2025-26 Cruise
We are now at the second stop on our December leisurely cruise through SIST: Excursion 3 Tour III. I am pasting the slides and video from this session during the LSE Research Seminars in 2020 (from which this cruise derives). (Remember it was early pandemic, and we weren’t so adept with zooming.) The Higgs discussion clarifies (and defends) a somewhat controversial interpretation of p-values. (If you’re interested in the Higgs discovery, there’s a lot more on this blog you can find with the search. I am not sure if I would include the section on “capability and severity” were I to write a second edition, though I would keep the duality of tests and CIs. My goal was to expose a fallacy that is even more common nowadays, but I would have placed a revised version later in the book. Share your remarks in the comments.
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III. Deeper Concepts: Confidence Intervals and Tests: Higgs’ Discovery: 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 