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Bayesian Statistics: An Introduction, 4th Edition by Peter M. Lee

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10.5 Reversible jump Markov chain Monte Carlo

The Metropolis–Hastings algorithm introduced in Section 9.6 can be generalized to deal with a situation in which we have a number of available models, each with unknown parameters, and we wish to choose between them.

The basic idea is that as well as considering moves within a model as in the basic Metropolis–Hastings algorithm we also consider possible moves between models. We can regard the chain as moving between states which are specified by a model and a set of parameters for that model. For the time being, we shall suppose that we have two models M(1) with parameters  and M(2) with parameters  , so that at time t we have model M(i[t]) with parameters  .

10.5.1 RJMCMC algorithm

1. Initialize by setting t=0 and choosing i[0] and hence model M(i[0]), and then initial parameters  .
2. For
a. Update the parameters  of the current model M(i[t–1]) as in the usual Metropolis–Hastings algorithm.
b. Propose to move to a new model with parameters ...

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