Bayesian Model Averaging Across Model Spaces via Compact Encoding

Bayesian Model Averaging (BMA) is well known for improving predictive accuracy by averaging inferences over all models in the model space. However, Markov chain Monte Carlo (MCMC) sampling, as the standard implementation for BMA, encounters difficulties in even relatively simple model spaces. We introduce a minimum message length (MML) coupled MCMC methodology, which not only addresses these difficulties but has additional benefits. The MML principle discretizes the model space and associates a probability mass with each region. This allows efficient sampling and jumping between model spaces of different complexity. We illustrate the methodology with a mixture component model example (clustering) and show that our approach produces more interpretable results when compared to Green’s popular reverse jump sampling across model subspaces technique. The MML principle mathematically embodies Occam’s razor since more complicated models take more information to describe. We find that BMA prediction based on sampling across multiple sub-spaces of different complexity makes much improved predictions compared to the single best (shortest) model.