Do we need an integrated Bayesian/likelihood inference?

Along with Andrew Gelman and Judith Rousseau, we turned our separate readings of Murray Aitkin’s Statistical Inference into a discussion paper, now arXived. This paper exposes why we feel Bayesian statistics does not need an integrated approach and why the idea of considering the posterior distribution of a likelihood function does not help in solving the difficulties with Bayesian model choice. We have submitted the paper to Bayesian Analysis but it was turned down immediately as Bayesian Analysis does not want to start an habit of publishing book reviews… I find  this disappointing as we were doing more than a mere book review in discussing whether or not Murray’s approach was part of Bayesian inference.  This was a good ground for debate and (healthy) controversy, so bound to attract readership. I still hope the paper can be made into a discussion paper so that Murray  is offered the opportunity to answer back.