A general proposal construction for reversible jump MCMC

We propose a general methodology to construct proposal densities in reversible jump MCMC algorithms so that consistent mappings across competing models are achieved. Unlike nearly all previous approaches our proposals are not restricted to operate to moves between local models, but they are applicable even to models that do not share any common parameters. We focus on linear regression models and produce concrete guidelines on proposal choices for moves between any models. These guidelines can be immediately applied to any regression models after applying some standard data transformations to near-normality. We illustrate our methodology by providing concrete guidelines for model determination problems in logistic regression and log-linear graphical models. Two real data analyses illustrate how our suggested proposal densities together with the resulting freedom to propose moves between any models improve the mixing of the reversible jump Metropolis algorithm.