The Ranked Sample-Mean Monte Carlo Method for Unidimensional Integral Estimation

Optimal Energy Estimation in Path-Integral Monte Carlo Simulations

We investigate the properties of two standard energy estimators used in path-integral Monte Carlo simulations. By disentangling the variance of the estimators and their autocorrelation times we analyse the dependence of the performance on the update algorithm and present a detailed comparison of refined update schemes such as multigrid and staging techniques. We show that a proper combination o...

Using Supervised Learning to Improve Monte Carlo Integral Estimation

Monte Carlo (MC) techniques are often used to estimate integrals of a multivariate function using randomly generated samples of the function. In light of the increasing interest in uncertainty quantification and robust design applications in aerospace engineering, the calculation of expected values of such functions (e.g. performance measures) becomes important. However, MC techniques often su ...

Quasi-monte Carlo Methods for Integral Equations

In this paper, we establish a deterministic error bound for estimating a functional of the solution of the integral transport equation via random walks that improves an earlier result of Chelson generalizing the Koksma-Hlawka inequality for nite dimensional quadrature. We solve such problems by simulation, using sequences that combine pseudorandom and quasirandom elements in the construction of...

The Monte-Carlo Method

The Monte Carlo Method

The Monte Carlo method is often referred to as a ‘computer experiment’. One might think of this as a way of conveying the fact that the output of simulations is not an equation, as in conventional theory. Instead, numbers appear on the computer screen in somewhat the same way that numbers appear on a measuring device in the laboratory. Thus there is the implication that somehow simulations are ...