Related papers: Discrepancy-based error estimates for Quasi-Monte …
Importance sampling has become an important tool for the computation of tail-based risk measures. Since such quantities are often determined mainly by rare events standard Monte Carlo can be inefficient and importance sampling provides a…
In this paper we present a rigorous cost and error analysis of a multilevel estimator based on randomly shifted Quasi-Monte Carlo (QMC) lattice rules for lognormal diffusion problems. These problems are motivated by uncertainty…
Monte Carlo methods play a central role in particle physics, where they are indispensable for simulating scattering processes, modeling detector responses, and performing multi-dimensional integrals. However, traditional Monte Carlo methods…
In Markov Chain Monte Carlo (MCMC) simulations, the thermal equilibria quantities are estimated by ensemble average over a sample set containing a large number of correlated samples. These samples are selected in accordance with the…
Current reporting of results based on Markov chain Monte Carlo computations could be improved. In particular, a measure of the accuracy of the resulting estimates is rarely reported. Thus we have little ability to objectively assess the…
Nested integration problems arise in various scientific and engineering applications, including Bayesian experimental design, financial risk assessment, and uncertainty quantification. These nested integrals take the form $\int f\left(\int…
The main idea of this work is that the quantum-classical isomorphism is a suitable framework for a generalization of the notion of detailed balance. The quantum-classical isomorphism is used in order to develop a Monte Carlo simulation with…
Kernel discrepancies are a powerful tool for analyzing worst-case errors in quasi-Monte Carlo (QMC) methods. Building on recent advances in optimizing such discrepancy measures, we extend the subset selection problem to the setting of…
Monte Carlo methods are widely used for approximating complicated, multidimensional integrals for Bayesian inference. Population Monte Carlo (PMC) is an important class of Monte Carlo methods, which utilizes a population of proposals to…
In this paper we propose and analyse a method for estimating three quantities related to an Asian option: the fair price, the cumulative distribution function, and the probability density. The method involves preintegration with respect to…
Gaussian mixture distributions are commonly employed to represent general probability distributions. Despite the importance of using Gaussian mixtures for uncertainty estimation, the entropy of a Gaussian mixture cannot be calculated…
We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…
Based on the central limit theorem, we discuss the problem of evaluation of the statistical error of Monte Carlo calculations using a time discretized diffusion process. We present a robust and practical method to determine the effective…
In this paper, we introduce the $\sigma$-antithetic multilevel Monte Carlo (MLMC) estimator for a multi-dimensional diffusion which is an extended version of the original antithetic MLMC one introduced by Giles and Szpruch \cite{a}. Our aim…
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…
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,…
Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in…
We introduce a discretization scheme for continuous localized frames using quasi-Monte Carlo integration and discrepancy theory. By generalizing classical concepts, we define a discrepancy measure on the entire phase space $\mathbb{R}^2$…
We present Bayesian techniques for solving inverse problems which involve mean-square convergent random approximations of the forward map. Noisy approximations of the forward map arise in several fields, such as multiscale problems and…
We are interested in computing the expectation of a functional of a PDE solution under a Bayesian posterior distribution. Using Bayes' rule, we reduce the problem to estimating the ratio of two related prior expectations. For a model…