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Ιδρυματικό Αποθετήριο [SANDBOX]
Πολυτεχνείο Κρήτης
Πολυτεχνείο Κρήτης
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| URI | http://purl.tuc.gr/dl/dias/AC7588E3-5CC0-43E9-B714-1379BE1D0AC1 | - |
| Αναγνωριστικό | https://doi.org/10.1023/A:1011095428063 | - |
| Γλώσσα | en | - |
| Μέγεθος | 25 pages | en |
| Τίτλος | Practical calculation of non-gaussian multivariate moments in spatiotemporal BME analysis | en |
| Δημιουργός | George Christakos | en |
| Δημιουργός | D.T. Hristopulos | en |
| Εκδότης | Kluwer Academic Publishers-Plenum Publishers | en |
| Περίληψη | During the past decade, the Bayesian maximum entropy (BME) approach has been used with considerable success in a variety of geostatistical applications, including the spatiotemporal analysis and estimation of multivariate distributions. In this work, we investigate methods for calculating the space/time moments of such distributions that occur in BME mapping applications, and we propose general expressions for non-Gaussian model densities based on Gaussian averages. Two explicit approximations for the covariance are derived, one based on leading-order perturbation analysis and the other on the diagrammatic method. The leading-order estimator is accurate only for weakly non-Gaussian densities. The diagrammatic estimator includes higher-order terms and is accurate for larger non-Gaussian deviations. We also formulate general expressions for Monte Carlo moment calculations including precision estimates. A numerical algorithm based on importance sampling is developed, which is computationally efficient for multivariate probability densities with a large number of points in space/time. We also investigate the BME moment problem, which consists in determining the general knowledge-based BME density from experimental measurements. In the case of multivariate densities, this problem requires solving a system of nonlinear integral equations. We refomulate the system of equations as an optimization problem, which we then solve numerically for a symmetric univariate pdf. Finally, we discuss theoretical and numerical issues related to multivariate BME solutions. | en |
| Τύπος | Peer-Reviewed Journal Publication | en |
| Τύπος | Δημοσίευση σε Περιοδικό με Κριτές | el |
| Άδεια Χρήσης | http://creativecommons.org/licenses/by/4.0/ | en |
| Ημερομηνία | 2015-09-25 | - |
| Ημερομηνία Δημοσίευσης | 2001 | - |
| Βιβλιογραφική Αναφορά | D.T. Hristopulos and G. Christakos," practical calculation of non-Gaussian multivariate moments in spatiotemporal BME analysis, Math. Geo.,vol. 33 ,no.5,pp. 543-568,2001.doi:10.1023/A:1011095428063 | en |
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