Reversible-jump Markov chain Monte Carlo

In computational statistics, reversible-jump Markov chain Monte Carlo is an extension to standard Markov chain Monte Carlo (MCMC) methodology that allows simulation of the posterior distribution on spaces of varying dimensions. Thus, the simulation is possible even if the number of parameters in the model is not known.

be a model indicator and

 . The model indication need not be finite. The stationary distribution is the joint posterior distribution of 

The proposal

 , where 

 . The move to state 

The function

must be one to one and differentiable, and have a non-zero support:

so that there exists an inverse function

that is differentiable. Therefore, the

is met where

 . This is known as dimension matching.

The acceptance probability will be given by