Gibbs sampling approach for generation of truncated multivariate Gaussian random variables

In many Monte Carlo simulations, it is important to generate samples from given densities. Researchers in statistical signal processing and related disciplines have shown increased interest for a generator of random vectors with truncated multivariate normal probability density functions (PDFs). A straightforward method for their generation is to draw samples from the multivariate normal density and reject the ones that are outside the acceptance region. This method, which is known as rejection sampling, can be very inefficient, especially for high dimensions and/or relatively small supports of the random vectors. We propose an approach for generation of vectors with truncated Gaussian densities based on Gibbs sampling, which is simple to use and does not reject any of the generated vectors.