Covariance structure of spatial and spatiotemporal processes

Guttorp, Peter; Schmidt, Alexandra M.

doi:10.1002/wics.1259

Cited by 17 publications

(15 citation statements)

References 71 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Higdon et al (1999) build non stationary RF using spatially varying kernels K s : R d → R (where s is the spatial location parameter) and white noise RFs ψ, as Z(s) := R d K s (u)ψ(u) du. In this case the covariance function is C(s 1 , s 2 ) := R d K s 1 (u)K s 2 (u) du, and the process can be chosen to be non Gaussian (Guttorp and Schmidt, 2013).…”

Section: Escaping From Stationaritymentioning

confidence: 99%

Models of Covariance Functions of Gaussian Random Fields Escaping From Isotropy, Stationarity and Non Negativity

2014

View full text Add to dashboard Cite

This paper represents a survey of recent advances in modeling of space or space-time Gaussian Random Fields (GRF), tools of Geostatistics at hand for the understanding of special cases of noise in image analysis. They can be used when stationarity or isotropy are unrealistic assumptions, or even when negative covariance between some couples of locations are evident. We show some strategies in order to escape from these restrictions, on the basis of rich classes of well known stationary or isotropic non negative covariance models, and through suitable operations, like linear combinations, generalized means, or with particular Fourier transforms.

show abstract

Section: Escaping From Stationaritymentioning

confidence: 99%

Models of Covariance Functions of Gaussian Random Fields Escaping From Isotropy, Stationarity and Non Negativity

2014

View full text Add to dashboard Cite

show abstract

“…Various approaches have been developped over the years to deal with non-stationarity through second order moments (see [1,2,3], for a review ). One of the most popular methods of introducing non-stationarity is the convolution approach.…”

Section: Introductionmentioning

confidence: 99%

A generalized convolution model and estimation for non-stationary random functions

2016

View full text Add to dashboard Cite

Standard geostatistical models assume second order stationarity of the underlying Random Function. In some instances, there is little reason to expect the spatial dependence structure to be stationary over the whole region of interest. In this paper, we introduce a new model for second order non-stationary Random Functions as a convolution of an orthogonal random measure with a spatially varying random weighting function. This new model is a generalization of the common convolution model where a non-random weighting function is used. The resulting class of non-stationary covariance functions is very general, flexible and allows to retrieve classes of closed-form nonstationary covariance functions known from the literature, for a suitable choices of the random weighting functions family. Under the framework of a single realization and local stationarity, we develop parameter inference procedure of these explicit classes of non-stationary covariance functions. From a local variogram non-parametric kernel estimator, a weighted local least-squares approach in combination with kernel smoothing method is developed to estimate the parameters. Performances are assessed on two real datasets: soil and rainfall data. It is shown in particular that the proposed approach outperforms the stationary one, according to several criteria. Beyond the spatial predictions, we also show how conditional simulations can be carried out in this non-stationary framework.

show abstract

“…Various approaches have been proposed over the years to deal with non-stationarity of the spatial dependence structure of data (Guttorp and Schmidt 2013;Sampson et al 2001;Guttorp and Sampson 1994). One of the most interesting is the classes of explicit non-stationary covariance functions with locally varying anisotropy developed by Paciorek and Schervish (2006) and Stein (2005).…”

Section: Introductionmentioning

confidence: 99%

Predictive Geological Mapping Using Closed-Form Non-stationary Covariance Functions with Locally Varying Anisotropy: Case Study at El Teniente Mine (Chile)

Fouedjio

Séguret

2016

Nat Resour Res

View full text Add to dashboard Cite

This paper is concerned with the problem of predicting the surface elevation of the Braden breccia pipe at the El Teniente mine in Chile. This mine is one of the worldÕs largest and most complex porphyry-copper ore systems. As the pipe surface constitutes the limit of the deposit and the mining operation, predicting it accurately is important. The problem is tackled by applying a geostatistical approach based on closed-form non-stationary covariance functions with locally varying anisotropy. This approach relies on the mild assumption of local stationarity and involves a kernel-based experimental local variogram a weighted local least-squares method for the inference of local covariance parameters and a kernel smoothing technique for knitting the local covariance parameters together for kriging purpose. According to the results, this non-stationary geostatistical method outperforms the traditional stationary geostatistical method in terms of prediction and prediction uncertainty accuracies.

show abstract

Covariance structure of spatial and spatiotemporal processes

Cited by 17 publications

References 71 publications

Models of Covariance Functions of Gaussian Random Fields Escaping From Isotropy, Stationarity and Non Negativity

Models of Covariance Functions of Gaussian Random Fields Escaping From Isotropy, Stationarity and Non Negativity

A generalized convolution model and estimation for non-stationary random functions

Predictive Geological Mapping Using Closed-Form Non-stationary Covariance Functions with Locally Varying Anisotropy: Case Study at El Teniente Mine (Chile)

Contact Info

Product

Resources

About