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    Hierarchical Decompositions for the Computation of High-Dimensional Multivariate Normal Probabilities

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    Type
    Article
    Authors
    Genton, Marc G. cc
    Keyes, David E. cc
    Turkiyyah, George
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Extreme Computing Research Center
    Statistics Program
    Date
    2018-05-17
    Online Publication Date
    2018-05-17
    Print Publication Date
    2018-04-03
    Permanent link to this record
    http://hdl.handle.net/10754/625457
    
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    Abstract
    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 Limited
    Journal
    Journal of Computational and Graphical Statistics
    DOI
    10.1080/10618600.2017.1375936
    Additional Links
    http://www.tandfonline.com/doi/full/10.1080/10618600.2017.1375936
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    • [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
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Extreme Computing Research Center; Statistics Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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