A quasi-Monte Carlo Metropolis algorithm

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.

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...

An Adaptive Quasi Monte Carlo Alternative to Metropolis

We present a manually-adaptive extension of Quasi Monte Carlo (QMC) integration for approximating marginal densities, moments, and quantiles when the joint density is known up to a normalization constant. Randomization and a batch-wise approach involving (0; s)-sequences are the cornerstones of the technique. By incorporating a variety of graphical diagnostics the method allows the user to adap...

Monte Carlo Methods in Physics Ising model and Metropolis Algorithm

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...