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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-
Identifierhttps://link.springer.com/article/10.1007%2Fs00477-016-1361-0-
Identifierhttps://doi.org/10.1007/s00477-016-1361-0-
Languageen-
Extent18 pagesen
TitleNon-parametric approximations for anisotropy estimation in two-dimensional differentiable Gaussian random fieldsen
CreatorPetrakis Emmanouilen
CreatorΠετρακης Εμμανουηλel
CreatorChristopoulos Dionysiosen
CreatorΧριστοπουλος Διονυσιοςel
PublisherSpringer Verlagen
Content SummarySpatially 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
Type of ItemPeer-Reviewed Journal Publicationen
Type of ItemΔημοσίευση σε Περιοδικό με Κριτέςel
Licensehttp://creativecommons.org/licenses/by/4.0/en
Date of Item2018-04-16-
Date of Publication2017-
SubjectAnisotropyen
SubjectIsotropyen
SubjectMonte Carlo simulationsen
SubjectNonparametricen
SubjectProbability regionsen
SubjectRadiation exposureen
Bibliographic CitationM. 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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