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 efficiency 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 identified 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.