Related papers: Alternative sampling for variational quantum Monte…
Importance sampling is a Monte Carlo method which designs estimators of expectations under a target distribution using weighted samples from a proposal distribution. When the target distribution is complex, such as multimodal distributions…
Estimating the unknown density from which a given independent sample originates is more difficult than estimating the mean, in the sense that for the best popular non-parametric density estimators, the mean integrated square error converges…
This article considers the sequential Monte Carlo (SMC) approximation of ratios of normalizing constants associated to posterior distributions which in principle rely on continuum models. Therefore, the Monte Carlo estimation error and the…
We have reformulated the quantum Monte Carlo (QMC) technique so that a large part of the calculation scales linearly with the number of atoms. The reformulation is related to a recent alternative proposal for achieving linear-scaling QMC,…
Metropolis Monte Carlo simulation is a powerful tool for studying the equilibrium properties of matter. In complex condensed-phase systems, however, it is difficult to design Monte Carlo moves with high acceptance probabilities that also…
We study random compressible viscous magnetohydrodynamic flows. Combining the Monte Carlo method with a deterministic finite volume method we solve the random system numerically. Quantitative error estimates including statistical and…
We propose a bilinear sampling algorithm in Green's function Monte Carlo for expectation values of operators that do not commute with the Hamiltonian and for differences between eigenvalues of different Hamiltonians. The integral…
This paper examines the precision of estimators of Quantile-Based Risk Measures (Value at Risk, Expected Shortfall, Spectral Risk Measures). It first addresses the question of how to estimate the precision of these estimators, and proposes…
Importance sampling has been known as a powerful tool to reduce the variance of Monte Carlo estimator for rare event simulation. Based on the criterion of minimizing the variance of Monte Carlo estimator within a parametric family, we…
In this paper, we propose a novel and generic family of multiple importance sampling estimators. We first revisit the celebrated balance heuristic estimator, a widely used Monte Carlo technique for the approximation of intractable…
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…
Solving the ground state of quantum many-body systems remains a fundamental challenge in physics and chemistry. Recent advancements in quantum hardware have opened new avenues for addressing this challenge. Inspired by the quantum-enhanced…
The Multilevel Monte Carlo method is an efficient variance reduction technique. It uses a sequence of coarse approximations to reduce the computational cost in uncertainty quantification applications. The method is nowadays often considered…
We propose extensions and improvements of the statistical analysis of distributed multipoles (SADM) algorithm put forth by Chipot et al. in [6] for the derivation of distributed atomic multipoles from the quantum-mechanical electrostatic…
The ability of widely used sampling methods, such as molecular dynamics or Monte Carlo, to explore complex free energy landscapes is severely hampered by the presence of kinetic bottlenecks. A large number of solutions have been proposed to…
Some classical uncertainty quantification problems require the estimation of multiple expectations. Estimating all of them accurately is crucial and can have a major impact on the analysis to perform, and standard existing Monte Carlo…
The control variates method is a classical variance reduction technique for Monte Carlo estimators that exploits correlated auxiliary variables without introducing bias. In many applications, the quantity of interest can be expressed as a…
Control variates are variance reduction tools for Monte Carlo estimators. They can provide significant variance reduction, but usually require a large number of samples, which can be prohibitive when sampling or evaluating the integrand is…
Markov chain Monte Carlo (MCMC) produces a correlated sample for estimating expectations with respect to a target distribution. A fundamental question is when should sampling stop so that we have good estimates of the desired quantities?…
Zero- and two-dimensional crystal defects form in open statistical ensembles, such as the grand canonical, that are usually inaccessible with conventional simulation techniques. This longstanding challenge is overcome with a new Hamiltonian…