Discrepancy-based error estimates for Quasi-Monte Carlo. III: Error distributions and central limits

Abstract

In Quasi-Monte Carlo integration, the integration error is believed to be generally smaller than in classical Monte Carlo with the same number of integration points. Using an appropriate definition of an ensemble of quasi-randompoint sets, we derive various results on the probability distribution of the integration error, which can be compared to the standard Central Limit theorem for normal stochastic sampling. In many cases, a Gaussian error distribution is obtained.

15 pages

References in corpus (2)

• Discrepancy-based error estimates for Quasi-Monte Carlo. I: General formalism
• Discrepancy-based error estimates for Quasi-Monte Carlo. II: Results in one dimension

Cited by in corpus (5)

• Error in Monte Carlo, quasi-error in Quasi-Monte Carlo
• Gaussian limits for discrepancies. I: Asymptotic results
• Quantum field theory for discrepancies
• Loaded Dice in Monte Carlo: importance sampling in phase space integration and probability distributions for discrepancies
• Quantum field theory for discrepancies II: 1/N corrections using fermions