Some Recent Developments in Bayesian Model Selection

 

We review two fairly recent developments in Bayesian model selection:

1. When the space of models is large, Search Strategies need to be carefully developed for exploration of the space. One successful strategy is to perform a stochastic search that (roughly) adds or removes variables based on their current estimated posterior inclusion probabilities. This approach, and related diagnostics, will be illustrated. One interesting phenomenon that seems to be frequently encountered us that no model receives significant posterior probability, so that the meaning of model selection needs to be reconsidered.

2. A generalization of BIC is available, for contexts common in the social sciences, that appropriately assesses the dimension of a model and the effective sample size for each parameter in a model. It also allows for the model dimension to grow with the sample size.