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.
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