The Normal Law Under Linear Restrictions: Simulation and Estimation via   Minimax Tilting
  Simulation from the truncated multivariate normal distribution in high dimensions is a recurrent problem in statistical computing, and is typically only feasible using approximate MCMC sampling. In this article we propose a minimax tilting method for exact iid simulation from the truncated multivariate normal distribution. The new methodology provides both a method for simulation and an efficient estimator to hitherto intractable Gaussian integrals. We prove that the estimator possesses a rare vanishing relative error asymptotic property. Numerical experiments suggest that the proposed scheme is accurate in a wide range of setups for which competing estimation schemes fail. We give an application to exact iid simulation from the Bayesian posterior of the probit regression model. 
Z. I. Botev
stat.CO