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Today is Jerzy Neyman’s birthday (April 16, 1894 – August 5, 1981). I’m posting a link to a quirky paper of his that explains one of the most misunderstood of his positions–what he was opposed to in opposing the “inferential theory”. The paper is Neyman, J. (1962), ‘Two Breakthroughs in the Theory of Statistical Decision Making‘ [i] It’s chock full of ideas and arguments. “In the present paper” he tells us, “the term ‘inferential theory’…will be used to describe the attempts to solve the Bayes’ problem with a reference to confidence, beliefs, etc., through some supplementation …either a substitute a priori distribution [exemplified by the so called principle of insufficient reason] or a new measure of uncertainty” such as Fisher’s fiducial probability. It arises on p. 391 of Excursion 5 Tour III of Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars (2018, CUP). Here’s a link to the proofs of that entire tour. If you hear Neyman rejecting “inferential accounts” you have to understand it in this very specific way: he’s rejecting “new measures of confidence or diffidence”. Here he alludes to them as “easy ways out”. He is not rejecting statistical inference in favor of behavioral performance as typically thought. Neyman always distinguished his error statistical performance conception from Bayesian and Fiducial probabilisms [ii]. The surprising twist here is semantical and the culprit is none other than…Allan Birnbaum. Yet Birnbaum gets short shrift, and no mention is made of our favorite “breakthrough” (or did I miss it?). You can find quite a lot on this blog searching Birnbaum. Continue reading →