mvtnorm: New numerical algorithm for multivariate normal probabilities

Miwa et al. (2003) proposed a numerical algorithm for evaluating multivariate normal probabilities. Starting with version 0.9-0 of the mvtnorm package (Hothorn et al., 2001; Genz et al., 2008), this algorithm is available to the R community. We give a brief introduction to Miwa's procedure and compare it, with respect to computing time and accuracy, to a quasi-randomized Monte-Carlo procedure proposed by Genz and Bretz (1999), which has been available through mvtnorm for some years now. The new algorithm is applicable to problems with dimension smaller than 20, whereas the procedures by Genz and Bretz (1999) can be used to evaluate 1000-dimensional normal distributions. At the end of this article, a suggestion is given for choosing a suitable algorithm in different situations