Reversible Jump MCMC

Algorithm Reversible Jump MCMC

1. Initialise and at iteration .
2. For iteration perform
   1. Within-model move: with a fixed model , update the parameters according to any MCMC updating scheme.
   2. Between-models move: simultaneously update model indicator and the parameters according to the general reversible proposal/acceptance mechanism.
3. Increment iteration . If ,go to Step 2.

Dimension Matching

Fact In order to match dimensions between the two model states, a random vector of length is generated from a known density . The current state and the random vector are then mapped to the new state through a one-to-one mapping function .

e.g. Suppose that model has states and model has states . Let denote the current state in and denote the proposed state in . Under dimension matching with a simple split/merge move, we might generate a random scalar , and let and , with the reverse move given deterministically by . For the same setup but with a simple birth/death move, we might specify and , with the reverse move given deterministically by .