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.

5 Responses to “Do we need an integrated Bayesian/likelihood inference?”

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

  2. […] 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 […]

  3. […] 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 […]

  4. […] 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 […]

  5. […] 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 […]

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