The precision frontier in collider physics is being pushed at impressive speed, from both the
experimental and the theoretical side. The aim of this review is to give an overview of recent …

This paper is a contemporary review of QMC ('quasi-Monte Carlo') methods, that is, equal-
weight rules for the approximate evaluation of high-dimensional integrals over the unit cube …

Multivariate normal and t probabilities are needed for statistical inference in many
applications. Modern statistical computation packages provide functions for the computation …

Quasi–Monte Carlo methods have become an increasingly popular alternative to Monte
Carlo methods over the last two decades. Their successful implementation on practical …

While Fubini's theorem states that the integral of a function on the s-dimensional unit cube
can be computed simply by computing iterated integrals, the attempt of doing so for a …

The purely numerical evaluation of multi-loop integrals and amplitudes can be a viable
alternative to analytic approaches, in particular in the presence of several mass scales …

This article provides a survey of recent research efforts on the application of quasi-Monte
Carlo (QMC) methods to elliptic partial differential equations (PDEs) with random diffusion …

This article compares methods for the numerical computation of multivariate t probabilities
for hyper-rectangular integration regions. Methods based on acceptance-rejection, spherical …

We review the basic principles of quasi-Monte Carlo (QMC) methods, the randomizations
that turn them into variance-reduction techniques, the integration error and variance bounds …

Lattice rules are particular instances of quasi-Monte Carlo rules for numerical integration of
functions over the 𝑑-dimensional unit cube [0, 1] 𝑑, where the emphasis lies on high …