Year: 2026
Type: preprint
Abstract: Quasi-Monte Carlo sampling is a numerical integration method that uses points with a space-filling property in $[0,1]^s$ designed to give better estimates than plain Monte Carlo methods do. For integrands of bounded variation in the sense of Hardy and Krause, errors of $O(n^{-1+ε})$ for any $ε>0$ are obtained from $n$ sample points. Randomized quasi-Monte Carlo (RQMC) points are individually uniformly distributed but collectively space-filling and then independent replications provide variance estimates. For smooth enough integrands the randomization can give a root mean squared error of $O(n^{-3/2+ε})$. This article explains RQMC for a statistical readership recounting some history and presenting some current directions.
Source: arXiv (Cornell University)
Author: Owen, Art B.
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7203753464
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