Nonseparable, Stationary Covariance Functions for Space–Time Data

By Tilmann Gneiting. 2002

823 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Environmental Engineering, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/c51f841b17cbb5b521f0a6709597c5dd86127ff7

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Citations in the corpus

Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations (2009, positive): “…dependences can be achieved either by using a spatiotemporal covariate .s, t/ or a corresponding spatiotemporal Gaussian field (Kamman and Wand, 2003; Cressie and Johannesson, 2008; Banerjee et al., 2008; Finkenstadt et al., 2006; Abellan et al., 2007; Gneiting, 2002; Banerjee et al., 2004).”
A kernel-based spectral model for non-Gaussian spatio-temporal processes (2002, methodology): “Methods have considered geostatistical approaches (see the review by Kyriakidis and Journel, 1999), multivariate time series approaches (Bennett, 1979), space–time dynamic model approaches (Guttorp et al., 1994; Mardia et al., 1998; Meiring et al., 1998; Wikle and Cressie, 1999), and hierarchical…”
Testing for directional symmetry in spatial dependence using the periodogram (2005, methodology): “The usage of these terms is quite widespread, though not universal: Gneiting (2002), for example, refers to a spatio-temporal version of reflection symmetry as “full symmetry.””
Spatio-temporal exceedance locations and confidence regions (2013, methodology): “It is easy to simulate directly from a multivariate normal distribution using a decomposition of its covariance matrix [Givens and Hoeting (2005), page 146], but this does not take into account the fact that our mean function is being estimated.”
Classes of Kernels for Machine Learning: A Statistics Perspective (2002, background): “Cressie and Huang (1999) and Gneiting (2002b) use (10) to derive nonseparable space-time stationary kernels, see also Christakos (2000) for illustrative examples.”
Convolutional autoregressive models for functional time series (2016, neutral): “…Lim, 1980; Chan, 1993), nonparametric (Chen and Tsay, 1993a,b; Härdle et al., 1997; Xia and Li, 1999; Cai et al., 2000; Fan and Yao, 2003), multivariate (Tiao and Tsay, 1983, 1989; Lüetkepohl, 2005) and spatial–temporal modeling (Handcock and Wallis, 1994; Cressie and Huang, 1999; Gneiting, 2002).”
On potentially negative space time covariances obtained as sum of products of marginal ones (2008, background): “In another notable work in Levinson et al. (1984), the problem of space time statistics of turbulences is faced up. In the merely temporal framework, it is worth citing Xu et al. (2003a,b). On the other hand, in the spatial context, Shkarofsky (1968) emphasised the fact that in the study of turbulen”
Statistical methods for regular monitoring data (2005, methodology): “However, for irregularly sited monitors and the non-separable models that are considered here and in, for example, Cressie and Huang (1999) and Gneiting (2002), there does not appear to be any additional structure to exploit.”
Geostatistical Space-Time Models, Stationarity, Separability, and Full Symmetry (2007, methodology): “…in d. Specifically, they considered functions of the form C(h, u) = ∫ e ih ′ ωρ(ω, u) dω, (h, u) ∈ d× , where ρ(ω, u), u ∈ is a continuous positive definite function for all ω ∈ d. Gneiting (2002a) gave a criterion that is based on this construction but does not depend on closed form Fourier…”
Detection of change in the spatiotemporal mean function (2017, neutral): “We conducted a small simulation study in which the errors "n.sk; t/ were generated to follow the non-separable covariance of Gneiting (2002): C.h; t|β/= σ 2 .a|t|2α +1/τ exp { − c‖h‖ 2γ .a|t|2α +1/βγ } .h; t/∈R2 ×R, with σ2 = 1, a = 1, c = 20, α = 0:7, γ = 0:7 and τ = 2:5: The parameter β ∈ [0, 1]…”
Non‐stationary Cross‐Covariance Models for Multivariate Processes on a Globe (2011, methodology): “Jun and Stein (2007) proposed an approach to produce nonstationary covariance models for a univariate process on a globe to capture space-time asymmetry, which is commonly found in environmental data (Gneiting 2002; Jun and Stein 2004; Li, Genton, and Sherman 2008).”
Random Fields Simplified: Preserving Marginal Distributions, Correlations, and Intermittency, With Applications From Rainfall to Humidity (2020, background): “The hypothesis of STCS separability means that the STCS can be decomposed into the product (or sum) of a purely spatial and a purely temporal correlation functions (e.g., Gneiting, 2002).”
Some covariance models based on normal scale mixtures (2011, methodology): “The subsequent proposition generalizes the results in Cressie and Huang (1999) and Theorem 1 in Gneiting (2002).”
2010 Rietz lecture: When does the screening effect hold? (2011, background): “Despite its flexibility, model (7) is still restrictive in some ways, in particular in exhibiting what Gneiting (2002) calls full symmetry, due to the fact that f(ω1, ω2) = f(ω1,−ω2), and hence the corresponding process has the same covariance structure with time running backwards as it does with ti”
Spatio-temporal variograms and covariance models (2005, background): “For instance, the model (3.3) in Ma (2003a) contains the main model (11) of Gneiting (2002) as a special case (see Ma (2005b)).”
Spatial dynamic factor analysis (2008, background): “Gneiting (2002) extends Cressie and Huang's (1999) classes by constructions directly in the space-time domain.”
Cross-covariance functions for multivariate random fields based on latent dimensions (2010, methodology): “Recall that a real and positive function ϕ is completely monotone if and only if its nth derivative ϕ(n) satisfies (−1)nϕ(n)(t) 0, for all n ∈ N. Based on Gneiting (2002), the following covariance function is positive definite in space-time lags (h, u) ∈ Rd+1: C(h, u) = σ 2 {ψ1(|u|2)}d/2 ϕ1 { ‖h‖2…”
Spatial–temporal mesoscale modeling of rainfall intensity using gage and radar data (2008, background): “Swall and Kern (1999), Nychka, Wikle and Royle (2002) and Fuentes (2002), among others. Another assumption of the commonly used spatial models is full symmetry. Under the assumption of full symmetry [Gneiting (2002)] we have C(h;u|θ)=C(h;−u|θ)=C(−h;u|θ)=C(−h;−u|θ). In the purely spatial context, thi”