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Anyone here remember that old Woody Allen movie, “Midnight in Paris,” where the main character (I forget who plays it, I saw it on a plane), a writer finishing a novel, steps into a cab that mysteriously picks him up at midnight and transports him back in time where he gets to run his work by such famous authors as Hemingway and Virginia Wolf? (It was a new movie when I began the blog in 2011.) He is wowed when his work earns their approval and he comes back each night in the same mysterious cab…Well, ever since I began this blog in 2011, I imagine being picked up in a mysterious taxi at midnight on New Year’s Eve, and lo and behold, find myself in the 1960s New York City, in the company of Allan Birnbaum who is is looking deeply contemplative, perhaps studying his 1962 paper…Birnbaum reveals some new and surprising twists this year! [i]
(The pic on the left is the only blurry image I have of the club I’m taken to.) It has been a decade since I published my article in Statistical Science (“On the Birnbaum Argument for the Strong Likelihood Principle”), which includes commentaries by A. P. David, Michael Evans, Martin and Liu, D. A. S. Fraser, Jan Hannig, and Jan Bjornstad. David Cox, who very sadly did in January 2022, is the one who encouraged me to write and publish it. Not only does the (Strong) Likelihood Principle (LP or SLP) remain at the heart of many of the criticisms of Neyman-Pearson (N-P) statistics and of error statistics in general, but a decade after my 2014 paper, it is more central than ever–even if it is often unrecognized.
OUR EXCHANGE:
ERROR STATISTICIAN: It’s wonderful to meet you Professor Birnbaum; I’ve always been extremely impressed with the important impact your work has had on philosophical foundations of statistics. I happen to have published on your famous argument about the likelihood principle (LP). (whispers: I can’t believe this!) Continue reading
A seminal controversy in statistical inference is whether error probabilities associated with an inference method are evidentially relevant once the data are in hand. Frequentist error statisticians say yes; Bayesians say no. A “no” answer goes hand in hand with holding the Likelihood Principle (LP), which follows from inference by Bayes theorem. A “yes” answer violates the LP (also called the strong LP). The reason error probabilities drop out according to the LP is that it follows from the LP that all the evidence from the data is contained in the likelihood ratios (at least for inference within a statistical model). For the error statistician, likelihood ratios are merely measures of comparative fit, and omit crucial information about their reliability. A dramatic illustration of this disagreement involves optional stopping, and it’s the one to which Roderick Little turns in the chapter “Do you like the likelihood principle?” in 
Error Statistics Philosophy 