Guido Consonni
University of Pavia (ITALY)

Prior specification across models with an application to Bayesian variable
selection in linear models           

Model determination and comparison is an important and active area
of research especially from the Bayesian viewpoint. One critical
issue emerges from the very beginning: the assignment  of prior
distributions on the parameter space of each model.

Often a model can be regarded as a submodel of a larger model, as
for example in variable selection for  linear models. Because of
the potentially very high number of models under investigation,
this suggests relating  priors across models, in order to enhance
the elicitation procedure.

Surprisingly relatively little is known in this area, and what is
available if often confusing.

We discuss some issues concerning the interpretation of submodels,
trying to clarify the appropriate notation, and show the
implications on prior specifications.

In particular we focus on three strategies for prior assignments:
marginalization, conditioning and Kullback-Leibler projection.

We exemplify our discussion with reference to the problem of
variable selection in linear models.