Conditional Importance Sampling Estimators

We give a unified presentation of the conditional importance sampling estimators. We show that they are always better than their nonconditional counterparts. We then present the large deviation theory associated with these estimators. In particular, we give conditional simulation distributions that are optimal in the sense that they are efficient. Interestingly enough, these distributions will not in general be the usual exponential shifts. We give examples showing how to use the theory developed