Related papers: Quasi-Monte Carlo confidence intervals using quant…

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…

Recent advances in quasi-Monte Carlo integration demonstrate that the median of linearly scrambled digital net estimators achieves near-optimal convergence rates for high-dimensional integrals without requiring a priori knowledge of the…

In Quasi-Monte Carlo integration, the integration error is believed to be generally smaller than in classical Monte Carlo with the same number of integration points. Using an appropriate definition of an ensemble of quasi-randompoint sets,…

Monte Carlo integration is a commonly used technique to compute intractable integrals and is typically thought to perform poorly for very high-dimensional integrals. To show that this is not always the case, we examine Monte Carlo…

We consider quantile estimation using Markov chain Monte Carlo and establish conditions under which the sampling distribution of the Monte Carlo error is approximately Normal. Further, we investigate techniques to estimate the associated…

Quasi-Monte Carlo sampling can attain far better accuracy than plain Monte Carlo sampling. However, with plain Monte Carlo sampling it is much easier to estimate the attained accuracy. This article describes methods old and new to quantify…

Quantiles and expected shortfalls are usually used to measure risks of stochastic systems, which are often estimated by Monte Carlo methods. This paper focuses on the use of quasi-Monte Carlo (QMC) method, whose convergence rate is…

We discuss the problem of defining an estimate for the error in quasi-Monte Carlo integration. The key issue is the definition of an ensemble of quasi-random point sets that, on the one hand, includes a sufficiency of equivalent point sets,…

Antithetic sampling, which goes back to the classical work by Hammersley and Morton (1956), is one of the well-known variance reduction techniques for Monte Carlo integration. In this paper we investigate its application to digital nets…

Quasi-Monte Carlo (QMC) methods for estimating integrals are attractive since the resulting estimators typically converge at a faster rate than pseudo-random Monte Carlo. However, they can be difficult to set up on arbitrary posterior…

While the Quasi-Monte Carlo method of numerical integration achieves smaller integration error than standard Monte Carlo, its use in particle physics phenomenology has been hindered by the abscence of a reliable way to estimate that error.…

This is basically a review of the field of Quasi-Monte Carlo intended for computational physicists and other potential users of quasi-random numbers. As such, much of the material is not new, but is presented here in a style hopefully more…

Quasi-Monte Carlo methods are a way of improving the efficiency of Monte Carlo methods. Digital nets and sequences are one of the low discrepancy point sets used in quasi-Monte Carlo methods. This thesis presents the three new results…

This paper studies the rate of convergence for conditional quasi-Monte Carlo (QMC), which is a counterpart of conditional Monte Carlo. We focus on discontinuous integrands defined on the whole of $R^d$, which can be unbounded. Under…

This study analyzes the nonasymptotic convergence behavior of the quasi-Monte Carlo (QMC) method with applications to linear elliptic partial differential equations (PDEs) with lognormal coefficients. Building upon the error analysis…

We study quasi-Monte Carlo (QMC) integration over the multi-dimensional unit cube in several weighted function spaces with different smoothness classes. We consider approximating the integral of a function by the median of several integral…

We show how information on the uniformity properties of a point set employed in numerical multidimensional integration can be used to improve the error estimate over the usual Monte Carlo one. We introduce a new measure of (non-)uniformity…

We consider the problem of estimating an expectation $ \mathbb{E}\left[ h(W)\right]$ by quasi-Monte Carlo (QMC) methods, where $ h $ is an unbounded smooth function on $ \mathbb{R}^d $ and $ W$ is a standard normal distributed random…

We consider the problem of computing an approximation to the integral $I=\int_{[0,1]^d}f(x) dx$. Monte Carlo (MC) sampling typically attains a root mean squared error (RMSE) of $O(n^{-1/2})$ from $n$ independent random function evaluations.…

Quasi-Monte Carlo rules are equal weight quadrature rules defined over the domain $[0,1]^s$. Here we introduce quasi-Monte Carlo type rules for numerical integration of functions defined on $\mathbb{R}^s$. These rules are obtained by way of…