The rejection Gibbs coupler: A perfect sampling algorithm and its application to truncated multivariate Gaussian distributions

A new Markov chain based algorithm for drawing samples from a desired distribution has been proposed. This algorithm, also known as the perfect sampling algorithm, can determine exactly when a Markov chain enters the equilibrium, and hence can output exact samples. We introduce a perfect sampling algorithm called the rejection Gibbs coupler for perfect sampling from bounded multivariate distributions. We demonstrate an application of the rejection coupler for generation of samples from truncated multivariate Gaussian distributions.