Computation of the Multivariate Normal Integral over a Complex Subspace

Kartlos Joseph Kachiashvili, Muntazim Abbas Hashmi

Abdul Salam School of Mathematical Sciences, GC Univer?sity, Lahore, Pakistan.
Air University Multan Campus, Multan, Pakistan.

DOI: 10.4236/am.2012.35074                

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.

Keywords

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

Conflicts of Interest

The authors declare no conflicts of interest.

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