Related papers: Monte Carlo uncertainty estimation for wavelength …
The combination of continuum Many-Body Quantum physics and Monte Carlo methods provide a powerful and well established approach to first principles calculations for large systems. Replacing the exact solution of the problem with a…
For many inference problems in statistics and econometrics, the unknown parameter is identified by a set of moment conditions. A generic method of solving moment conditions is the Generalized Method of Moments (GMM). However, classical GMM…
Quantum Monte Carlo approaches such as the diffusion Monte Carlo (DMC) method are among the most accurate many-body methods for extended systems. Their scaling makes them well suited for defect calculations in solids. We review the various…
In this paper the application of the multi-level Monte Carlo (MLMC) method on numerical simulations of turbulent flows with uncertain parameters is investigated. Several strategies for setting up the MLMC method are presented, and the…
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…
We interpret uncertainty in a model for seismic wave propagation by treating the model parameters as random variables, and apply the Multilevel Monte Carlo (MLMC) method to reduce the cost of approximating expected values of selected,…
Practical structural engineering problems are often characterized by significant uncertainties. Historically, one of the prevalent methods to account for this uncertainty has been the standard Monte Carlo (MC) method. Recently, improved…
To facilitate robust and trustworthy deployment of large language models (LLMs), it is essential to quantify the reliability of their generations through uncertainty estimation. While recent efforts have made significant advancements by…
The nuclear shell model is known to describe the properties of various nuclei extremely well. However, the auxiliary-field quantum Monte Carlo calculations cannot be applied to it with general interactions due to the sign problem. The model…
This paper develops a novel sequential Monte Carlo (SMC) approach for joint state and parameter estimation that can deal efficiently with abruptly changing parameters which is a common case when tracking maneuvering targets. The approach…
Monte Carlo methods are used to approximate the means, $\mu$, of random variables $Y$, whose distributions are not known explicitly. The key idea is that the average of a random sample, $Y_1, ..., Y_n$, tends to $\mu$ as $n$ tends to…
We introduce a new class of Monte Carlo based approximations of expectations of random variables such that their laws are only available via certain discretizations. Sampling from the discretized versions of these laws can typically…
Through the Bayesian lens of data assimilation, uncertainty on model parameters is traditionally quantified through the posterior covariance matrix. However, in modern settings involving high-dimensional and computationally expensive…
The Monte Carlo method is a powerful tool for performing radiative equilibrium calculations, even in complex geometries. The main drawback of the standard Monte Carlo radiative equilibrium methods is that they require iteration, which makes…
Monte-Carlo (MC) methods, based on random updates and the trial-and-error principle, are well suited to retrieve particle size distributions from small-angle scattering patterns of dilute solutions of scatterers. The size sensitivity of…
Quantifying uncertainty associated with the microstructure variation of a material can be a computationally daunting task, especially when dealing with advanced constitutive models and fine mesh resolutions in the crystal plasticity finite…
In the study of complex systems, evaluating physical observables often requires sampling representative configurations via Monte Carlo techniques. These methods rely on repeated evaluations of the system's energy and force fields, which can…
While considerable advance has been made to account for statistical uncertainties in astronomical analyses, systematic instrumental uncertainties have been generally ignored. This can be crucial to a proper interpretation of analysis…
Markov chain Monte Carlo (MCMC) is a simulation method commonly used for estimating expectations with respect to a given distribution. We consider estimating the covariance matrix of the asymptotic multivariate normal distribution of a…
This paper considers uncertainty quantification for an elliptic nonlocal equation. In particular, it is assumed that the parameters which define the kernel in the nonlocal operator are uncertain and a priori distributed according to a…