Confronted with the position that “arguments for this personalistic theory were so persuasive that anything to any extent inconsistent with that theory should be discarded” (Cox 2006, 196), frequentists might have seen themselves in a kind of exile when it came to foundations, even those who had been active in the dialogues of an earlier period. Sometime around the late 1990s there were signs that this was changing. Regardless of the explanation, the fact that it did occur and is occurring is of central importance to statistical philosophy.
Now that Bayesians have stepped off their a priori pedestal, it may be hoped that a genuinely deep scrutiny of the frequentist and Bayesian accounts will occur. In some corners of practice it appears that frequentist error statistical foundations are being discovered anew. Perhaps frequentist foundations, never made fully explicit, but at most lying deep below the ocean floor, are finally being disinterred. But let’s learn from some of the mistakes in the earlier attempts to understand it. With this goal I invite you to join me in some deep water drilling, here as I cast about on my Isle of Elba.
Cox, D. R. (2006), Principles of Statistical Inference, CUP.