Simple Monte Carlo and the Metropolis algorithm

Simple Monte Carlo and the Metropolis algorithm

We study the integration of functions with respect to an unknown density. Information is available as oracle calls to the integrand and to the nonnormalized density function. We are interested in analyzing the integration error of optimal algorithms (or the complexity of the problem) with emphasis on the variability of the weight function. For a corresponding large class of problem instances we...

A quasi-Monte Carlo Metropolis algorithm.

This work presents a version of the Metropolis-Hastings algorithm using quasi-Monte Carlo inputs. We prove that the method yields consistent estimates in some problems with finite state spaces and completely uniformly distributed inputs. In some numerical examples, the proposed method is much more accurate than ordinary Metropolis-Hastings sampling.

N ov 2 00 6 SIMPLE MONTE CARLO AND THE METROPOLIS ALGORITHM

We study the integration of functions with respect to an unknown density. Information is available as oracle calls to the integrand and to the non-normalized density function. We are interested in analyzing the integration error of optimal algorithms (or the complexity of the problem) with emphasis on the variability of the weight function. For a corresponding large class of problem instances w...

Monte Carlo Methods in Physics Ising model and Metropolis Algorithm

Metropolis Methods for Quantum Monte Carlo Simulations

Since its first description fifty years ago, the Metropolis Monte Carlo method has been used in a variety of different ways for the simulation of continuum quantum many-body systems. This paper will consider some of the generalizations of the Metropolis algorithm employed in quantum Monte Carlo: Variational Monte Carlo, dynamical methods for projector monte carlo (i.e. diffusion Monte Carlo wit...