In this paper some Monte Carlo integration methods are discussed that can be used for the efficient computation of posterior moments and densities of parameters of econometric and, more generally, statistical models. The methods are based on the principle of importance sampling and are intended for the evaluation of multi-dimensional integrals where the integrand is unimodal and multivariate skew. That is, the integrand has different tail behavior in different directions. Illustrative results are presented on the dynamic behavior and the probability of explosion of a small scale macro-economic model. This application involves nine-dimensional numerical integration.