Reviews: PAC-Bayesian Theory Meets Bayesian Inference

The paper is well written and theoretically strong. It's been conjectured in the past that there should be links between PAC-Bayes theory and Bayesian inference, but to my knowledge this is the first theoretically complete demonstration of such links. Some comments: - In eq(8) (and above) the notion of a prior with bounded likelihood is introduced. Am I right in thinking that this is a data-dependent prior, since it can only be known if the likelihood will be bounded for a given prior after observing the data? If this is not the case can you explain how such a prior is possible?