The class of Metropolis-Hastings algorithms can be modified by delaying the rejection of proposed moves. The new samplers are proved to perform better than the original ones in terms of asymptotic variance of the estimates on a sweep by sweep basis. The delaying rejection algorithms also allow...

An overview of ordering defined on the space of Markov chains having a pre-specified distribution as their unique stationary distribution is provided. The intuition gained by studying these orderings is used to improve existing Markov chain Monte Carlo algorithms.