Current advances in Monte Carlo methods

Current Advances in Monte Carlo Methods

In this review paper, we outline the principles of Monte Carlo simulation of fluid mixtures, with emphasis on methods for calculation of free energies and phase equilibria. We begin with a brief introduction to common intermolecular potential models. We discuss density-dependent potentials that can accurately represent properties over a wide range of densities. A number of Monte Carlo technique...

Advances in Markov chain Monte Carlo methods

Probability distributions over many variables occur frequently in Bayesian inference, statistical physics and simulation studies. Samples from distributions give insight into their typical behavior and can allow approximation of any quantity of interest, such as expectations or normalizing constants. Markov chain Monte Carlo (MCMC), introduced by Metropolis et al. (1953), allows sampling from d...

Advances in Quantum 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...

Recent Advances in Monte Carlo Offline Rendering

The research problems in Monte Carlo rendering have changed over the years. At first, the question was one of efficiency: how can we render an image quickly? Recent research has focused on rendering more complex effects, such as soft shadows and motion blur. There has also been research into the Monte Carlo technique itself; while it is a wellknown numerical technique, many subtleties have been...