On Metropolis-Hastings algorithms with delayed rejection

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 some space for local adaptation of the proposal distribution. We give an iterative formula for the acceptance probability at the i-th iteration of the delaying process. A special case is discussed in detail: the delaying rejection algorithm with symmetric proposal distribution