Metropolis Methods, Gaussian Proposals and Antithetic Variables

Various aspects of a class of dynamic Monte Carlo methods, that generalises the Metropolis algorithm and includes the Gibbs sampler as a special case, are investigated, which can be used to estimate expectations of marginal distributions in stochastic systems.

Abstract

We investigate various aspects of a class of dynamic Monte Carlo methods, that generalises the Metropolis algorithm and includes the Gibbs sampler as a special case. These can be used to estimate expectations of marginal distributions in stochastic systems. A distinction is drawn between speed of weak convergence and precision of estimation. For continuously distributed processes, a particular gaussian proposal distribution is suggested: this incorporates a parameter that may be varied to improve the performance of the sampling method, by adjusting the magnitude of an “antithetic” element introduced into the sampling. The suggestion is examined in detail in some experiments based on an image analysis problem.