Related papers: High-dimensional and higher-order multifidelity Mo…

For qubits, Monte Carlo estimation of the average fidelity of Clifford unitaries is efficient -- it requires a number of experiments that is independent of the number $n$ of qubits and classical computational resources that scale only…

Monte Carlo experiments produce samples in order to estimate features of a given distribution. However, simultaneous estimation of means and quantiles has received little attention, despite being common practice. In this setting we…

While generally considered computationally expensive, Uncertainty Quantification using Monte Carlo sampling remains beneficial for applications with uncertainties of high dimension. As an extension of the naive Monte Carlo method, the…

Variational inference lies at the core of many state-of-the-art algorithms. To improve the approximation of the posterior beyond parametric families, it was proposed to include MCMC steps into the variational lower bound. In this work we…

The Multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty Quantification (UQ) in Partial Differential Equation (PDE) models, combining model computations at different levels…

Markov chain Monte Carlo algorithms are used to simulate from complex statistical distributions by way of a local exploration of these distributions. This local feature avoids heavy requests on understanding the nature of the target, but it…

In this paper we propose a general framework for the uncertainty quantification of quantities of interest for high-contrast single-phase flow problems. It is based on the generalized multiscale finite element method (GMsFEM) and multilevel…

In many real-world engineering systems, the performance or reliability of the system is characterised by a scalar parameter. The distribution of this performance parameter is important in many uncertainty quantification problems, ranging…

We consider the application of multilevel Monte Carlo methods to elliptic PDEs with random coefficients. We focus on models of the random coefficient that lack uniform ellipticity and boundedness with respect to the random parameter, and…

In this paper, a Monte Carlo based approach for the quantification of the importance of the scattering input parameters with respect to the failure probability is presented. Using the basic idea of the alpha-factors of the First Order…

Least squares Monte Carlo methods are a popular numerical approximation method for solving stochastic control problems. Based on dynamic programming, their key feature is the approximation of the conditional expectation of future rewards by…

Markov chain Monte Carlo (MCMC) simulation methods are widely used to assess parametric uncertainties of hydrologic models conditioned on measurements of observable state variables. However, when the model is CPU-intensive and…

In this paper we develop a very efficient approach to the Monte Carlo estimation of the expected value of partial perfect information (EVPPI) that measures the average benefit of knowing the value of a subset of uncertain parameters…

In this note we study the numerical stability problem that may take place when calculating the cumulative distribution function of the {\it Hypoexponential} random variable. This computation is extensively used during the execution of Monte…

Uncertainty analysis in the outcomes of model predictions is a key element in decision-based material design to establish confidence in the models and evaluate the fidelity of models. Uncertainty Propagation (UP) is a technique to determine…

Hamiltonian Monte Carlo has emerged as a standard tool for posterior computation. In this article, we present an extension that can efficiently explore target distributions with discontinuous densities. Our extension in particular enables…

In this paper, we investigate the use of multilevel Monte Carlo (MLMC) methods for estimating the expectation of discretized random fields. Specifically, we consider a setting in which the input and output vectors of numerical simulators…

Frequentist and likelihood methods of inference based on the multivariate skew-normal model encounter several technical difficulties with this model. In spite of the popularity of this class of densities, there are no broadly satisfactory…

We present simple and practical strategies to reduce the variance of Monte Carlo estimators. Our focus is on variational Monte Carlo calculations of atomic forces and pressure in electronic systems, although we show that the underlying…

In this study, we give an extension of Montanaro's arXiv/archive:1504.06987 quantum Monte Carlo method, tailored for computing expected values of random variables that exhibit infinite variance. This addresses a challenge in analyzing…