Computation of the Multivariate Normal Integral over a Complex Subspace

Affiliation(s)

Abdul Salam School of Mathematical Sciences, GC Univer?sity, Lahore, Pakistan.

Air University Multan Campus, Multan, Pakistan.

Abdul Salam School of Mathematical Sciences, GC Univer?sity, Lahore, Pakistan.

Air University Multan Campus, Multan, Pakistan.

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.

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.

Cite this paper

K. Kachiashvili and M. Hashmi, "Computation of the Multivariate Normal Integral over a Complex Subspace,"*Applied Mathematics*, Vol. 3 No. 5, 2012, pp. 489-498. doi: 10.4236/am.2012.35074.

K. Kachiashvili and M. Hashmi, "Computation of the Multivariate Normal Integral over a Complex Subspace,"

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