Related papers: Adaptive Monte Carlo applied to uncertainty estima…

We prove explicit, i.e. non-asymptotic, error bounds for Markov chain Monte Carlo methods. The problem is to compute the expectation of a function f with respect to a measure {\pi}. Different convergence properties of Markov chains imply…

Variational Monte Carlo is a many-body numerical method that scales well with system size. It has been extended to study the Green function only recently by Charlebois and Imada (2020). Here we generalize the approach to systems with open…

While kinetic Monte Carlo simulations can provide long-time simulations of the dynamics of physical and chemical systems, it is not yet possible in general to identify the inverse Monte Carlo attempt frequency with a physical timescale.…

Single-chain Markov chain Monte Carlo simulates realizations from a Markov chain to estimate expectations with the empirical average. The single-chain simulation is generally of considerable length and restricts many advantages of modern…

While recent work towards the development of tight-binding and ab-initio algorithms has focused on molecular dynamics, Monte Carlo methods can often lead to better results with relatively little effort. We present here a multi-step Monte…

We introduce an exact Monte Carlo approach to the statistics of discrete quantum systems which does not rely on the standard fragmentation of the imaginary time, or any small parameter. The method deals with discrete objects, kinks,…

Numerical models are increasingly used for non-invasive diagnosis and treatment planning in coronary artery disease, where service-based technologies have proven successful in identifying hemodynamically significant and hence potentially…

The fidelity susceptibility is a general purpose probe of phase transitions. With its origin in quantum information and in the differential geometry perspective of quantum states, the fidelity susceptibility can indicate the presence of a…

Markov chain Monte Carlo (MCMC) is widely regarded as one of the most important algorithms of the 20th century. Its guarantees of asymptotic convergence, stability, and estimator-variance bounds using only unnormalized probability functions…

This article develops general conditions for weak convergence of adaptive Markov chain Monte Carlo processes and is shown to imply a weak law of large numbers for bounded Lipschitz continuous functions. This allows an estimation theory for…

A method for the multifidelity Monte Carlo (MFMC) estimation of statistical quantities is proposed which is applicable to computational budgets of any size. Based on a sequence of optimization problems each with a globally minimizing…

Multi-fidelity Monte Carlo methods leverage low-fidelity and surrogate models for variance reduction to make tractable uncertainty quantification even when numerically simulating the physical systems of interest with high-fidelity models is…

The Self-Learning Monte Carlo (SLMC) method is a Monte Carlo approach that has emerged in recent years by integrating concepts from machine learning with conventional Monte Carlo techniques. Designed to accelerate the numerical study of…

We consider the problem of sequentially choosing between a set of unbiased Monte Carlo estimators to minimize the mean-squared-error (MSE) of a final combined estimate. By reducing this task to a stochastic multi-armed bandit problem, we…

Markov chain Monte Carlo is a method of producing a correlated sample in order to estimate features of a target distribution via ergodic averages. A fundamental question is when should sampling stop? That is, when are the ergodic averages…

Accurate brain tumor segmentation from MRI is vital for diagnosis and treatment planning. Although Monte Carlo (MC) Dropout is widely used to estimate model uncertainty, the effectiveness of variance-based uncertainty - computed as…

Practical structural engineering problems often exhibit a significant degree of uncertainty in the material properties being used, the dimensions of the modeled structures, etc. In this paper, we consider a cantilever beam and a beam…

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.…

As the size of engineered systems grows, problems in reliability theory can become computationally challenging, often due to the combinatorial growth in the cut sets. In this paper we demonstrate how Multilevel Monte Carlo (MLMC) - a…

Estimating predictive uncertainty is crucial for many computer vision tasks, from image classification to autonomous driving systems. Hamiltonian Monte Carlo (HMC) is an sampling method for performing Bayesian inference. On the other hand,…