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dc.contributor.authorCao, Jian
dc.contributor.authorGenton, Marc G.
dc.contributor.authorKeyes, David E.
dc.contributor.authorTurkiyyah, George
dc.date.accessioned2018-12-31T13:14:42Z
dc.date.available2018-12-31T13:14:42Z
dc.date.issued2018-07-30
dc.identifier.citationCao J, Genton MG, Keyes DE, Turkiyyah GM (2018) Hierarchical-block conditioning approximations for high-dimensional multivariate normal probabilities. Statistics and Computing. Available: http://dx.doi.org/10.1007/s11222-018-9825-3.
dc.identifier.issn0960-3174
dc.identifier.issn1573-1375
dc.identifier.doi10.1007/s11222-018-9825-3
dc.identifier.urihttp://hdl.handle.net/10754/630440
dc.description.abstractThis paper presents a new method to estimate large-scale multivariate normal probabilities. The approach combines a hierarchical representation with processing of the covariance matrix that decomposes the n-dimensional problem into a sequence of smaller m-dimensional ones. It also includes a d-dimensional conditioning method that further decomposes the m-dimensional problems into smaller d-dimensional problems. The resulting two-level hierarchical-block conditioning method requires Monte Carlo simulations to be performed only in d dimensions, with d≪n, and allows the complexity of the algorithm’s major cost to be O(nlogn). The run-time cost of the method depends on two parameters, m and d, where m represents the diagonal block size and controls the sizes of the blocks of the covariance matrix that are replaced by low-rank approximations, and d allows a trade-off of accuracy for expensive computations in the evaluation of the probabilities of m-dimensional blocks. We also introduce an inexpensive block reordering strategy to provide improved accuracy in the overall probability computation. The downside of this method, as with other such conditioning approximations, is the absence of an internal estimate of its error to use in tuning the approximation. Numerical simulations on problems from 2D spatial statistics with dimensions up to 16,384 indicate that the algorithm achieves a 1% error level and improves the run time over a one-level hierarchical Quasi-Monte Carlo method by a factor between 10 and 15.
dc.description.sponsorshipThis research was supported by King Abdullah University of Science and Technology (KAUST).
dc.publisherSpringer Nature
dc.relation.urlhttps://link.springer.com/article/10.1007%2Fs11222-018-9825-3
dc.subjectBlock reordering
dc.subjectd-Dimensional conditioning
dc.subjectHierarchical representation
dc.subjectSpatial covariance functions
dc.subjectUnivariate reordering
dc.titleHierarchical-block conditioning approximations for high-dimensional multivariate normal probabilities
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentStatistics Program
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentExtreme Computing Research Center
dc.identifier.journalStatistics and Computing
kaust.personCao, Jian
kaust.personGenton, Marc G.
kaust.personKeyes, David E.
kaust.personTurkiyyah, George
dc.date.accepted2019
refterms.dateFOA2020-01-16T05:41:30Z


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