A sampling approach to estimate the log determinant used in spatial likelihood problems
Document Type
Article
Publication Date
1-1-2009
Abstract
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. © Springer-Verlag 2009.
Publication Source (Journal or Book title)
Journal of Geographical Systems
First Page
209
Last Page
225
Recommended Citation
Pace, R., & LeSage, J. (2009). A sampling approach to estimate the log determinant used in spatial likelihood problems. Journal of Geographical Systems, 11 (3), 209-225. https://doi.org/10.1007/s10109-009-0087-7