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Non-parametric approximations for anisotropy estimation in two-dimensional differentiable Gaussian random fields

Petrakis Emmanouil, Christopoulos Dionysios

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URIhttp://purl.tuc.gr/dl/dias/DADCB779-C8D0-4433-9745-62450E9AB794-
Αναγνωριστικόhttps://link.springer.com/article/10.1007%2Fs00477-016-1361-0-
Αναγνωριστικόhttps://doi.org/10.1007/s00477-016-1361-0-
Γλώσσαen-
Μέγεθος18 pagesen
ΤίτλοςNon-parametric approximations for anisotropy estimation in two-dimensional differentiable Gaussian random fieldsen
ΔημιουργόςPetrakis Emmanouilen
ΔημιουργόςΠετρακης Εμμανουηλel
ΔημιουργόςChristopoulos Dionysiosen
ΔημιουργόςΧριστοπουλος Διονυσιοςel
ΕκδότηςSpringer Verlagen
ΠερίληψηSpatially referenced data often have autocovariance functions with elliptical isolevel contours, a property known as geometric anisotropy. The anisotropy parameters include the tilt of the ellipse (orientation angle) with respect to a reference axis and the aspect ratio of the principal correlation lengths. Since these parameters are unknown a priori, sample estimates are needed to define suitable spatial models for the interpolation of incomplete data. The distribution of the anisotropy statistics is determined by a non-Gaussian sampling joint probability density. By means of analytical calculations, we derive an explicit expression for the joint probability density function of the anisotropy statistics for Gaussian, stationary and differentiable random fields. Based on this expression, we obtain an approximate joint density which we use to formulate a statistical test for isotropy. The approximate joint density is independent of the autocovariance function and provides conservative probability and confidence regions for the anisotropy parameters. We validate the theoretical analysis by means of simulations using synthetic data, and we illustrate the detection of anisotropy changes with a case study involving background radiation exposure data. The approximate joint density provides (i) a stand-alone approximate estimate of the anisotropy statistics distribution (ii) informed initial values for maximum likelihood estimation, and (iii) a useful prior for Bayesian anisotropy inference.en
ΤύποςPeer-Reviewed Journal Publicationen
ΤύποςΔημοσίευση σε Περιοδικό με Κριτέςel
Άδεια Χρήσηςhttp://creativecommons.org/licenses/by/4.0/en
Ημερομηνία2018-04-16-
Ημερομηνία Δημοσίευσης2017-
Θεματική ΚατηγορίαAnisotropyen
Θεματική ΚατηγορίαIsotropyen
Θεματική ΚατηγορίαMonte Carlo simulationsen
Θεματική ΚατηγορίαNonparametricen
Θεματική ΚατηγορίαProbability regionsen
Θεματική ΚατηγορίαRadiation exposureen
Βιβλιογραφική ΑναφοράM. P. Petrakis and D. T. Hristopulos, "Non-parametric approximations for anisotropy estimation in two-dimensional differentiable Gaussian random fields," Stoch. Env. Res. and Risk A, vol. 31, no. 7, pp. 1853-1870, Sept. 2017. doi:10.1007/s00477-016-1361-0en

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