Posterior model probabilities computed from model-specific Gibbs output

TL;DR

This paper introduces a Gibbs sampling approach for Bayesian multimodel inference that simplifies RJMCMC by using a shared parameter palette, enabling easier computation of model probabilities from standard MCMC outputs.

Contribution

It presents a novel Gibbs sampling framework for RJMCMC that allows model-specific parameters to be derived from a common palette, simplifying implementation and post-processing.

Findings

Enables computation of model probabilities from standard MCMC outputs.

Provides a clearer understanding of RJMCMC through the palette analogy.

Demonstrates the method with multiple examples.

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.