Related papers: Adaptive Quasi-Monte Carlo Methods for Cubature
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…
In this study, we consider the development of tailored quasi-Monte Carlo (QMC) cubatures for non-conforming discontinuous Galerkin (DG) approximations of elliptic partial differential equations (PDEs) with random coefficients. We consider…
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…
Bayesian cubature (BC) is a popular inferential perspective on the cubature of expensive integrands, wherein the integrand is emulated using a stochastic process model. Several approaches have been put forward to encode sequential…
Automatic cubatures approximate multidimensional integrals to user-specified error tolerances. For high dimensional problems, it makes sense to fix the sampling density but determine the sample size, $n$, automatically. Bayesian cubature…
Quasi-Monte Carlo methods have become the industry standard in computer graphics. For that purpose, efficient algorithms for low discrepancy sequences are discussed. In addition, numerical pitfalls encountered in practice are revealed. We…
Classical algorithms in numerical analysis for numerical integration (quadrature/cubature) follow the principle of approximate and integrate: the integrand is approximated by a simple function (e.g. a polynomial), which is then integrated…
Approximate Bayesian computation allows for inference of complicated probabilistic models with intractable likelihoods using model simulations. The Markov chain Monte Carlo implementation of approximate Bayesian computation is often…
Driven by several successful applications such as in stochastic gradient descent or in Bayesian computation, control variates have become a major tool for Monte Carlo integration. However, standard methods do not allow the distribution of…
This project investigates the applicability of quasi-Monte Carlo methods to Euclidean lattice systems in order to improve the asymptotic error scaling of observables for such theories. The error of an observable calculated by averaging over…
We study the feature-scaled version of the Monte Carlo algorithm with linear function approximation. This algorithm converges to a scale-invariant solution, which is not unduly affected by states having feature vectors with large norms. The…
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, provided sufficient accuracy can be achieved in an acceptable…
Adaptive Monte Carlo methods are very efficient techniques designed to tune simulation estimators on-line. In this work, we present an alternative to stochastic approximation to tune the optimal change of measure in the context of…
The efficient approximation of quantity of interest derived from PDEs with lognormal diffusivity is a central challenge in uncertainty quantification. In this study, we propose a multilevel quasi-Monte Carlo framework to approximate…
The theme of the present paper is numerical integration of $C^r$ functions using randomized methods. We consider variance reduction methods that consist in two steps. First the initial interval is partitioned into subintervals and the…
We study numerical integration over bounded regions in $\mathbb{R}^s, s\ge1$ with respect to some probability measure. We replace random sampling with quasi-Monte Carlo methods, where the underlying point set is derived from deterministic…
In this note, we study a concatenation of quasi-Monte Carlo and plain Monte Carlo rules for high-dimensional numerical integration in weighted function spaces. In particular, we consider approximating the integral of periodic functions…
We study quasi-Monte Carlo integration for twice differentiable functions defined over a triangle. We provide an explicit construction of infinite sequences of points including one by Basu and Owen (2015) as a special case, which achieves…
Quasi-Monte Carlo methods are designed for integrands of bounded variation, and this excludes singular integrands. Several methods are known for integrands that become singular on the boundary of the unit cube $[0,1]^d$ or at isolated…
Niederreiter [H.Niederreiter, Error bounds for quasi-Monte Carlo integration with uniform point sets, Journal of computational and applied mathematics 150 (2003), 283-292] established new bounds for quasi-Monte Carlo integration for nodes…