Covariance Models and Simulation Algorithm for Stationary Vector Random Fields on Spheres Crossed with Euclidean Spaces

2021 ◽  
Vol 43 (5) ◽  
pp. A3114-A3134
Author(s):  
Xavier Emery ◽  
Alfredo Alegría ◽  
Daisy Arroyo
Keyword(s):  
Random Fields ◽  
Simulation Algorithm ◽  
Euclidean Spaces ◽  
Covariance Models ◽  
Stationary Vector

Simulation of Homogeneous Two-Dimensional Random Fields: Part II—MA and ARMA Models

1992 ◽  
Vol 59 (2S) ◽  
pp. S270-S277 ◽  
Author(s):  
Pol D. Spanos ◽  
Marc P. Mignolet
Keyword(s):  
Random Fields ◽  
Moving Average ◽  
Autoregressive Moving Average ◽  
Mathematical Form ◽  
Simulation Algorithm ◽  
Arma Models ◽  
Spectral Matrix ◽  
Target Power ◽  
Ar Models

Alternatively to the autoregressive (AR) models examined in Part I, the determination of moving average (MA) algorithms for simulating realizations of twodimensional random fields with a specified (target) power spectrum is presented. First, the mathematical form of these models is addressed by considering infinitevariate vector processes of an appropriate spectral matrix. Next, the MA parameters are determined by relying on the maximization of an energy-like quantity. Then, a technique is formulated to derive an autoregressive moving average (ARMA) simulation algorithm from a prior MA approximation by relying on the minimization of frequency domain errors. Finally, these procedures are critically assessed and an example of application is presented.

Simulation of Homogeneous Two-Dimensional Random Fields: Part I—AR and ARMA Models

1992 ◽  
Vol 59 (2S) ◽  
pp. S260-S269 ◽  
Author(s):  
Marc P. Mignolet ◽  
Pol D. Spanos
Keyword(s):  
Power Spectrum ◽  
Random Fields ◽  
Moving Average ◽  
Autoregressive Moving Average ◽  
Simulation Algorithm ◽  
Two Dimensional ◽  
Arma Models ◽  
Spectral Matrix ◽  
Target Power

The determination of autoregressive (AR) and autoregressive moving average (ARMA) algorithms for simulating realizations of two-dimensional random fields with a specified (target) power spectrum is examined. The form of both of these models is justified first by considering infinite-variate vector processes of appropriate spectral matrix. Next, the AR parameters are selected to achieve the minimum of a positive integral. Then, a technique is formulated to derive an ARM A simulation algorithm from the prior AR approximation by relying on the minimization of frequency domain errors. Finally, these procedures are critically assessed and an example of application is presented.

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.

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