A review of uncertainty quantification for quasi-Monte Carlo that recommends Student's t intervals from at least 10 randomized replicates and identifies near-symmetry of RQMC errors as a promising but unproven basis for confidence intervals.
Automatic optimal-rate convergence of randomized nets using median-of-means
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We study the sample median of independently generated quasi-Monte Carlo estimators based on randomized digital nets and prove it approximates the target integral value at almost the optimal convergence rate for various function spaces. In contrast to previous methods, the algorithm does not require a priori knowledge of underlying function spaces or even an input of pre-designed $(t,m,s)$-digital nets, and is therefore easier to implement. This study provides further evidence that quasi-Monte Carlo estimators are heavy-tailed when applied to smooth integrands and taking the median can significantly improve the error by filtering out the outliers.
fields
math.NA 1years
2024 1verdicts
ACCEPT 1representative citing papers
citing papers explorer
-
Error estimation for quasi-Monte Carlo
A review of uncertainty quantification for quasi-Monte Carlo that recommends Student's t intervals from at least 10 randomized replicates and identifies near-symmetry of RQMC errors as a promising but unproven basis for confidence intervals.