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D. V. Lindley, “The Use of Prior Probability Distributions in Statistical Inference and Decisions,” Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1, 1961, pp. 453-468.

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• TITLE: Computation of the Multivariate Normal Integral over a Complex Subspace

  AUTHORS: Kartlos Joseph Kachiashvili, Muntazim Abbas Hashmi

  KEYWORDS: Multivariate Normal Integral; Random Variable; Probability; Moments; Series

  JOURNAL NAME: Applied Mathematics, Vol.3 No.5, May 16, 2012

  ABSTRACT: The computation of the multivariate normal integral over a Complex Subspace is a challenge, especially when the inte-gration region is of a complex nature. Such integrals are met with, for example, in the generalized Neyman-Pearson criterion, conditional Bayesian problems of testing many hypotheses and so on. The Monte-Carlo methods could be used for their computation, but at increasing dimensionality of the integral the computation time increases unjustifiedly. Therefore a method of computation of such integrals by series after reduction of dimensionality to one without information loss is offered below. The calculation results are given.