1 Comments on “Mixtures of g-priors for Bayesian Variable Selection”

I congratulate the authors of this very interesting paper on their work in which they implement my suggestion in Zellner (1986) to put an informative prior on the g parameter. The authors have introduced hierarchical priors on g and shown how they can be used to solve model comparison and selection problems. Thanks to them for this valuable extension of my earlier results and for comparing their results to Zellner and Siow’s (1980) use of multivariate Cauchy priors in computing Bayes ’ factors for model comparison and selection problems. However, there are some points about “undesirable consistency issues ” and “paradoxes”, to use the authors ’ terms, and g − priors that require comment in order to acquire an appropriate understanding of important underlying testing methodological issues. For example, does a perfect model fit, 2 1,R = require that the posterior odds for this model relative to others under consideration go to infinity? And if so, is it the true model? Let us start with what the authors call the “Bartlett Paradox”, considered in Section 2.3 of their paper, that supposedly is a negative aspect of the use of g-priors with a fixed value for the prior parameter g. They state that when one attempts to be “non-informative ” by letting the value of g approach + infinity, the Bayes ’ factor for comparing two models will go to 0 an