An accept-reject algorithm for the positive multivariate normal distribution

The need to simulate from a positive multivariate normal distribution arises in several settings, specifically in Bayesian analysis. A variety of algorithms can be used to sample from this distribution, but most of these algorithms involve Gibbs sampling. Since the sample is generated from a Markov chain, the user has to account for the fact that sequential draws in the sample depend on one another and that the sample generated only follows a positive multivariate normal distribution asymptotically. The user would not have to account for such issues if the sample generated was i.i.d. In this paper, an accept-reject algorithm is introduced in which variates from a positive multivariate normal distribution are proposed from a multivariate skew-normal distribution. This new algorithm generates an i.i.d. sample and is shown, under certain conditions, to be very efficient.