Clustered Bayesian Model Averaging

It is sometimes preferable to conduct statistical analyses based on the combination of several models rather than on the selection of a single model, thus taking into account the uncertainty about the true model. Models are usually combined using constant weights that do not distinguish between different regions of the covariate space. However, a procedure that performs well in a given situation may not do so in another situation. In this paper, we propose the concept of local Bayes factors, where we calculate the Bayes factors by restricting the models to regions of the covariate space. The covariate space is split in such a way that the relative model efficiencies of the various Bayesian models are about the same in the same region while differing in different regions. An algorithm for clustered Bayes averaging is then proposed for model combination, where local Bayes factors are used to guide the weighting of the Bayesian models. Simulations and real data studies show that clustered Bayesian averaging results in better predictive performance compared to a single Bayesian model or Bayesian model averaging where models are combined using the same weights over the entire covariate space.