Numerical computation of multivariate normal probabilities using bivariate conditioning

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.