Quasi-Monte Carlo Software Article

We recently uploaded an article on Quasi-Monte Carlo Software to https://arxiv.org/abs/2102.07833. Abstract: Practitioners wishing to experience the efficiency gains from using low discrepancy sequences need correct, well-written software. This article, based on our MCQMC 2020 tutorial, describes some of the better quasi-Monte Carlo (QMC) software available. We highlight the key software components required to approximateContinue reading “Quasi-Monte Carlo Software Article”

QMCPy Version 1.0

The developers of QMCPy are happy to announce the release of version 1.0 on February 12, 2021, Chinese New Year! We would like to thank all those who have made this development possible. A special thank you to Developers: Sou-Cheng T. Choi, Fred J. Hickernell, Michael McCourt, Jagadeeswaran Rathinavel, and Aleksei Sorokin; Collaborators: Mike Giles,Continue reading “QMCPy Version 1.0”

What Makes a Sequence “Low Discrepancy”?

The first blog post, “Why add Q to MC?”, introduced the concept of evenly spread points, which are commonly referred to as low discrepancy (LD) points. This is in contrast to independent and identically distributed (IID) points. Consider two sequences, $\boldsymbol{T}_1, \boldsymbol{T}_2, \ldots \overset{\text{IID}}{\sim} \mathcal{U}[0,1]^d$ \[\boldsymbol{X}_1, \boldsymbol{X}_2, \ldots \overset{\text{LD}}{\sim} \mathcal{U}[0,1]^d.\] Both sequences are expected toContinue reading “What Makes a Sequence “Low Discrepancy”?”