Abstract: By building on the stochastic search approach (George and McCulloch (1993)) we propose a strategy for performing constrained variable selection. We discuss hierarchical and grouping constraints, and introduce anti-hierarchical constraints in which the inclusion of a variable forces another to be excluded from the model. We prove consistency results about models receiving maximal posterior probability, and about the median model (Barbieri and Berger (2004)), and discuss extensions to generalized linear models.
Key words and phrases: Constraints, Gibbs sampler, hierarchical models, variable selection.