The Shkarofsky-Gneiting class of covariance models for bivariate Gaussian random fields

Stat ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. e207
Author(s):  
Emilio Porcu ◽  
Moreno Bevilacqua ◽  
Amanda S. Hering
Keyword(s):  
Random Fields ◽  
Gaussian Random Fields ◽  
Covariance Models

scholarly journals MODELS OF COVARIANCE FUNCTIONS OF GAUSSIAN RANDOM FIELDS ESCAPING FROM ISOTROPY, STATIONARITY AND NON NEGATIVITY

2014 ◽  
Vol 33 (1) ◽  
pp. 75
Author(s):  
Pablo Gregori ◽  
Emilio Porcu ◽  
Jorge Mateu
Keyword(s):  
Image Analysis ◽  
Random Fields ◽  
Fourier Transforms ◽  
Gaussian Random Fields ◽  
Space Time ◽  
Linear Combinations ◽  
Covariance Functions ◽  
Recent Advances ◽  
Special Cases ◽  
Covariance Models

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.

Comparison of Nonlinear Spatial Correlation Models by the Influence of the Data Augmentation to the Classification Risk

2002 ◽  
Vol 7 (1) ◽  
pp. 31-42
Author(s):  
J. Šaltytė ◽  
K. Dučinskas
Keyword(s):  
Spatial Correlation ◽  
Random Fields ◽  
Data Augmentation ◽  
Gaussian Random Fields ◽  
Classification Rule ◽  
Numerical Comparison ◽  
First Order ◽  
Bayesian Risk ◽  
Correlation Models

The Bayesian classification rule used for the classification of the observations of the (second-order) stationary Gaussian random fields with different means and common factorised covariance matrices is investigated. The influence of the observed data augmentation to the Bayesian risk is examined for three different nonlinear widely applicable spatial correlation models. The explicit expression of the Bayesian risk for the classification of augmented data is derived. Numerical comparison of these models by the variability of Bayesian risk in case of the first-order neighbourhood scheme is performed.

scholarly journals Random Marked Sets

2012 ◽  
Vol 44 (3) ◽  
pp. 603-616 ◽  
Author(s):  
F. Ballani ◽  
Z. Kabluchko ◽  
M. Schlather
Keyword(s):  
Random Fields ◽  
Covariance Function ◽  
Point Processes ◽  
Marked Point ◽  
Positive Definiteness ◽  
Gaussian Random Fields ◽  
Marked Point Processes ◽  
Random Set ◽  
Geostatistical Methods ◽  
New Class

We aim to link random fields and marked point processes, and, therefore, introduce a new class of stochastic processes which are defined on a random set in . Unlike for random fields, the mark covariance function of a random marked set is in general not positive definite. This implies that in many situations the use of simple geostatistical methods appears to be questionable. Surprisingly, for a special class of processes based on Gaussian random fields, we do have positive definiteness for the corresponding mark covariance function and mark correlation function.

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