Error Estimates in Monte Carlo and Quasi-Monte Carlo Integration

摘要

While the Monte Carlo approach to integration dominates any numerical calculation in particle physics phenomenology, the Quasi-Monte Carlo method, which promises better performance, is restrained to relatively minor applications. One of the reasons is the difficulty in estimating reliably the error when using Quasi-Monte Carlo point sequences. The classical Monte Carlo estimator, that consistently overestimates the error, has been used up to now. We review the situation on the error estimators for classical Monte Carlo and present a new estimator for Quasi-Monte Carlo.