: 99%

30 Years of space–time covariance functions

Porcu

Furrer

Nychka

2020

WIREs Computational Stats

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“…Some other constructions based on physical characteristics of the space–time process might be appealing for modeling several real processes. In this direction, it would be desirable to study the approaches proposed in Christakos () as well as Kolovos et al (), Christakos (), Christopoulos and Tsantili () and Christakos et al (). Multivariate Space–Time Models. Often, several variables are observed over the same spatial location and same temporal resolution.…”

Section: Research Problemsmentioning

confidence: 99%

“…Some other constructions based on physical characteristic of the space-time process might be appealing for modeling several real processes. In this direction, it would be desirable to study the approaches proposed in Christakos (2000) as well as Kolovos et al (2004); Christakos (1991); Christopoulos and Tsantili (2016) and Christakos et al (2000a).…”

Section: Research Problemsmentioning

confidence: 99%

Modeling Temporally Evolving and Spatially Globally Dependent Data

Porcu

Alegría

Furrer

2018

Int Statistical Rev

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Summary The last decades have seen an unprecedented increase in the availability of data sets that are inherently global and temporally evolving, from remotely sensed networks to climate model ensembles. This paper provides an overview of statistical modeling techniques for space–time processes, where space is the sphere representing our planet. In particular, we make a distintion between (a) second order‐based approaches and (b) practical approaches to modeling temporally evolving global processes. The former approaches are based on the specification of a class of space–time covariance functions, with space being the two‐dimensional sphere. The latter are based on explicit description of the dynamics of the space–time process, that is, by specifying its evolution as a function of its past history with added spatially dependent noise. We focus primarily on approach (a), for which the literature has been sparse. We provide new models of space–time covariance functions for random fields defined on spheres cross time. Practical approaches (b) are also discussed, with special emphasis on models built directly on the sphere, without projecting spherical coordinates onto the plane. We present a case study focused on the analysis of air pollution from the 2015 wildfires in Equatorial Asia, an event that was classified as the year's worst environmental disaster. The paper finishes with a list of the main theoretical and applied research problems in the area, where we expect the statistical community to engage over the next decade.

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“…SSRFs have been generalized to represent non-separable vector-valued functions [12]. In addition, SSRFs have been extended to the space-time domain [13].…”

Section: Covariance Models Gibbs Rfs Can Effectively Express Correlamentioning

confidence: 99%

A Computational Stochastic Methodology for the Design of Random Meta-materials under Geometric Constraints

Tsantili¹,

Cho²,

Cai³

et al. 2018

SIAM J. Sci. Comput.

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We present a computational stochastic methodology for generating and optimizing random meta-material configurations with non-overlapping geometric constraints subject to various types of covariances and distributions characterizing the randomness of the meta-material configurations. The methodology developed consists of three main components: (1) A deterministic solver for electromagnetic scattering from multiple objects. (2) The Karhunen-Loève (K-L) expansion to represent the correlated configurations of the scattering objects. (3) The Multi-element probabilistic collocation method (ME-PCM) to provide flexibility in achieving desired distributions of the meta-materials. In the current work, we employ random fields from a Spartan family that includes covariance functions with damped oscillatory behavior. The algorithm is applied to study light propagation through random layered heterojunctions and random 3-D meta-materials. We found that greater transmission and reflection, compared to the uniformly spaced structures, can be achieved for a structure with an oscillatory spacing profile along the propagation direction. Optimized configurations of the heterojunctions and 3-D meta-materials have been found with larger or smaller transmission coefficients for different wave numbers of the incoming wave and different correlations.

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Space-time models based on random fields with local interactions

Cited by 7 publications

References 74 publications

30 Years of space–time covariance functions

30 Years of space–time covariance functions

Modeling Temporally Evolving and Spatially Globally Dependent Data

A Computational Stochastic Methodology for the Design of Random Meta-materials under Geometric Constraints

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