The performance of most vanilla Metropolis-Hastings MCMC methods is pretty awful, but there are some good improvements. I use DREAM (a non-Markovian and paralle

The performance of most vanilla Metropolis-Hastings MCMC methods is pretty awful, but there are some good improvements. I use DREAM (a non-Markovian and parallelizable extension of M-H) with realistic problems and its convergence rate is much much much better, to the point that I can use it for what I'm working on while regular M-H methods are just too slow.