The results reported in this article suggest that it is possible to
reliably compute
moderately accurate multivariate normal probabilities for practical
problems with as many as ten variables, in a few seconds or less of
workstation time, if relatively straightforward transformations of the
integrals are initially carried out.
It is then possible to use standard numerical integration software for the
computations. For higher accuracy work, the simple Monte-Carlo algorithm
converges slowly (this is expected theoretically)
and the use of some type of adaptive algorithm is probably necessary.
2004-11-30