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dc.contributor.authorGenton, Marc G.
dc.contributor.authorKeyes, David E.
dc.contributor.authorTurkiyyah, George
dc.date.accessioned2017-09-14T06:03:52Z
dc.date.available2017-09-14T06:03:52Z
dc.date.issued2018-05-17
dc.identifier.citationGenton 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.
dc.identifier.issn1061-8600
dc.identifier.issn1537-2715
dc.identifier.doi10.1080/10618600.2017.1375936
dc.identifier.urihttp://hdl.handle.net/10754/625457
dc.description.abstractWe 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.
dc.publisherInforma UK Limited
dc.relation.urlhttp://www.tandfonline.com/doi/full/10.1080/10618600.2017.1375936
dc.rightsThis is an Accepted Manuscript of an article published by Taylor & Francis in Journal of Computational and Graphical Statistics on 07 Sep 2017, available online: http://wwww.tandfonline.com/10.1080/10618600.2017.1375936.
dc.subjectHierarchical low-rank structure
dc.subjectMax-stable process
dc.subjectMultivariate cumulative distribution function
dc.subjectMultivariate skew-normal distribution
dc.subjectSpatial statistics
dc.titleHierarchical Decompositions for the Computation of High-Dimensional Multivariate Normal Probabilities
dc.typeArticle
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentExtreme Computing Research Center
dc.contributor.departmentStatistics Program
dc.identifier.journalJournal of Computational and Graphical Statistics
dc.eprint.versionPost-print
dc.contributor.institutionDepartment of Computer Science, American University of Beirut, Beirut, Lebanon.
kaust.personGenton, Marc G.
kaust.personKeyes, David E.
dc.relation.issupplementedbyDOI:10.6084/m9.figshare.5386996
display.relations<b>Is Supplemented By:</b><br/> <ul><li><i>[Dataset]</i> <br/> Genton, M. G., Keyes, D. E., &amp; Turkiyyah, G. (2017). <i>Hierarchical Decompositions for the Computation of High-Dimensional Multivariate Normal Probabilities</i> [Data set]. Taylor &amp; Francis. https://doi.org/10.6084/M9.FIGSHARE.5386996. DOI: <a href="https://doi.org/10.6084/m9.figshare.5386996" >10.6084/m9.figshare.5386996</a> Handle: <a href="http://hdl.handle.net/10754/663816" >10754/663816</a></a></li></ul>
dc.date.published-online2018-05-17
dc.date.published-print2018-04-03


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