Related papers: Adaptive Quasi-Monte Carlo Methods for Cubature
A method for tuning parameters in Monte Carlo generators is described and applied to a specific case. The method works in the following way: each observable is generated several times using different values of the parameters to be tuned.…
We study a Monte Carlo algorithm that is based on a specific (randomly shifted and dilated) lattice point set. The main result of this paper is that the mean squared error for a given compactly supported, square-integrable function is…
Hybrid quantum/molecular mechanics models (QM/MM methods) are widely used in material and molecular simulations when MM models do not provide sufficient accuracy but pure QM models are computationally prohibitive. Adaptive QM/MM coupling…
Bayesian inverse problems highly rely on efficient and effective inference methods for uncertainty quantification (UQ). Infinite-dimensional MCMC algorithms, directly defined on function spaces, are robust under refinement of physical…
A method is developed to compute analytically fully symmetric cubature rules on the triangle by using symmetric polynomials to express the two kinds of invariance inherent in these rules. Rules of degree up to 15, some of them new and of…
Adaptive Markov chains are an important class of Monte Carlo methods for sampling from probability distributions. The time evolution of adaptive algorithms depends on past samples, and thus these algorithms are non-Markovian. Although there…
The cubature on Wiener space method, a high-order weak approximation scheme, is established for SPDEs in the case of unbounded characteristics and unbounded payoffs. We first introduce a recently described flexible functional analytic…
The quasicontinuum approximation is a method to reduce the atomistic degrees of freedom of a crystalline solid by piecewise linear interpolation from representative atoms that are nodes for a finite element triangulation. In regions of the…
The classical approaches to numerically integrating a function $f$ are Monte Carlo (MC) and quasi-Monte Carlo (QMC) methods. MC methods use random samples to evaluate $f$ and have error $O(\sigma(f)/\sqrt{n})$, where $\sigma(f)$ is the…
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…
Quantum measurements are a fundamental component of quantum computing. However, on modern-day quantum computers, measurements can be more error prone than quantum gates, and are susceptible to non-unital errors as well as non-local…
Global sensitivity analysis is a powerful set of ideas and heuristics for understanding the importance and interplay between uncertain parameters in a computational model. Such a model is characterized by a set of input parameters and an…
Bayesian cubature provides a flexible framework for numerical integration, in which a priori knowledge on the integrand can be encoded and exploited. This additional flexibility, compared to many classical cubature methods, comes at a…
The standard Kernel Quadrature method for numerical integration with random point sets (also called Bayesian Monte Carlo) is known to converge in root mean square error at a rate determined by the ratio $s/d$, where $s$ and $d$ encode the…
Quasi-Monte Carlo (QMC) is a powerful method for evaluating high-dimensional integrals. However, its use is typically limited to distributions where direct sampling is straightforward, such as the uniform distribution on the unit hypercube…
We consider Monte Carlo approximations to the maximum likelihood estimator in models with intractable norming constants. This paper deals with adaptive Monte Carlo algorithms, which adjust control parameters in the course of simulation. We…
Three sampling methods are compared for efficiency on a number of test problems of various complexity for which analytic quadratures are available. The methods compared are Monte Carlo with pseudo-random numbers, Latin Hypercube Sampling,…
Large-scale quantum computation will only be achieved if experimentally implementable quantum error correction procedures are devised that can tolerate experimentally achievable error rates. We describe a quantum error correction procedure…
Methods for generating sequences of surrogates approximating fine scale models of two-phase random heterogeneous media are presented that are designed to adaptively control the modeling error in key quantities of interest (QoIs). For…
We study the integration of functions with respect to an unknown density. We compare the simple Monte Carlo method (which is almost optimal for a certain large class of inputs) and compare it with the Metropolis algorithm (based on a…