Misadventures in Monte Carlo

Monte Carlo and quasi-Monte Carlo methods

Monte Carlo is one of the most versatile and widely used numerical methods. Its convergence rate, O(N~^), is independent of dimension, which shows Monte Carlo to be very robust but also slow. This article presents an introduction to Monte Carlo methods for integration problems, including convergence theory, sampling methods and variance reduction techniques. Accelerated convergence for Monte Ca...

Monte Carlo Extension of Quasi-monte Carlo

This paper surveys recent research on using Monte Carlo techniques to improve quasi-Monte Carlo techniques. Randomized quasi-Monte Carlo methods provide a basis for error estimation. They have, in the special case of scrambled nets, also been observed to improve accuracy. Finally through Latin supercube sampling it is possible to use Monte Carlo methods to extend quasi-Monte Carlo methods to hi...

Error in Monte Carlo, quasi-error in Quasi-Monte Carlo

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. The standard Monte Carlo error estimator relies on the assumption that the points are generated independently of each other and, therefore, fails to account ...

Monte Carlo

In this lecture, we cover the other major method for generating atomic trajectories: the Monte Carlo (MC) approach. Unlike MD, Monte Carlo methods are stochastic in nature—the time progression of the atomic positions proceeds randomly and is not predictable given a set of initial conditions. The dynamic principles by which we evolve the atomic positions incorporate random moves or perturbations...

On Monte Carlo and Quasi-Monte Carlo for Matrix Computations