Related papers: Randomized Quasi-Monte Carlo Features for Kernel A…
Parametric regularity of discretizations of flux vector fields satisfying a balance law is studied under some assumptions on a random parameter that links the flux with an unknown primal variable (often through a constitutive law). In the…
Quasi-Monte Carlo (QMC) methods are equal weight quadrature rules to approximate integrals over the unit cube with respect to the uniform measure. In this paper we discuss QMC integration with respect to general product measures defined on…
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…
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…
We consider the problem of estimating expectations with respect to a target distribution with an unknown normalizing constant, and where even the unnormalized target needs to be approximated at finite resolution. Under such an assumption,…
Sequential Monte Carlo (SMC) methods, also known as particle filters, constitute a class of algorithms used to approximate expectations with respect to a sequence of probability distributions as well as the normalising constants of those…
In the quest for quantum advantage, a central question is under what conditions can classical algorithms achieve a performance comparable to quantum algorithms--a concept known as dequantization. Random Fourier features (RFFs) have…
The Rational Hybrid Monte Carlo (RHMC) algorithm extends the Hybrid Monte Carlo algorithm for lattice QCD simulations to situations involving fractional powers of the determinant of the quadratic Dirac operator. This avoids the updating…
In a previous paper (J. Comp. Phys. 230 (2011), 3668--3694), the authors proposed a new practical method for computing expected values of functionals of solutions for certain classes of elliptic partial differential equations with random…
We introduce Preconditioned Monte Carlo (PMC), a novel Monte Carlo method for Bayesian inference that facilitates efficient sampling of probability distributions with non-trivial geometry. PMC utilises a Normalising Flow (NF) in order to…
While multilevel Monte Carlo (MLMC) methods for the numerical approximation of partial differential equations with random coefficients enjoy great popularity, combinations with spatial adaptivity seem to be rare. We present an adaptive MLMC…
Markov chain Monte Carlo (MCMC) simulations are modeled as driven by true random numbers. We consider variance bounding Markov chains driven by a deterministic sequence of numbers. The star-discrepancy provides a measure of efficiency of…
Continuous level Monte Carlo is an unbiased, continuous version of the celebrated multilevel Monte Carlo method. The approximation level is assumed to be continuous resulting in a stochastic process describing the quantity of interest.…
In this project we initiate an investigation of the applicability of Quasi-Monte Carlo methods to lattice field theories in order to improve the asymptotic error behavior of observables for such theories. In most cases the error of an…
Designing clinical trials requires evaluating multiple operating characteristics (OCs), such as the likelihood of an early stopping decision, the probability of detecting a treatment effect, and the Type I error rate. In most cases, these…
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…
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 paper provides a comprehensive error analysis of learning with vector-valued random features (RF). The theory is developed for RF ridge regression in a fully general infinite-dimensional input-output setting, but nonetheless applies to…
We present an adaptive multilevel Monte Carlo (AMLMC) algorithm for approximating deterministic, real-valued, bounded linear functionals that depend on the solution of a linear elliptic PDE with a lognormal diffusivity coefficient and…
We apply the Quasi Monte Carlo (QMC) and recursive numerical integration methods to evaluate the Euclidean, discretized time path-integral for the quantum mechanical anharmonic oscillator and a topological quantum mechanical rotor model.…