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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Bibliographic Details
Published in:Journal of geographical systems 2009-09, Vol.11 (3), p.209-225
Main Authors: Pace, R. Kelley, LeSage, James P.
Format: Article
Language:English
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
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Summary: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.
ISSN:1435-5930
1435-5949
DOI:10.1007/s10109-009-0087-7