Efficient Quantile Estimation When Applying Stratified Sampling and Conditional Monte Carlo, With Applications to Nuclear Safety

摘要

We describe how to estimate a quantile when applying a combination of stratified sampling and conditional Monte Carlo, which are variance-reduction techniques for Monte Carlo simulations. We establish a central limit theorem for the resulting quantile estimator. We further prove that for any fixed stratification allocation, the asymptotic variance of the quantile estimator with a combination of stratified sampling and conditional Monte Carlo is no greater than that for stratified sampling alone. We explain how the methods may be used to efficiently perform a safety analysis of a nuclear power plant.