Related papers: Discrepancy-based error estimates for Quasi-Monte …

We establish epigraphical and uniform laws of large numbers for sample-based approximations of law invariant risk functionals. These sample-based approximation schemes include Monte Carlo (MC) and certain randomized quasi-Monte Carlo…

In this paper we give explicit constructions of point sets in the $s$ dimensional unit cube yielding quasi-Monte Carlo algorithms which achieve the optimal rate of convergence of the worst-case error for numerically integrating high…

A key limitation of sampling algorithms for approximate inference is that it is difficult to quantify their approximation error. Widely used sampling schemes, such as sequential importance sampling with resampling and Metropolis-Hastings,…

Quasi-Monte Carlo methods are used for numerically integrating multivariate functions. However, the error bounds for these methods typically rely on a priori knowledge of some semi-norm of the integrand, not on the sampled function values.…

We explain in detail how to estimate mean values and assess statistical errors for arbitrary functions of elementary observables in Monte Carlo simulations. The method is to estimate and sum the relevant autocorrelation functions, which is…

In this work, we show that uniform integrability is not a necessary condition for central limit theorems (CLT) to hold for normalized multilevel Monte Carlo (MLMC) estimators and we provide near optimal weaker conditions under which the CLT…

Importance Sampling (IS), an effective variance reduction strategy in Monte Carlo (MC) simulation, is frequently utilized for Bayesian inference and other statistical challenges. Quasi-Monte Carlo (QMC) replaces the random samples in MC…

When applying the quasi-Monte Carlo (QMC) method of numerical integration of univariate functions, Koksma's inequality provides a basic estimate of the error in terms of the discrepancy of the used evaluation points and the total variation…

We present bounds for the finite sample error of sequential Monte Carlo samplers on static spaces. Our approach explicitly relates the performance of the algorithm to properties of the chosen sequence of distributions and mixing properties…

Monte Carlo methods represent the "de facto" standard for approximating complicated integrals involving multidimensional target distributions. In order to generate random realizations from the target distribution, Monte Carlo techniques use…

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…

The present work addresses the question how sampling algorithms for commonly applied copula models can be adapted to account for quasi-random numbers. Besides sampling methods such as the conditional distribution method (based on a…

Deep learning algorithms have been widely used to solve linear Kolmogorov partial differential equations~(PDEs) in high dimensions, where the loss function is defined as a mathematical expectation. We propose to use the randomized…

We obtain non asymptotic concentration bounds for two kinds of stochastic approximations. We first consider the deviations between the expectation of a given function of the Euler scheme of some diffusion process at a fixed deterministic…

This paper gives foundational results for the application of quasi-stationarity to Monte Carlo inference problems. We prove natural sufficient conditions for the quasi-limiting distribution of a killed diffusion to coincide with a target…

In clinical chemistry, a number of studies shows that the probability of very large errors is much greater than expected from the Gaussian distribution. In addition, it has been empirically found that the behavior of nonlinear complex…

Some recent work on confidence intervals for randomized quasi-Monte Carlo (RQMC) sampling found a surprising result: ordinary Student $t$ 95% confidence intervals based on a modest number of replicates were seen to be very effective and…

Reinforcement learning constantly deals with hard integrals, for example when computing expectations in policy evaluation and policy iteration. These integrals are rarely analytically solvable and typically estimated with the Monte Carlo…

We investigate the application of randomized quasi-Monte Carlo (RQMC) methods in random feature approximations for kernel-based learning. Compared to the classical Monte Carlo (MC) approach \citep{rahimi2007random}, RQMC improves the…

In this article we consider the approximation of expectations w.r.t. probability distributions associated to the solution of partial differential equations (PDEs); this scenario appears routinely in Bayesian inverse problems. In practice,…