  We develop a theoretical framework for studying numerical estimation of lower
previsions, generally applicable to two-level Monte Carlo methods, importance
sampling methods, and a wide range of other sampling methods one might devise.
We link consistency of these estimators to Glivenko-Cantelli classes, and for
the sub-Gaussian case we show how the correlation structure of this process can
be used to bound the bias and prove consistency. We also propose a new upper
estimator, which can be used along with the standard lower estimator, in order
to provide a simple confidence interval. As a case study of this framework, we
then discuss how importance sampling can be exploited to provide accurate
numerical estimates of lower previsions. We propose an iterative importance
sampling method to drastically improve the performance of imprecise importance
sampling. We demonstrate our results on the imprecise Dirichlet model.
