  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.
