Related papers: Quasi-Monte Carlo Algorithms (not only) for Graphi…
Generation of pseudorandom numbers from different probability distributions has been studied extensively in the Monte Carlo simulation literature. Two standard generation techniques are the acceptance-rejection and inverse transformation…
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 $\mathbb{R}^2$…
Gerber and Chopin (2015) recently introduced Sequential quasi-Monte Carlo (SQMC) algorithms as an efficient way to perform filtering in state-space models. The basic idea is to replace random variables with low-discrepancy point sets, so as…
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…
Monte Carlo sampling is a powerful toolbox of algorithmic techniques widely used for a number of applications wherein some noisy quantity, or summary statistic thereof, is sought to be estimated. In this paper, we survey the literature for…
Quasi-Monte Carlo (QMC) methods have developed over several decades. With the explosion in computational science, there is a need for great software that implements QMC algorithms. We summarize the QMC software that has been developed to…
This paper provides a framework in which multilevel Monte Carlo and continuous level Monte Carlo can be compared. In continuous level Monte Carlo the level of refinement is determined by an exponentially distributed random variable, which…
This paper introduces a class of Monte Carlo algorithms which are based upon the simulation of a Markov process whose quasi-stationary distribution coincides with a distribution of interest. This differs fundamentally from, say, current…
Quasi-Monte Carlo methods have proven to be effective extensions of traditional Monte Carlo methods in, amongst others, problems of quadrature and the sample path simulation of stochastic differential equations. By replacing the random…
Many questions in quantitative finance, uncertainty quantification, and other disciplines are answered by computing the population mean, $\mu := \mathbb{E}(Y)$, where instances of $Y:=f(\boldsymbol{X})$ may be generated by numerical…
This article provides an overview of some interfaces between the theory of quasi-Monte Carlo (QMC) methods and applications. We summarize three QMC theoretical settings: first order QMC methods in the unit cube $[0,1]^s$ and in…
Contemporary scientific studies often rely on the understanding of complex quantum systems via computer simulation. This paper initiates the statistical study of quantum simulation and proposes a Monte Carlo method for estimating…
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…
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…
The standard kinetic Monte Carlo algorithm is an extremely efficient method to carry out serial simulations of dynamical processes such as thin-film growth. However, in some cases it is necessary to study systems over extended time and…
Intractable generative models are models for which the likelihood is unavailable but sampling is possible. Most approaches to parameter inference in this setting require the computation of some discrepancy between the data and the…
Monte Carlo (MC) methods for numerical integration seem to be embarassingly parallel on first sight. When adaptive schemes are applied in order to enhance convergence however, the seemingly most natural way of replicating the whole job on…
We present a highly scalable Monte Carlo (MC) three-dimensional photon transport simulation platform designed for heterogeneous computing systems. Through the development of a massively parallel MC algorithm using the Open Computing…
Sequential Monte Carlo samplers represent a compelling approach to posterior inference in Bayesian models, due to being parallelisable and providing an unbiased estimate of the posterior normalising constant. In this work, we significantly…
Low-discrepancy point sets and digital sequences underpin quasi-Monte Carlo (QMC) methods for high-dimensional integration. We cast two long-standing QMC design problems as program synthesis and solve them with an LLM-guided evolutionary…