Posterior model probabilities computed from model-specific Gibbs output

Abstract: Reversible jump Markov chain Monte Carlo (RJMCMC) extends ordinary MCMC methods for use in Bayesian multimodel inference. We show that RJMCMC can be implemented as Gibbs sampling with alternating updates of a model indicator and a vector-valued "palette" of parameters denoted $\bm \psi$. Like an artist uses the palette to mix dabs of color for specific needs, we create model-specific parameters from the set available in $\bm \psi$. This description not only removes some of the mystery of RJMCMC, but also provides a basis for fitting models one at a time using ordinary MCMC and computing model weights or Bayes factors by post-processing the Monte Carlo output. We illustrate our procedure using several examples.