Computing Multivariate Normal Probabilities Using Rank-1 Lattice Sequences ?

Multivariate normal probabilities, which are used for statistical inference, must be computed numerically. This article describes a new rank-1 lattice quadrature rule and its application to computing multivariate normal probabilities. In contrast to existing lattice rules the number of integrand evaluations need not be speciied in advance. When compared to existing algorithms for computing multivariate normal probabilities the new algorithm is more eecient when high accuracy is required and/or the number of variables is large.