Efficient sampling using metropolis algorithms:: Applications of optimal scaling results

We recently considered the optimal scaling problem of Metropolis algorithms for multidimensional target distributions with non-IID components. The results that were proven have wide applications and the aim of this article is to show how practitioners can take advantage of them. In particular, we use several examples to illustrate the case where the asymptotically optimal acceptance rate is the usual 0.234, and also the latest developments where smaller acceptance rates should be adopted for optimal sampling from the target distributions involved. We study the impact of the proposal scaling on the performance of the algorithm, and finally perform simulation studies exploring the efficiency of the algorithm when sampling from some popular statistical models.