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Monte Carlo and Quasi-Monte Carlo Methods pp 289–302Cite as

Numerical Computation of Multivariate Normal Probabilities Using Bivariate Conditioning

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 163))

Abstract

New methods are derived for the computation of multivariate normal probabilities defined for hyper-rectangular probability regions. The methods use conditioning with a sequence of truncated bivariate probability densities. A new approximation algorithm based on products of bivariate probabilities will be described. Then a more general method, which uses sequences of simulated pairs of bivariate normal random variables, will be considered. Simulations methods which use Monte Carlo, and quasi-Monte Carlo point sets will be described. The new methods will be compared with methods which use univariate normal conditioning, using tests with random multivariate normal problems.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Washington State University, Pullman, WA, 99164-3113, USA

    Alan Genz & Giang Trinh

Authors
  1. Alan Genz
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  2. Giang Trinh
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Corresponding author

Correspondence to Alan Genz .

Editor information

Editors and Affiliations

  1. Department of Computer Science, KU Leuven, Heverlee, Belgium

    Ronald Cools

  2. Department of Computer Science, KU Leuven, Heverlee, Belgium

    Dirk Nuyens

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Genz, A., Trinh, G. (2016). Numerical Computation of Multivariate Normal Probabilities Using Bivariate Conditioning. In: Cools, R., Nuyens, D. (eds) Monte Carlo and Quasi-Monte Carlo Methods. Springer Proceedings in Mathematics & Statistics, vol 163. Springer, Cham. https://doi.org/10.1007/978-3-319-33507-0_13

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