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A sampling approach to estimate the log determinant used in spatial likelihood problems
Likelihood-based methods for modeling multivariate Gaussian spatial data have desirable statistical characteristics, but the practicality of these methods for massive georeferenced data sets is often questioned. A sampling algorithm is proposed that exploits a relationship involving log-pivots arisi...
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Published in: | Journal of geographical systems 2009-09, Vol.11 (3), p.209-225 |
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description | Likelihood-based methods for modeling multivariate Gaussian spatial data have desirable statistical characteristics, but the practicality of these methods for massive georeferenced data sets is often questioned. A sampling algorithm is proposed that exploits a relationship involving log-pivots arising from matrix decompositions used to compute the log determinant term that appears in the model likelihood. We demonstrate that the method can be used to successfully estimate log-determinants for large numbers of observations. Specifically, we produce an log-determinant estimate for a 3,954,400 by 3,954,400 matrix in less than two minutes on a desktop computer. The proposed method involves computations that are independent, making it amenable to out-of-core computation as well as to coarse-grained parallel or distributed processing. The proposed technique yields an estimated log-determinant and associated confidence interval. |
doi_str_mv | 10.1007/s10109-009-0087-7 |
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Kelley ; LeSage, James P.</creator><creatorcontrib>Pace, R. Kelley ; LeSage, James P.</creatorcontrib><description>Likelihood-based methods for modeling multivariate Gaussian spatial data have desirable statistical characteristics, but the practicality of these methods for massive georeferenced data sets is often questioned. A sampling algorithm is proposed that exploits a relationship involving log-pivots arising from matrix decompositions used to compute the log determinant term that appears in the model likelihood. We demonstrate that the method can be used to successfully estimate log-determinants for large numbers of observations. Specifically, we produce an log-determinant estimate for a 3,954,400 by 3,954,400 matrix in less than two minutes on a desktop computer. The proposed method involves computations that are independent, making it amenable to out-of-core computation as well as to coarse-grained parallel or distributed processing. 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subjects | Areal geology. Maps Computer Appl. in Social and Behavioral Sciences Datasets Dependent variables Distributed processing Earth sciences Earth, ocean, space Econometrics Economics Economics and Finance Eigenvalues Estimates Exact sciences and technology Geographical Information Systems/Cartography Geologic maps, cartography Grants Landscape/Regional and Urban Planning Maximum likelihood method Methods Original Article Regional/Spatial Science Regression analysis Spatial data Statistical analysis Studies Urban Economics |
title | A sampling approach to estimate the log determinant used in spatial likelihood problems |
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