Hierarchical Decompositions for the Computation of High-Dimensional Multivariate Normal Probabilities
Type
ArticleKAUST Department
Applied Mathematics and Computational Science ProgramComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Extreme Computing Research Center
Statistics Program
Date
2018-05-17Online Publication Date
2018-05-17Print Publication Date
2018-04-03Permanent link to this record
http://hdl.handle.net/10754/625457
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Show full item recordAbstract
We present a hierarchical decomposition scheme for computing the n-dimensional integral of multivariate normal probabilities that appear frequently in statistics. The scheme exploits the fact that the formally dense covariance matrix can be approximated by a matrix with a hierarchical low rank structure. It allows the reduction of the computational complexity per Monte Carlo sample from O(n2) to O(mn+knlog(n/m)), where k is the numerical rank of off-diagonal matrix blocks and m is the size of small diagonal blocks in the matrix that are not well-approximated by low rank factorizations and treated as dense submatrices. This hierarchical decomposition leads to substantial efficiencies in multivariate normal probability computations and allows integrations in thousands of dimensions to be practical on modern workstations.Citation
Genton MG, Keyes DE, Turkiyyah G (2017) Hierarchical Decompositions for the Computation of High-Dimensional Multivariate Normal Probabilities. Journal of Computational and Graphical Statistics: 0–0. Available: http://dx.doi.org/10.1080/10618600.2017.1375936.Publisher
Informa UK LimitedAdditional Links
http://www.tandfonline.com/doi/full/10.1080/10618600.2017.1375936Relations
Is Supplemented By:- [Dataset]
Genton, M. G., Keyes, D. E., & Turkiyyah, G. (2017). Hierarchical Decompositions for the Computation of High-Dimensional Multivariate Normal Probabilities [Data set]. Taylor & Francis. https://doi.org/10.6084/M9.FIGSHARE.5386996. DOI: 10.6084/m9.figshare.5386996 Handle: 10754/663816
ae974a485f413a2113503eed53cd6c53
10.1080/10618600.2017.1375936