Perfectly random sampling of truncated multinormal distributions

Abstract

The target measure $μ$ is the distribution of a random vector in a box $\cB$, a Cartesian product of bounded intervals. The Gibbs sampler is a Markov chain with invariant measure $μ$. A ``coupling from the past'' construction of the Gibbs sampler is used to show ergodicity of the dynamics and to perfectly simulate $μ$. An algorithm to sample vectors with multinormal distribution truncated to $\cB$ is then implemented.