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