Monte Carlo evaluation of multivariate normal probabilities

This paper extends research on the simulation of multivariate normal probabilities of high-order dimension by developing a new family of simulators. Such simulators are useful for models with limited dependent variables, including multinomial probit, in panel studies, spatial analysis, and time series analysis. The simulators are derived from a Cholesky decomposition of the covariance matrix, combined with a suitable choice of an importance sampling distribution. The paper studies, among others, the impact of antithetical sampling. The insights gained in this paper are of use in Bayesian analysis as well, in the evaluation of posterior densities.