Abstract

Reversible jump Markov chain Monte Carlo (RJMCMC) is an extension of the Metropolis-Hastings algorithm for stationary distributions of variable dimension. It has been successfully applied in a wide variety of settings, including the challenging problem of determining the number of components in a finite mixture and determining the number of states in a hidden Markov model. In this talk, RJMCMC is considered as an approach to Bayesian model selection problems and for this reason, it is used to explore the sampling space that consists of several models of different dimension. The RJMCMC algorithm usually considers a selection of move types, some of which explore the parameter space within a model, and others which propose changes to the dimensionality of the model. The choice of the proposal mechanism is crucial to the performance of the algorithm. Therefore, several methods have been proposed in the literature on how to choose the proposal mechanism of the algorithm. In this talk, I will describe some of these methods and I will also introduce a new one.

The original reversible jump MCMC paper can be found here