Delayed rejection in reversible jump Metropolis-Hastings

Peter J. Green & Antonietta Mira
In a Metropolis-Hastings algorithm, rejection of proposed moves is an intrinsic part of ensuring that the chain converges to the intended target distribution. However, persistent rejection, perhaps in particular parts of the state space, may indicate that locally the proposal distribution is badly calibrated to the target. As an alternative to careful off-line tuning of state-dependent proposals, the basic algorithm can be modified so that on rejection, a second attempt to move is made. A different proposal can be generated from a new distribution, that is allowed to depend on the previously rejected proposal. We generalise this idea of delaying the rejection and adapting the proposal distribution, due to Tierney and Mira (1999), to generate a more flexible class of methods, that in particular applies to a variable dimension setting. The approach is illustrated by two pedagogical examples, and a more realistic application, to a change-point analysis for point processes.

Some key words: Change points, Detailed balance, MCMC, Mixing, Reversibility, Splitting rejection.

Back to Peter Green's research page