Monte Carlo Methods and Applications

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 methods and applications for the nuclear shell model

The shell-model Monte Carlo (SMMC) technique transforms the traditional nuclear shell-model problem into a path-integral over auxiliary fields. We describe below the method and its applications to four physics issues: calculations of sd-pf shell nuclei, a discussion of electron-capture rates in pf -shell nuclei, exploration of pairing correlations in unstable nuclei, and level densities in rare...

Monte Carlo sampling methods using Markov chains and their applications

A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising ...

Some Non-Standard Sequential Monte Carlo Methods and Their Applications

Monte Carlo Sampling Methods Using Markov Chains and Their Applications