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 $O(n^{-1+\epsilon})$ for any $\epsilon>0$ 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 $O(n^{-3/2+\epsilon})$. This article explains RQMC for a statistical readership recounting some history and presenting some current directions.
Numerical integration studies how well one can estimate the integral of a function $f$ over $[0,1)^d$ using $n$ sample points. The two classical methods, Monte Carlo (MC) and quasi-Monte Carlo (QMC), have complementary strengths and weaknesses, and a fundamental question is to design an approach that combines the benef...
Numerical integration---approximating the integral of a function $f$ using $n$ point evaluations---is a central task in science and engineering. The two main paradigms for this problem, the Monte Carlo and quasi-Monte Carlo methods, have distinct strengths and limitations, and a fundamental question is to design a meth...
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Timothy Sudijono, Edgar Dobriban, E. Tchetgen· 1 citation
Resolvent Monte Carlo estimates eigenvalues of large matrices by sampling Markov chains and reading the target value off a truncated resolvent quotient, trading exact arithmetic for a stochastic error that the almost-optimal sampling scheme is designed to suppress. This paper studies when that error vanishes outright....
Tsvetelina Kostadinov, I. Dimov· Mathematics· 0 citations
Sign-Corrected Bessel Debiasing (SCBD), a signed pseudo-marginal method based on independent block estimates of the loss, is introduced and its ordinary-MC and independently randomised quasi-Monte Carlo (RQMC) implementations are studied.
Yingkai Lu, J. Lee, Geoff K. Nicholls· 0 citations
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