Geostatistical Space-Time Models, Stationarity, Separability, and Full Symmetry

By Tilmann Gneiting, Marc G. Genton, Peter Guttorp. 2007

352 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Economics and Econometrics, Environmental Engineering

View Paper: https://www.semanticscholar.org/paper/7821894d36ebd0333487d5107731c80616c5ab9c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Economics and Econometrics

In Environmental Engineering

Citations in the corpus

changepoint: An R Package for Changepoint Analysis (2014, methodology): “The data has previously been analysed by several authors including Haslett and Raftery (1989) and Gneiting et al. (2007).”
Spatio-Temporal Covariance and Cross-Covariance Functions of the Great Circle Distance on a Sphere (2016, methodology): “We also use the proposed spatio-temporal models to analyze Level-3 Total Ozone Mapping Spectrometer (TOMS) data, which include the daily total column ozone levels, as studied with chordal distances and only purely spatial models by Jun and Stein (2008). Environmental data are typically characterized”
Separable approximations of space‐time covariance matrices (2007, methodology): “Gneiting et al. (2007) considered a stationary but generally nonseparable correlation function model of the form C(h, u) = 1 1+a|u|2α if h = 0, 1−ν 1+a|u|2α exp ( −c‖h‖ (1+a|u|2α)β/2 ) otherwise, (9) where a and c are temporal and spatial nonnegative scale parameters, respectively, and α ∈ (0, 1]…”
Gaussian Processes for Independence Tests with Non-iid Data in Causal Inference (2015, methodology): “ACM Transactions on Intelligent Systems and Technology, Vol. 7, No. 2, Article 22, Publication date: November 2015. data, much recent work has focused on designing classes of sophisticated nonseparable and nonstationary covariance functions for capturing complex dependencies [Gneiting et al. 2007].”
Cross-covariance functions for multivariate random fields based on latent dimensions (2010, methodology): “We propose an approach based on existing covariance models for univariate (p = 1) random fields; see, for instance, Cressie & Huang (1999), Gneiting (2002) and Gneiting et al. (2007).”
Estimating Space and Space-Time Covariance Functions for Large Data Sets: A Weighted Composite Likelihood Approach (2012, methodology): “This method is one of the most widely used estimation methods for space-time data (see, eg, Cressie and Huang 1999 ; Gneiting, Genton, and Guttorp 2007 );”
A Valid Matérn Class of Cross-Covariance Functions for Multivariate Random Fields With Any Number of Components (2012, methodology): “The simulation scenarios are motivated by a meteorological dataset discussed by Gneiting et al. (2010). It consists of temperature and pressure observations, as well as forecasts, at 157 locations in the North American Pacific Northwest.”
Space–time modelling of extreme events (2012, background): “For a good review of space–time correlation functions and a discussion of properties such as stationarity, separability and full symmetry, see Gneiting et al. (2007) and the references therein.”
Partial Separability and Functional Graphical Models for Multivariate Gaussian Processes (2019, background): “In many instances, it is assumed that the covariance of X is separable , meaning that there exists a p × p covariance matrix ∆ and covariance operator B on L 2 [0 , 1] such that G = ∆ B (Gneiting et al. 2006, Genton 2007, Aston et al. 2017).”
Some covariance models based on normal scale mixtures (2011, methodology): “Gneiting et al. (2007) distinguish between the properties of covariance functions, such as motion invariance, separability, full symmetry, or conformity with Taylor’s hypothesis.”
Space‐time modelling of trends in temperature series (2011, background): “Gneiting et al. (2007) showed that a non-separable covariance structure gave a better fit and could describe that the empirical covariance was asymmetric in lags, due to the prevailing westerly winds.”
Tests for separability in nonparametric covariance operators of random surfaces (2015, background): “The separability assumption (see e.g. Gneiting et al. 2007, Genton 2007) simplifies the covariance structure of the process and makes it far easier to estimate; in some sense, the separability assumption results in a estimator of the covariance which has less variance, at the expense of a possible…”
Random Fields Simplified: Preserving Marginal Distributions, Correlations, and Intermittency, With Applications From Rainfall to Humidity (2020, background): “Intuitively, this hypothesis corresponds to assuming that the cross correlation (spatial correlation) can be studied independently of the autocorrelation (temporal correlation; see, e.g., Genton, 2007; Gneiting et al., 2006, and references therein for a technical discussion).”
Factor Copula Models for Replicated Spatial Data (2015, methodology): “To capture low correlations, wemight need to use correlation functions for Z that can take negative values, such as the damped cosine function ρ(h) = cos(h) exp(−λh), λ > 0; see Gneiting, Genton, and Guttorp (2007) for a review of correlation functions.”