Efficient parallelisation of Metropolis-Hastings algorithms using a prefetching approach

Prefetching is a simple and general method for single-chain parallelisation of the Metropolis-Hastings algorithm based on the idea of evaluating the posterior in parallel and ahead of time. Improved Metropolis-Hastings prefetching algorithms are presented and evaluated. It is shown how to use available information to make better predictions of the future states of the chain and increase the e¢ ciency of prefetching considerably. The optimal acceptance rate for the prefetching random walk Metropolis-Hastings algorithm is obtained for a special case and it is shown to decrease in the number of processors employed. The performance of the algorithms is illustrated using a well-known macroeconomic model. Bayesian estimation of DSGE models, linearly or nonlinearly approximated, is identi…ed as a potential area of application for prefetching methods. The generality of the proposed method, however, suggests that it could be applied in other contexts as well.