Dr. Dimitris Fouskakis (National Technical University of Athens, currently visiting PSTAT-UCSB)

Title: Power Intrinsic Variable Selection for Normal Models based on Zellner’s g-Prior

Abstract: In order to express prior ignorance in Bayesian variable selection problems, proper prior distributions with large variances or non-informative improper distributions can be used. Bayes factors are well known for their sensitivity on prior variances, while, when using improper priors, Bayes factors cannot be determined because of the involvement of the unknown normalizing constants. This has urged the Bayesian community to develop various methodologies to overcome the problem of prior specification in model comparison and variable selection problems. An important part of this research is focused on the so-called objective model selection methods having their source on the intrinsic priors in order to provide an approximate proper Bayesian interpretation for intrinsic Bayes factors. These intrinsic priors use improper priors as a starting point and overcome the problem of indeterminacy of the Bayes factor since the same constant is involved in all marginal likelihoods. In this paper we develop the methodology of intrinsic priors when using proper priors as a starting point. Specifically we focus on normal linear models and we use initially the Normal-inverse gamma Zellner’s g-prior. We introduce the power intrinsic Zellner’s g-prior where we use the intrinsic prior methodology in order to define the joint prior distribution of the model parameters and the error variance. Moreover, by borrowing ideas from the power prior approach we avoid the use of a minimal training sample and the sensitivity of posterior results on the selection (and size) of this training sample in our intrinsic prior methodology. The methodology is illustrated on both simulated and real examples and sensitivity analysis reveals broad stability of our conclusions.