In a previous work, I showed that the use of I-priors in various linear models can be considered as a solution to the over-fitting problem. In that work, estimation was still done using maximum likelihood, so in a sense it was a kind of frequentist-Bayes approach. Switching over to a fully Bayesian framework, we now look at the problem of variable selection, specifically in an ordinary linear regression setting. The appeal of Bayesian methods are that it reduces the selection problem to one of estimation, rather than a true search of the variable space for the model that optimises a certain criterion. I will talk about several Bayesian variable selection methods out there in the literature, and how we can make use of I-priors to improve on results in the presence of multicollinearity.