Bayesian Statistics: An Introduction, 4th Edition

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 ...