A class of optimum importance sampling strategies
The authors determine the optimal biasing density from a constraint class whose controlling parameter is fundamental in the performance analysis of Importance Sampling. In addition, it is shown that the constrained optimal distribution from this class minimizes every statistical distance measure to the global optimal distribution and as a consequence is optimal with respect to a large family of nonlinear cost functions. Salient features of this distribution are: (1) unlike the unconstrained optimal solution, this distribution can be made independent of the parameter to be estimated and thus can admit to implementation, and (2) this distribution renders performance gains which can be made arbitrarily close to the optimal gains. Applications to estimating probabilities of rare events (e.g., error rates in communication systems) will be presented. Further analysis will show that in this case the savings over Monte Carlo simulations become unbounded as the probability of the rare event diminishes.
scientific article; zbMATH DE number 1025624
scientific article