PRACTICAL CALCULATION OF NON-GAUSSIAN MULTIVARIATE MOMENTS IN SPATIOTEMPORAL BAYESIAN MAXIMUM ENTROPY ANALYSIS
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dc.contributor.author | Hristopulos D.T. | |
dc.contributor.author | Christakos G. | |
dc.date.accessioned | 2021-03-14T04:33:24Z | |
dc.date.available | 2021-03-14T04:33:24Z | |
dc.date.issued | 2001 | |
dc.identifier | https://www.elibrary.ru/item.asp?id=795857 | |
dc.identifier.citation | Mathematical Geology, 2001, 33, 5, 543-568 | |
dc.identifier.issn | 0882-8121 | |
dc.identifier.uri | https://repository.geologyscience.ru/handle/123456789/26684 | |
dc.description.abstract | 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. | |
dc.subject | BAYESIAN MAXIMUM ENTROPY | |
dc.subject | RANDOM FIELD | |
dc.subject | PERTURBATION | |
dc.subject | DIAGRAMMATIC | |
dc.subject | MONTE CARLO | |
dc.subject | OPTIMIZATION | |
dc.title | PRACTICAL CALCULATION OF NON-GAUSSIAN MULTIVARIATE MOMENTS IN SPATIOTEMPORAL BAYESIAN MAXIMUM ENTROPY ANALYSIS | |
dc.type | Статья |
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