First people deny a thing.
Then they belittle it.
Then they say they knew it all along.
I don’t know who was first to state it in one form or another. Here’s Schopenhauer with a slightly different variant:
“All truth passes through three stages: First, it is ridiculed; Second, it is violently opposed; and Third, it is accepted as self-evident.” – Arthur Schopenhauer
After recently presenting my paper criticizing the Birnbaum result on the likelihood principle (LP) the reception of my analysis seems somewhere around stage two, in some cases, moving into stage three (see my blogposts of December 6 and 7, 2011).
But it is time to make good on my promise to return to concerns of those (at least in the blogosphere), who were or are still at the first stage of denial (or Schopenhauer’s second stage of violent opposition). Doing so will advance our goal of drilling deeply into some fundamental, puzzling misunderstandings of frequentist error statistical (or sampling) theory. Consider Christian Robert’s October 6, 2011 post:
“Coming to Section III in Chapter Seven of Error and Inference, written by Deborah Mayo, I discovered that she considers that the likelihood principle does not hold (at least as a logical consequence of the combination of the sufficiency and of the conditionality principles), thus that Allan Birnbaum was wrong…. As well as the dozens of people working on the likelihood principle after him! …I had not heard of (nor seen) this argument previously, even though it has apparently created enough of … a stir around the likelihood principle page on Wikipedia. It does not seem the result is published anywhere but in the book, and I doubt it would get past a review process in a statistics journal.” http://xianblog.wordpress.com/2011/10/06/that-the-likelihood-principle-does-not-hold/
Robert later added the remark: “[Judging from a serious conversation in Zürich this morning, I may however be wrong!]” But, surely the reader is curious to know where Robert’s critique of my argument breaks down. Where does Robert think his easy-going critique (upholding Birnbaum) goes wrong, if he does? I don’t know.
 Birnbaum’s result purports to show that frequentist error statisticians must (if they be consistent) give up error probabilities in their drawing inferences from data. Recall that Birnbaum himself denied the LP because it entailed giving up the control of error probabilities.