## Do we need an integrated Bayesian/likelihood inference?

**A**long 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

**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.**

*Bayesian Analysis*
December 5, 2011 at 12:54 pm

Just read a review by Alan Welsh of the book in the Australian and New Zealand Journal of Statistics

October 31, 2011 at 12:15 am

[...] predictive densities. This pseudo-marginal likelihood allows for improper priors and, like Aitkin’s integrated likelihood, it is not a Bayesian procedure in that the data is used several times to construct the [...]

October 11, 2011 at 12:11 am

[...] of the book, if time allows, although I am pessimistic at the chances of getting it published given our current difficulties with the critical review of Murray Aitkin’s Statistical Inference. However, as a coincidence, we got back last [...]

September 8, 2011 at 12:15 am

[...] debated several times on Andrew’s blog and this is one of the main criticisms raised against Aitkin’s posterior/integrated likelihood. Worrall’s perspective is both related and unrelated to this purely statistical issue, when [...]

March 31, 2011 at 12:21 am

[...] Inference, with Andrew Gelman and Judith Rousseau, to the review section of JASA, but were again unsuccessful as the paper was sent back with the comments that “this paper is not a good fit [...]